Author name code: brandenburg ADS astronomy entries on 2022-09-14 author:"Brandenburg, Axel" ------------------------------------------------------------------------ Title: A Comparative Analysis of Machine-learning Models for Solar Flare Forecasting: Identifying High-performing Active Region Flare Indicators Authors: Sinha, Suvadip; Gupta, Om; Singh, Vishal; Lekshmi, B.; Nandy, Dibyendu; Mitra, Dhrubaditya; Chatterjee, Saikat; Bhattacharya, Sourangshu; Chatterjee, Saptarshi; Srivastava, Nandita; Brandenburg, Axel; Pal, Sanchita Bibcode: 2022ApJ...935...45S Altcode: 2022arXiv220405910S Solar flares create adverse space weather impacting space- and Earth-based technologies. However, the difficulty of forecasting flares, and by extension severe space weather, is accentuated by the lack of any unique flare trigger or a single physical pathway. Studies indicate that multiple physical properties contribute to active region flare potential, compounding the challenge. Recent developments in machine learning (ML) have enabled analysis of higher-dimensional data leading to increasingly better flare forecasting techniques. However, consensus on high-performing flare predictors remains elusive. In the most comprehensive study to date, we conduct a comparative analysis of four popular ML techniques (k nearest neighbors, logistic regression, random forest classifier, and support vector machine) by training these on magnetic parameters obtained from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory for the entirety of solar cycle 24. We demonstrate that the logistic regression and support vector machine algorithms perform extremely well in forecasting active region flaring potential. The logistic regression algorithm returns the highest true skill score of 0.967 ± 0.018, possibly the highest classification performance achieved with any strictly parametric study. From a comparative assessment, we establish that magnetic properties like total current helicity, total vertical current density, total unsigned flux, R_VALUE, and total absolute twist are the top-performing flare indicators. We also introduce and analyze two new performance metrics, namely, severe and clear space weather indicators. Our analysis constrains the most successful ML algorithms and identifies physical parameters that contribute most to active region flare productivity. Title: Magnetohydrodynamics predicts heavy-tailed distributions of axion-photon conversion Authors: Carenza, Pierluca; Sharma, Ramkishor; Marsh, M. C. David; Brandenburg, Axel; Müller, Eike Bibcode: 2022arXiv220804333C Altcode: The conversion of axionlike particles (ALPs) and photons in magnetised astrophysical environments provides a promising route to search for ALPs. The strongest limits to date on light ALPs use galaxy clusters as ALP--photon converters. However, such studies traditionally rely on simple models of the cluster magnetic fields, with the state-of-the-art being Gaussian random fields (GRFs). We present the first systematic study of ALP-photon conversion in more realistic, turbulent fields from dedicated magnetohydrodynamic (MHD) simulations, which we compare with GRF models. For GRFs, we analytically derive the distribution of conversion ratios at fixed energy and find that it follows an exponential law. We find that the MHD models agree with the exponential law for typical, small amplitude mixings but exhibit distinctly heavy tails for rare and large mixings. We explain how non-Gaussian, local spikes in the MHD magnetic field are mainly responsible for the heavy tail. Our results indicate that limits placed on ALPs using GRFs are conservative but that MHD models are necessary to reach the full potential of these searches. Title: Batchelor, Saffman, and Kazantsev spectra in galactic small-scale dynamos Authors: Brandenburg, Axel; Zhou, Hongzhe; Sharma, Ramkishor Bibcode: 2022arXiv220709414B Altcode: The magnetic fields in galaxy clusters and probably also in the interstellar medium are believed to be generated by a small-scale dynamo. Theoretically, during its kinematic stage, it is characterized by a Kazantsev spectrum, which peaks at the resistive scale. It is only slightly shallower than the Saffman spectrum that is expected for random and causally connected magnetic fields. Causally disconnected fields have the even steeper Batchelor spectrum. Here we show that all three spectra are present in the small-scale dynamo. During the kinematic stage, the Batchelor spectrum occurs on scales larger than the energy-carrying scale of the turbulence, and the Kazantsev spectrum on smaller scales within the inertial range of the turbulence -- even for a magnetic Prandtl number of unity. In the saturated state, the dynamo develops a Saffman spectrum on large scales. At large magnetic Prandtl numbers, elongated structures are seen in the parity-even E polarization, but not in the parity-odd B polarization. We also observe a significant excess in the E polarization over the B polarization at subresistive scales, and a deficiency at larger scales. This finding is at odds with the observed excess in the Galactic microwave foreground emission. The E and B polarizations become Gaussian in the saturated state, but may be highly non-Gaussian and skewed in the kinematic regime of the dynamo. Title: Scaling of the Saffman helicity integral in decaying magnetically-dominated turbulence Authors: Zhou, Hongzhe; Sharma, Ramkishor; Brandenburg, Axel Bibcode: 2022arXiv220607513Z Altcode: The Saffman helicity integral of Hosking and Schekochihin (2021, PRX 11, 041005) has emerged as an important quantity that may govern the decay properties of magnetically dominated turbulence. Using a range of different computational methods, we confirm that this quantity is indeed gauge-invariant and nearly perfectly conserved in the limit of large Lundquist numbers. For direct numerical simulations with ordinary viscosity and magnetic diffusivity operators, we find that the solution develops in a nearly self-similar fashion. In a diagram quantifying the instantaneous decay coefficients of magnetic energy and integral scale, we find that the solution evolves along a line that is indeed suggestive of the governing role of the Saffman helicity integral. The solution settles near a line in this diagram that is expected for a self-similar evolution of the magnetic energy spectrum. However, the solution may settle in a slightly different position when the magnetic diffusivity decreases with time, which would be compatible with the decay being governed by the reconnection time scale rather than the Alfvén time. Title: Compressible Test-field Method and Its Application to Shear Dynamos Authors: Käpylä, Maarit J.; Rheinhardt, Matthias; Brandenburg, Axel Bibcode: 2022ApJ...932....8K Altcode: 2021arXiv210601107K In this study, we present a compressible test-field method (CTFM) for computing α-effect and turbulent magnetic diffusivity tensors, as well as those relevant for the mean ponderomotive force and mass source, applied to the full MHD equations. We describe the theoretical background of the method and compare it to the quasi-kinematic test-field method and to the previously studied variant working in simplified MHD (SMHD). We present several test cases using velocity and magnetic fields of the Roberts geometry and also compare with the imposed-field method. We show that, for moderate imposed-field strengths, the nonlinear CTFM (nCTFM) gives results in agreement with the imposed-field method. A comparison of different flavors of the nCTFM in the shear dynamo case also yields agreement up to equipartition field strengths. Some deviations between the CTFM and SMHD variants exist. As a relevant physical application, we study nonhelically forced shear flows, which exhibit large-scale dynamo action, and present a reanalysis of low-Reynolds-number, moderate shear systems, where we previously ignored the pressure gradient in the momentum equation and found no coherent shear-current effect. Another key difference is that in the earlier study we used magnetic forcing to mimic small-scale dynamo action, while here it is self-consistently driven by purely kinetic forcing. The kinematic CTFM with general validity forms the core of our analysis. We still find no coherent shear-current effect, but do recover strong large-scale dynamo action that, according to our analysis, is driven by incoherent effects. Title: Chiral Magnetic Fields and Gravitational Waves Authors: Stepp, Jonathan; Kahniashvili, Tina; Clarke, Emma; Brandenburg, Axel Bibcode: 2022AAS...24020202S Altcode: In the early universe, asymmetry in the number density between right and left-handed fermions causes chiral magnetic fields to grow exponentially due to the chiral magnetic effect. Since the total chirality of both the magnetic field and fermions is conserved, the asymmetry limits the maximum strength of these magnetic fields due to this effect. Updated values for effective neutrino count, primordial hydrogen abundance and baryon-photon ratio allow us to constrain the lepton asymmetry due to neutrino species and compute new limits on primordial chiral magnetic fields. We also compute the energy and polarization of gravitational waves generated by these helical sources and compare them to current detection prospects. Title: Big Bang Nucleosynthesis Limits and Relic Gravitational-Wave Detection Prospects Authors: Kahniashvili, Tina; Clarke, Emma; Stepp, Jonathan; Brandenburg, Axel Bibcode: 2022PhRvL.128v1301K Altcode: 2021arXiv211109541K We revisit the big bang nucleosynthesis limits on primordial magnetic fields and/or turbulent motions accounting for the decaying nature of turbulent sources between the time of generation and big bang nucleosynthesis. This leads to larger estimates for the gravitational wave signal than previously expected. We address the detection prospects through space-based interferometers and pulsar timing arrays or astrometric missions for gravitational waves generated around the electroweak and quantum chromodynamics energy scale, respectively. Title: Dynamo effect in unstirred self-gravitating turbulence Authors: Brandenburg, Axel; Ntormousi, Evangelia Bibcode: 2022MNRAS.513.2136B Altcode: 2022MNRAS.tmp..975B; 2021arXiv211203838B In many astrophysical environments, self-gravity can generate kinetic energy, which, in principle, is available for driving dynamo action. Using direct numerical simulations, we show that in unstirred self-gravitating subsonic turbulence with helicity and a magnetic Prandtl number of unity, there is a critical magnetic Reynolds number of about 25 above which the work done against the Lorentz force exceeds the Ohmic dissipation. The collapse itself drives predominantly irrotational motions that cannot be responsible for dynamo action. We find that, with a weak magnetic field, one-third of the work done by the gravitational force goes into compressional heating and the remaining two-thirds go first into kinetic energy of the turbulence before a fraction of it is converted further into magnetic and finally thermal energies. Close to the collapse, however, these fractions change toward 1/4 and 3/4 for compressional heating and kinetic energy, respectively. When the magnetic field is strong, the compressional heating fraction is unchanged. Out of the remaining kinetic energy, one quarter goes directly into magnetic energy via work against the Lorentz force. The fraction of vortical motions diminishes in favour of compressive motions that are almost exclusively driven by the Jeans instability. For an initially uniform magnetic field, field amplification at scales larger than those of the initial turbulence are driven by tangling. Title: Low frequency tail of gravitational wave spectra from hydromagnetic turbulence Authors: Sharma, Ramkishor; Brandenburg, Axel Bibcode: 2022arXiv220600055S Altcode: Hydrodynamic and magnetohydrodynamic (MHD) turbulence in the early Universe can drive gravitational waves (GWs) and imprint their spectrum onto that of GWs, which might still be observable today. We study the production of the GW background from freely decaying MHD turbulence for helical and nonhelical initial magnetic fields. To understand the produced GW spectra, we develop a simple model on the basis of the evolution of the magnetic stress tensor. We find that the GW spectra obtained in this model reproduce those obtained in numerical simulations if we consider the time evolution of the low frequency tail of the stress spectrum from numerical simulations. We also show that the shapes of the produced GW frequency spectra are different for helical and nonhelical cases for the same initial magnetic energy spectra. Such differences can help distinguish helical and nonhelical initial magnetic fields from a polarized background of GWs -- especially when the expected circular polarization cannot be detected directly. Title: Evolution of Primordial Magnetic Fields during Large-scale Structure Formation Authors: Mtchedlidze, Salome; Domínguez-Fernández, Paola; Du, Xiaolong; Brandenburg, Axel; Kahniashvili, Tina; O'Sullivan, Shane; Schmidt, Wolfram; Brüggen, Marcus Bibcode: 2022ApJ...929..127M Altcode: 2021arXiv210913520M Primordial magnetic fields (PMFs) could explain the large-scale magnetic fields present in the universe. Inflation and phase transitions in the early universe could give rise to such fields with unique characteristics. We investigate the magnetohydrodynamic evolution of these magnetogenesis scenarios with cosmological simulations. We evolve inflation-generated magnetic fields either as (i) uniform (homogeneous) or as (ii) scale-invariant stochastic fields, and phase-transition-generated ones either as (iii) helical or as (iv) nonhelical fields from the radiation-dominated epoch. We find that the final distribution of magnetic fields in the simulated cosmic web shows a dependence on the initial strength and the topology of the seed field. Thus, the observed field configuration retains information on the initial conditions at the moment of the field generation. If detected, PMF observations would open a new window for indirect probes of the early universe. The differences between the competing models are revealed on the scale of galaxy clusters, bridges, as well as filaments and voids. The distinctive spectral evolution of different seed fields produces imprints on the correlation length today. We discuss how the differences between rotation measures from highly ionized regions can potentially be probed with forthcoming surveys. Title: Polarization of gravitational waves from helical MHD turbulent sources Authors: Roper Pol, Alberto; Mandal, Sayan; Brandenburg, Axel; Kahniashvili, Tina Bibcode: 2022JCAP...04..019R Altcode: 2021arXiv210705356R We use direct numerical simulations of decaying primordial hydromagnetic turbulence with helicity to compute the resulting gravitational wave (GW) production and its degree of circular polarization. The turbulence is sourced by magnetic fields that are either initially present or driven by an electromotive force applied for a short duration, given as a fraction of one Hubble time. In both types of simulations, we find a clear dependence of the polarization of the resulting GWs on the fractional helicity of the turbulent source. We find a low frequency tail below the spectral peak shallower than the f 3 scaling expected at super-horizon scales, in agreement with similar recent numerical simulations. This type of spectrum facilitates its observational detection with the planned Laser Interferometer Space Antenna (LISA). We show that driven magnetic fields produce GWs more efficiently than magnetic fields that are initially present, leading to larger spectral amplitudes, and to modifications of the spectral shape. In particular, we observe a sharp drop of GW energy above the spectral peak that is in agreement with the previously obtained results. The helicity does not have a huge impact on the maximum spectral amplitude in any of the two types of turbulence considered. However, the GW spectrum at wave numbers away from the peak becomes smaller for larger values of the magnetic fractional helicity. Such variations of the spectrum are most noticeable when magnetic fields are driven. The degree of circular polarization approaches zero at frequencies below the peak, and reaches its maximum at the peak. At higher frequencies, it stays finite if the magnetic field is initially present, and it approaches zero if it is driven. We predict that the spectral peak of the GW signal can be detected by LISA if the turbulent energy density is at least ~3% of the radiation energy density, and the characteristic scale is a hundredth of the horizon at the electroweak scale. We show that the resulting GW polarization is unlikely to be detectable by the anisotropies induced by our proper motion in the dipole response function of LISA. Such signals can, however, be detectable by cross-correlating data from the LISA-Taiji network for turbulent energy densities of ~5%, and fractional helicity of 0.5 to 1. Second-generation space-base GW detectors, such as BBO and DECIGO, would allow for the detection of a larger range of the GW spectrum and smaller amplitudes of the magnetic field. Title: Spectral characterisation of inertial particle clustering in turbulence Authors: Haugen, Nils E. L.; Brandenburg, Axel; Sandin, Christer; Mattsson, Lars Bibcode: 2022JFM...934A..37H Altcode: 2021arXiv210501539H Clustering of inertial particles is important for many types of astrophysical and geophysical turbulence, but it has been studied predominately for incompressible flows. Here, we study compressible flows and compare clustering in both compressively (irrotationally) and vortically (solenoidally) forced turbulence. Vortically and compressively forced flows are driven stochastically either by solenoidal waves or by circular expansion waves, respectively. For compressively forced flows, the power spectrum of the density of inertial particles is a useful tool for displaying particle clustering relative to the fluid density enhancement. Power spectra are shown to be particularly sensitive for studying large-scale particle clustering, while conventional tools such as radial distribution functions are more suitable for studying small-scale clustering. Our primary finding is that particle clustering through shock interaction is particularly prominent in turbulence driven by spherical expansion waves. It manifests itself through a double-peaked distribution of spectral power as a function of Stokes number. The two peaks are associated with two distinct clustering mechanisms; shock interaction for smaller Stokes numbers and the centrifugal sling effect for larger values. The clustering of inertial particles is associated with the formation of caustics. Such caustics can only be captured in the Lagrangian description, which allows us to assess the relative importance of caustics in vortically and compressively forced turbulence. We show that the statistical noise resulting from the limited number of particles in the Lagrangian description can be removed from the particle power spectra, allowing us a more detailed comparison of the residual spectra. We focus on the Epstein drag law relevant for rarefied gases, but show that our findings apply also to the usual Stokes drag. Title: Skumanich-55 revisited Authors: Brandenburg, A. Bibcode: 2022fysr.confE..53B Altcode: When I started my undergraduate research in Hamburg in 1984, my professor pointed me to Skumanich-55. It is interesting to review the thinking at the time. The Vitense-53 paper laid the foundation for thinking that the Schwarzschild-unstable layer was at least 70 Mm deep, contrary to the earlier picture of the 1930s of less than 1 Mm. In Skumanich-55, the governing idea is not to postulate a characteristic size of eddies, but to ask which eddies grow the fastest. In unstratified Rayleigh-Benard convection, they all grow at the same rate, but in a polytropic layer, smaller eddies are more unstable, which led Skumanich to argue that small eddies should be predominant. This is different from standard mixing length ideas and perhaps also from some simulations. However, both ignore the phenomenon of entropy rain and the possibility of the convective flux in the deeper layers not being carried by a gradient flux, but predominantly by the Deardorff flux. Although none of this was part of the Skumanich model, it also suggests a predominance of smaller eddies. In this sense, his model deserves some renewed attention! Title: Dynamo instabilities in plasmas with inhomogeneous chiral chemical potential Authors: Schober, Jennifer; Rogachevskii, Igor; Brandenburg, Axel Bibcode: 2022PhRvD.105d3507S Altcode: 2021arXiv210713028S We study the dynamics of magnetic fields in chiral magnetohydrodynamics, which takes into account the effects of an additional electric current related to the chiral magnetic effect in high-energy plasmas. We perform direct numerical simulations, considering weak seed magnetic fields and inhomogeneities of the chiral chemical potential μ5 with a zero mean. We demonstrate that a small-scale chiral dynamo can occur in such plasmas if fluctuations of μ5 are correlated on length scales that are much larger than the scale on which the dynamo growth rate reaches its maximum. Magnetic fluctuations grow by many orders of magnitude due to the small-scale chiral dynamo instability. Once the nonlinear backreaction of the generated magnetic field on fluctuations of μ5 sets in, the ratio of these scales decreases and the dynamo saturates. When magnetic fluctuations grow sufficiently to drive turbulence via the Lorentz force before reaching maximum field strength, an additional mean-field dynamo phase is identified. The mean magnetic field grows on a scale that is larger than the integral scale of turbulence after the amplification of the fluctuating component saturates. The growth rate of the mean magnetic field is caused by a magnetic α effect that is proportional to the current helicity. With the onset of turbulence, the power spectrum of μ5 develops a universal k-1 scaling independently of its initial shape, while the magnetic energy spectrum approaches a k-3 scaling. Title: Production of a Chiral Magnetic Anomaly with Emerging Turbulence and Mean-Field Dynamo Action Authors: Schober, Jennifer; Rogachevskii, Igor; Brandenburg, Axel Bibcode: 2022PhRvL.128f5002S Altcode: 2021arXiv210712945S In relativistic magnetized plasmas, asymmetry in the number densities of left- and right-handed fermions, i.e., a nonzero chiral chemical potential μ5, leads to an electric current along the magnetic field. This causes a chiral dynamo instability for a uniform μ5, but our simulations reveal a dynamo even for fluctuating μ5 with zero mean. It produces magnetically dominated turbulence and generates mean magnetic fields via the magnetic α effect. Eventually, a universal scale-invariant k-1 spectrum of μ5 and a k-3 magnetic spectrum are formed independently of the initial condition. Title: Big Bang Nucleosynthesis Limits and Relic Gravitational Wave Detection Prospects Authors: Clarke, Emma; Kahniashvili, Tina; Stepp, Jonathan; Brandenburg, Axel Bibcode: 2022APS..APRT14003C Altcode: Big bang nucleosynthesis (BBN) places upper limits on the relativistic energy density in the early universe, which places bounds on the strength of primordial magnetic fields and/or turbulent motions in the early universe and their resulting relic gravitational wave (GW) signals. Previous studies assumed that velocity and magnetic fields are ``frozen-in'' to the primordial plasma and that the ratio between the turbulent source energy density and thermal energy density remain unchanged during the radiation-dominated epoch. We revisit the BBN limits and properly account for the decaying nature of turbulent sources from their generation until BBN. We find that allowed values for the magnetic fields at the moment of generation are not constrained by order of microGauss as was claimed previously based on BBN bounds without accounting for decaying turbulence. This allows larger estimates for the initial magnetic field strength and stronger GW signals than were previously expected. We address the prospects of detecting these GW signals through space-based interferometers (for GWs generated around the electroweak scale) and by pulsar timing arrays and astrometric missions (for GWs generated around the quantum chromodynamics energy scale). Title: Simulations of Helical Inflationary Magnetogenesis and Gravitational Waves Authors: Brandenburg, Axel; He, Yutong; Sharma, Ramkishor Bibcode: 2021ApJ...922..192B Altcode: 2021arXiv210712333B Using numerical simulations of helical inflationary magnetogenesis in a low reheating temperature scenario, we show that the magnetic energy spectrum is strongly peaked at a particular wavenumber that depends on the reheating temperature. Gravitational waves (GWs) are produced at frequencies between 3 nHz and 50 mHz for reheating temperatures between 150 MeV and 3 × 105 GeV, respectively. At and below the peak frequency, the stress spectrum is always found to be that of white noise. This implies a linear increase of GW energy per logarithmic wavenumber interval, instead of a cubic one. Both in the helical and nonhelical cases, the GW spectrum is followed by a sharp drop for frequencies above the respective peak frequency. In this magnetogenesis scenario, the presence of a helical term extends the peak of the GW spectrum and therefore also the position of the aforementioned drop toward larger frequencies compared to the case without helicity. This might make a difference in it being detectable with space interferometers. The efficiency of GW production is found to be almost the same as in the nonhelical case, and independent of the reheating temperature, provided the electromagnetic energy at the end of reheating is fixed to be a certain fraction of the radiation energy density. Also, contrary to the case without helicity, the electric energy is now less than the magnetic energy during reheating. The fractional circular polarization is found to be nearly 100% in a certain range below the peak frequency range. Title: Chirality in Astrophysics Authors: Brandenburg, Axel Bibcode: 2021arXiv211008117B Altcode: Chirality, or handedness, enters astrophysics in three distinct ways. Magnetic field and vortex lines tend to be helical and have a systematic twist in the northern and southern hemispheres of a star or a galaxy. Helicity is here driven by external factors. Chirality can also enter at the microphysical level and can then be traced back to the parity-breaking weak force. Finally, chirality can arise spontaneously, but this requires not only the presence of an instability, but also the action of nonlinearity. Examples can be found both in magnetohydrodynamics and in astrobiology, where homochirality among biomolecules probably got established at the origin of life. In this review, all three types of chirality production will be explored and compared. Title: Leading-order nonlinear gravitational waves from reheating magnetogeneses Authors: He, Yutong; Roper Pol, Alberto; Brandenburg, Axel Bibcode: 2021arXiv211014456H Altcode: We study the leading-order nonlinear gravitational waves (GWs) produced by an electromagnetic (EM) stress in reheating magnetogenesis scenarios. Both nonhelical and helical magnetic fields are considered. By numerically solving the linear and leading-order nonlinear GW equations, we find that the GW energy from the latter is usually larger. We compare their differences in terms of the GW spectrum and parameterize the GW energy difference due to the nonlinear term, $\Delta\mathcal{E}_{\rm GW}$, in terms of EM energy $\mathcal{E}_{\rm EM}$ as $\Delta\mathcal{E}_{\rm GW}=(\tilde p\mathcal{E}_{\rm EM}/k_*)^3$, where $k_*$ is the characteristic wave number, $\tilde p=0.84$ and $0.88$ are found in the nonhelical and helical cases, respectively, with reheating around the QCD energy scale, while $\tilde p=0.45$ is found at the electroweak energy scale. We also compare the polarization spectrum of the linear and nonlinear cases and find that adding the nonlinear term usually yields a decrease in the polarization that is proportional to the EM energy density. We parameterize the fractional polarization suppression as $|\Delta \mathcal{P}_{\rm GW}/\mathcal{P}_{\rm GW}|=\tilde r \mathcal{E}_{\rm EM}/k_*$ and find $\tilde r = 1.2 \times 10^{-1}$, $7.2 \times 10^{-4}$, and $3.2 \times 10^{-2}$ for the helical cases with reheating temperatures $T_{\rm r} = 300 {\rm TeV}$, $8 {\rm GeV}$, and $120 {\rm MeV}$, respectively. Prospects of observation by pulsar timing arrays, space-based interferometers, and other novel detection proposals are also discussed. Title: Simulating Relic Gravitational Waves from Inflationary Magnetogenesis Authors: Brandenburg, Axel; Sharma, Ramkishor Bibcode: 2021ApJ...920...26B Altcode: 2021arXiv210603857B We present three-dimensional direct numerical simulations of the production of magnetic fields and gravitational waves (GWs) in the early universe during a low energy scale matter-dominated post-inflationary reheating era, and during the early subsequent radiative era, which is strongly turbulent. The parameters of the model are determined such that it avoids a number of known physical problems and produces magnetic energy densities between 0.03% and 0.5% of the critical energy density at the end of reheating. During the subsequent development of a turbulent magnetohydrodynamic cascade, magnetic fields and GWs develop a spectrum that extends to higher frequencies in the millihertz (nanohertz) range for models with reheating temperatures of around 100 GeV (150 MeV) at the beginning of the radiation-dominated era. However, even though the turbulent cascade is fully developed, the GW spectrum shows a sharp drop for frequencies above the peak value. This suggests that the turbulence is less efficient in driving GWs than previously thought. The peaks of the resulting GW spectra may well be in the range accessible to space interferometers, pulsar timing arrays, and other facilities. Title: Turbulent radiative diffusion and turbulent Newtonian cooling Authors: Brandenburg, Axel; Das, Upasana Bibcode: 2021PhFl...33i5125B Altcode: 2020arXiv201007046B Radiation transport plays an important role in stellar atmospheres, but the effects of turbulence are being obscured by other effects such as stratification. Using radiative hydrodynamic simulations of forced turbulence, we determine the decay rates of sinusoidal large-scale temperature perturbations of different wavenumbers in the optically thick and thin regimes. Increasing the wavenumber increases the rate of decay in both regimes, but this effect is much weaker than for the usual turbulent diffusion of passive scalars, where the increase is quadratic for small wavenumbers. The turbulent decay is well described by an enhanced Newtonian cooling process in the optically thin limit, which is found to show a weak increase proportional to the square root of the wavenumber. In the optically thick limit, the increase in turbulent decay is somewhat steeper for wavenumbers below the energy-carrying wavenumber of the turbulence, but levels off toward larger wavenumbers. In the presence of turbulence, the typical cooling time is comparable to the turbulent turnover time. We observe that the temperature takes a long time to reach equilibrium in both the optically thin and thick cases, but in the former, the temperature retains smaller scale structures for longer. Title: Can we observe the QCD phase transition-generated gravitational waves through pulsar timing arrays? Authors: Brandenburg, Axel; Clarke, Emma; He, Yutong; Kahniashvili, Tina Bibcode: 2021PhRvD.104d3513B Altcode: 2021arXiv210212428B We perform numerical simulations of gravitational waves (GWs) induced by hydrodynamic and hydromagnetic turbulent sources that might have been present at cosmological quantum chromodynamic (QCD) phase transitions. For turbulent energies of about 4% of the radiation energy density, the typical scale of such motions may have been a sizable fraction of the Hubble scale at that time. The resulting GWs are found to have an energy fraction of about 10-9 of the critical energy density in the nHz range today and may already have been observed by the NANOGrav Collaboration. This is further made possible by our findings of shallower spectra proportional to the square root of the frequency for nonhelical hydromagnetic turbulence. This implies more power at low frequencies than for the steeper spectra previously anticipated. The behavior toward higher frequencies depends strongly on the nature of the turbulence. For vortical hydrodynamic and hydromagnetic turbulence, there is a sharp drop of spectral GW energy by up to five orders of magnitude in the presence of helicity, and somewhat less in the absence of helicity. For acoustic hydrodynamic turbulence, the sharp drop is replaced by a power law decay, albeit with a rather steep slope. Our study supports earlier findings of a quadratic scaling of the GW energy with the magnetic energy of the turbulence and inverse quadratic scaling with the peak frequency, which leads to larger GW energies under QCD conditions. Title: Tensor spectrum of turbulence-sourced gravitational waves as a constraint on graviton mass Authors: He, Yutong; Brandenburg, Axel; Sinha, Aditya Bibcode: 2021JCAP...07..015H Altcode: 2021arXiv210403192H; 2021JCAP...08..015H We consider a generic dispersive massive gravity theory and numerically study its resulting modified energy and strain spectra of tensor gravitational waves (GWs) sourced by (i) fully developed turbulence during the electroweak phase transition (EWPT) and (ii) forced hydromagnetic turbulence during the QCD phase transition (QCDPT). The GW spectra are then computed in both spatial and temporal Fourier domains. We find, from the spatial spectra, that the slope modifications are weakly dependent on the eddy size at QCDPT, and, from the temporal spectra, that the modifications are pronounced in the 1-10 range - the sensitivity range of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) - for a graviton mass in the range 2×10-23 c27×10-22. Title: The scalar, vector, and tensor modes in gravitational wave turbulence simulations Authors: Brandenburg, Axel; Gogoberidze, Grigol; Kahniashvili, Tina; Mandal, Sayan; Roper Pol, Alberto; Shenoy, Nakul Bibcode: 2021CQGra..38n5002B Altcode: 2021arXiv210301140B We study the gravitational wave (GW) signal sourced by primordial turbulence that is assumed to be present at cosmological phase transitions like the electroweak and quantum chromodynamics phase transitions. We consider various models of primordial turbulence, such as those with and without helicity, purely hydrodynamical turbulence induced by fluid motions, and magnetohydrodynamic turbulence whose energy can be dominated either by kinetic or magnetic energy, depending on the nature of the turbulence. We also study circularly polarized GWs generated by parity violating sources such as helical turbulence. Our ultimate goal is to determine the efficiency of GW production through different classes of turbulence. We find that the GW energy and strain tend to be large for acoustic or irrotational turbulence, even though its tensor mode amplitude is relatively small at most wave numbers. Only at very small wave numbers is the spectral tensor mode significant, which might explain the efficient GW production in that case. Title: Can We Observe QCD Phase Transition-Generated Gravitational Waves Through Pulsar Timing Arrays? Authors: Clarke, E.; Brandenburg, A.; He, Y.; Kahniashvili, T. Bibcode: 2021AAS...23823006C Altcode: The NANOGrav collaboration recently reported evidence of a stochastic common-spectrum process which might be interpreted as a stochastic gravitational wave background in the nHz frequency range. One possible explanation for this signal is gravitational waves (GWs) generated at quantum chromodynamic (QCD) scales in the early universe. I will discuss numerical simulations of GWs induced by hydrodynamic and hydromagnetic turbulent sources that might have been present at cosmological QCD phase transitions. For turbulent energies of about 4% of the radiation energy density, the typical scale of such motions may have been a sizable fraction of the Hubble scale at that time. The resulting GWs are found to have an energy fraction of about 10-9 of the critical energy density in the nHz range today. Our finding of shallower GW spectra proportional to the square root of the frequency for nonhelical hydromagnetic turbulence implies more power at low frequencies than for the steeper spectra previously anticipated. The behavior toward higher frequencies depends strongly on the nature of the turbulence. For vortical hydrodynamic and hydromagnetic turbulence, there is a sharp drop of spectral GW energy by up to five orders of magnitude in the presence of helicity, and somewhat less in the absence of helicity. For acoustic hydrodynamic turbulence, the sharp drop is replaced by a power law decay with a rather steep slope. These results support earlier findings of a quadratic scaling of the GW energy with the magnetic energy of the turbulence and an inverse quadratic scaling with the peak frequency, leading to larger GW energies under QCD conditions. Title: Relic Gravitational Waves From The Chiral Magnetic Effect Authors: He, Y.; Brandenburg, A.; Kahniashvili, T.; Rheinhardt, M.; Schober, J. Bibcode: 2021AAS...23823005H Altcode: A system of fermions can exhibit chiral asymmetry, which can be quantified by the chiral chemical potential μ5, proportional to the number density difference between left- and right-handed fermions, i.e. μ5 ∝ (nL − nR). If μ5 is large enough, it can work as a dynamo effect and exponentially increase a seed magnetic field. This is known as the chiral magnetic effect (CME). While active, the CME converts the initial chiral asymmetry μ50 into magnetic helicity on the order of BrmsξM, where ξM is the magnetic correlation length. Although magnetic helicity generated by CME alone is too small compared to the constraint inferred from the non-observations of GeV-energy halos around TeV blazars, and the frequency of CME-induced gravitational waves (GWs) is too high compared to current and future detectors' sensitivity, we could still treat the CME as a proxy of other sourcing mechanisms for primordial GWs. In terms of GW production, we identify two regimes of interest, distinguished by the relative magnitude of two characteristic velocities vλ = μ501/2 and vμ = μ50η, where λ characterises the depletion of μ5 and η is the magnetic diffusivity. So vλ characterises the depletion of chiral asymmetry and vμ characterises the generation of magnetic field. We therefore say that η k1 < vμ < vλ is in regime I, and η k1 < vλ < vμ is in regime II, where k1 is the smallest wavenumber in the domain and μ50 > k1 is excitation threshold for CME. In both regimes, we note that there are two evolutionary phases, where in phase 1) the magnetic field is CME-driven and reaches maximum, which determines the GW energy, and in phase 2) the magnetic length scales increase as its energy decreases, which is probably irrelevant to GW production. In this study, we performed a series of numerical simulations, where η was varied by more than 4 orders of magnitude, μ50 and λ1/2 by about 2 orders of magnitude each. We have found that the GW energy goes as ΩGWsat ∝ vλ5 vμ. Perhaps a counterintuitive finding is that in regime II, large GW energies can be generated. However, we note that, in general, the overall conversion from CME-induced magnetic to GW energy is less efficient than for forced and decaying turbulence due to the small length scales associated with the CME.

References: Brandenburg, A., He, Y., Kahniashvili, T., Rheinhardt, M. & Schober, J. Relic gravitational waves from the chiral magnetic effect. ApJ, in press (2021). 2101.08178. Title: Primordial Magnetic Fields through Large Scale Structure Authors: Mtchedlidze, S.; Domínguez-Fernández, P.; Du, X.; Brandenburg, A.; Kahniashvili, T. Bibcode: 2021AAS...23810909M Altcode: The existence of magnetic fields is ubiquitous on astrophysical and cosmological scales: from planets andstars to galaxies and galaxy clusters. It is commonly assumed that the observed fields today are originated from either astrophysical or cosmological magnetic seeds.The recent observations of blazar spectra by the Fermi Gamma Ray Observatory provides an intriguing possibility of detecting very weak magnetic fields in cosmic voids.This poses an exciting avenue for studying the generation mechanisms and evolution of observed large-scale correlated magnetic fields. Notably, numerical (cosmological) simulations and faraday rotation measure maps show the large scale morphology of these fields, i.e the magnetic correlation lengths extending beyond the galaxy clusters' scales. This, in principle, is hard to explain by the astrophysical sources of the field generation and amplification such as the Biermann battery and dynamo even with the various mechanisms of magnetic seed transport (in a few Gyr timeframe). On the other hand, primordial magnetic fields (PMFs), being good candidates for the seed magnetic fields, might be generated in the early Universe through different processes such as quantum-mechanical fluctuations during inflation, bubble collisions during cosmological first order phase transitions, primordial turbulent motions, etc. Interestingly, inflationary generated magnetic fields might have unlimited (i.e.not constrained by the Hubble scale) correlations length scale, while causally generated magnetic fields (for example during the phase transitions) are characterized by the correlation length having an upper limit equal to the Hubble length scale. In our work, using numerical magnetized cosmological simulations we explore the evolution of the primordial magnetic fields (assuming various models of the field generation) during the structure formation (i.e. late stages). We properly account for the magnetic field dynamics prior recombination as well as development of turbulent motions. We study how these seed magnetic fields evolve during structure formation and what can be the observable traces of such fields. Our findings include: the distinctive spectral evolution of different seed fields imprinted on the scale of galaxy clusters, bridges, as well as filaments and voids, and differences in the rotation measure maps. Title: Relic Gravitational Waves from the Chiral Magnetic Effect Authors: Brandenburg, Axel; He, Yutong; Kahniashvili, Tina; Rheinhardt, Matthias; Schober, Jennifer Bibcode: 2021ApJ...911..110B Altcode: 2021arXiv210108178B Relic gravitational waves (GWs) can be produced by primordial magnetic fields. However, not much is known about the resulting GW amplitudes and their dependence on the details of the generation mechanism. Here we treat magnetic field generation through the chiral magnetic effect (CME) as a generic mechanism and explore its dependence on the speed of generation (the product of magnetic diffusivity and characteristic wavenumber) and the speed characterizing the maximum magnetic field strength expected from the CME. When the latter exceeds the former (regime I), which is the regime applicable to the early universe, we obtain an inverse cascade with moderate GW energy that scales with the third power of the magnetic energy. When the generation speed exceeds the CME limit (regime II), the GW energy continues to increase without a corresponding increase of magnetic energy. In the early kinematic phase, the GW energy spectrum (per linear wavenumber interval) has opposite slopes in both regimes and is characterized by an inertial range spectrum in regime I and a white noise spectrum in regime II. The occurrence of these two slopes is shown to be a generic consequence of a nearly monochromatic exponential growth of the magnetic field. The resulting GW energy is found to be proportional to the fifth power of the limiting CME speed and the first power of the generation speed. Title: The effect of a dynamo-generated field on the Parker wind Authors: Jakab, P.; Brandenburg, A. Bibcode: 2021A&A...647A..18J Altcode: 2020arXiv200602971J Context. Stellar winds are an integral part of the underlying dynamo, the motor of stellar activity. The wind controls the star's angular momentum loss, which depends on the magnetic field geometry which, in turn, varies significantly in time and latitude.
Aims: Here we study basic properties of a self-consistent model that includes simple representations of both the global stellar dynamo in a spherical shell and the exterior in which the wind accelerates and becomes supersonic.
Methods: We numerically solved an axisymmetric mean-field model for the induction, momentum, and continuity equations using an isothermal equation of state. The model allows for the simultaneous generation of a mean magnetic field and the development of a Parker wind. The resulting flow is transonic at the critical point, which we arranged to be between the inner and outer radii of the model. The boundary conditions are assumed to be such that the magnetic field is antisymmetric about the equator, that is to say dipolar.
Results: At the solar rotation rate, the dynamo is oscillatory and of α2 type. In most of the domain, the magnetic field corresponds to that of a split monopole. The magnetic energy flux is largest between the stellar surface and the critical point. The angular momentum flux is highly variable in time and can reach negative values, especially at midlatitudes. At a rapid rotation of up to 50 times the solar value, most of the magnetic field is lost along the axis within the inner tangential cylinder of the model.
Conclusions: The model reveals unexpected features that are not generally anticipated from models that are designed to reproduce the solar wind: highly variable angular momentum fluxes even from just an α2 dynamo in the star. A major caveat of our isothermal models with a magnetic field produced by a dynamo is the difficulty to reach small enough plasma betas without the dynamo itself becoming unrealistically strong inside the star.

The source code used for the simulations of this study, the PENCIL CODE (Pencil Code Collaboration 2020), is freely available on https://github.com/pencil-code/. The DOI of the code is https://doi.org/10.5281/zenodo.2315093 (Pencil Code Collaboration 2018). The simulation setups and corresponding data are freely available on https://doi.org/10.5281/zenodo.4284439 (Jakab & Brandenburg 2020). Title: Circular polarization of gravitational waves from early-Universe helical turbulence Authors: Kahniashvili, Tina; Brandenburg, Axel; Gogoberidze, Grigol; Mandal, Sayan; Pol, Alberto Roper Bibcode: 2021PhRvR...3a3193K Altcode: 2020arXiv201105556K We perform direct numerical simulations to compute the net circular polarization of gravitational waves from helical (chiral) turbulent sources in the early Universe for a variety of initial conditions, including driven (stationary) and decaying turbulence. We investigate the resulting gravitational wave signal assuming different turbulent geneses such as magnetically or kinetically driven cases. Under realistic physical conditions in the early Universe we compute numerically the wave number-dependent polarization degree of the gravitational waves. We find that the spectral polarization degree strongly depends on the initial conditions. The peak of the spectral polarization degree occurs at twice the typical wave number of the source, as expected, and for fully helical decaying turbulence, it reaches its maximum of nearly 100% only at the peak. We determine the temporal evolution of the turbulent sources as well as the resulting gravitational waves, showing that the dominant contribution to their spectral energy density happens shortly after the activation of the source. Only through an artificially prolonged decay of the turbulence can further increase of the gravitational wave amplitude be achieved. We estimate the detection prospects for the net polarization, arguing that its detection contains clean information (including the generation mechanisms, time, and strength) about the sources of possible parity violations in the early Universe. Title: The Pencil Code, a modular MPI code for partial differential equations and particles: multipurpose and multiuser-maintained Authors: Pencil Code Collaboration; Brandenburg, Axel; Johansen, Anders; Bourdin, Philippe; Dobler, Wolfgang; Lyra, Wladimir; Rheinhardt, Matthias; Bingert, Sven; Haugen, Nils; Mee, Antony; Gent, Frederick; Babkovskaia, Natalia; Yang, Chao-Chin; Heinemann, Tobias; Dintrans, Boris; Mitra, Dhrubaditya; Candelaresi, Simon; Warnecke, Jörn; Käpylä, Petri; Schreiber, Andreas; Chatterjee, Piyali; Käpylä, Maarit; Li, Xiang-Yu; Krüger, Jonas; Aarnes, Jørgen; Sarson, Graeme; Oishi, Jeffrey; Schober, Jennifer; Plasson, Raphaël; Sandin, Christer; Karchniwy, Ewa; Rodrigues, Luiz; Hubbard, Alexander; Guerrero, Gustavo; Snodin, Andrew; Losada, Illa; Pekkilä, Johannes; Qian, Chengeng Bibcode: 2021JOSS....6.2807P Altcode: 2021JOSS....6.2807C; 2020arXiv200908231B The Pencil Code is a highly modular physics-oriented simulation code that can be adapted to a wide range of applications. It is primarily designed to solve partial differential equations (PDEs) of compressible hydrodynamics and has lots of add-ons ranging from astrophysical magnetohydrodynamics (MHD) to meteorological cloud microphysics and engineering applications in combustion. Nevertheless, the framework is general and can also be applied to situations not related to hydrodynamics or even PDEs, for example when just the message passing interface or input/output strategies of the code are to be used. The code can also evolve Lagrangian (inertial and noninertial) particles, their coagulation and condensation, as well as their interaction with the fluid. Title: Homochirality: A Prerequisite or Consequence of Life? Authors: Brandenburg, Axel Bibcode: 2021pcol.book...87B Altcode: 2020arXiv201212850B Many of the building blocks of life such as amino acids and nucleotides are chiral, i.e., different from their mirror image. Contemporary life selects and synthesizes only one of two possible handednesses. In an abiotic environment, however, there are usually equally many left- and right-handed molecules. If homochirality was a prerequisite of life, there must have been physical or chemical circumstances that led to the selection of a certain preference. Conversely, if it was a consequence of life, we must identify possible pathways for accomplishing a transition from a racemic to a homochiral chemistry. After a discussion of the observational evidence, we review ideas where homochirality of any handedness could emerge as a consequence of the first polymerization events of nucleotides in an emerging RNA world. These mechanisms are not limited to nucleotides, but can also occur for peptides, as a precursor to the RNA world. The question of homochirality is, in this sense, intimately tied to the origin of life. Future Mars missions may be able to detect biomolecules of extant or extinct life. We therefore also discuss possible experimental setups for determining the chirality of primitive life forms in situ on Mars. Title: Magnetic Helicity: diagnostic signatures and effects Authors: Brandenburg, A. Bibcode: 2020AGUFMNG011..02B Altcode: In situ measurements of the solar wind provide us with a unique opportunity to determine the magnetic helicity and to look for a systematic hemispheric dependence. Although this has been done, the results still remain puzzling and point to a reversal of magnetic helicity some distance above the solar surface. No observational evidence for an actual reversal exists as yet. This leads us to the exploration of proxies of helicity, which could be used to verify the reality of a reversal and to determine its location. Of particular interest is the technique of decomposing images of linear polarization into its parity-even and parity-odd constituents, and to associate the latter with a helicity proxy. In my talk, I will illuminate the dynamo-theoretical background of helicity, such as what is known as catastrophic quenching, and will then discuss the status of magnetic helicity proxies using both observational and numerical results. Many of these techniques are rather general and can also be applied to intensity maps, including terrestrial cloud patterns of hurricanes, for example. Title: On the Existence of Shear-current Effects in Magnetized Burgulence Authors: Käpylä, Maarit J.; Vizoso, Javier Álvarez; Rheinhardt, Matthias; Brandenburg, Axel; Singh, Nishant K. Bibcode: 2020ApJ...905..179K Altcode: 2020arXiv200605661K The possibility of explaining shear flow dynamos by a magnetic shear-current (MSC) effect is examined via numerical simulations. Our primary diagnostics is the determination of the turbulent magnetic diffusivity tensor η. In our setup, a negative sign of its component ηyx is necessary for coherent dynamo action by the SC effect. To be able to measure turbulent transport coefficients from systems with magnetic background turbulence, we present an extension of the test-field method (TFM) applicable to our setup where the pressure gradient is dropped from the momentum equation: the nonlinear TFM (NLTFM). Our momentum equation is related to Burgers' equation and the resulting flows are referred to as magnetized burgulence. We use both stochastic kinetic and magnetic forcings to mimic cases without and with simultaneous small-scale dynamo action. When we force only kinetically, negative ηyx are obtained with exponential growth in both the radial and azimuthal mean magnetic field components. Using magnetokinetic forcing, the field growth is no longer exponential, while NLTFM yields positive ηyx. By employing an alternative forcing from which wavevectors whose components correspond to the largest scales are removed, the exponential growth is recovered, but the NLTFM results do not change significantly. Analyzing the dynamo excitation conditions for the coherent SC and incoherent α and SC effects shows that the incoherent effects are the main drivers of the dynamo in the majority of cases. We find no evidence for MSC-effect-driven dynamos in our simulations. Title: Numerical simulations of gravitational waves from early-universe turbulence Authors: Roper Pol, Alberto; Mandal, Sayan; Brandenburg, Axel; Kahniashvili, Tina; Kosowsky, Arthur Bibcode: 2020PhRvD.102h3512R Altcode: 2019arXiv190308585R We perform direct numerical simulations of magnetohydrodynamic turbulence in the early universe and numerically compute the resulting stochastic background of gravitational waves and relic magnetic fields. These simulations do not make the simplifying assumptions of earlier analytic work. If the turbulence is assumed to have an energy-carrying scale that is about a hundredth of the Hubble radius at the time of generation, as expected in a first-order phase transition, the peak of gravitational wave power will be in the mHz frequency range for a signal produced at the electroweak scale. The efficiency of gravitational wave (GW) production varies significantly with how the turbulence is driven. Detectability of turbulence at the electroweak scale by the planned Laser Interferometer Space Antenna (LISA) requires anywhere from 0.1% to 10% of the thermal plasma energy density to be in plasma motions or magnetic fields, depending on the model of the driving process. Our results predict a new universal form below the spectral peak frequency that is shallower than previously thought. This implies larger values of the GW energy spectra in the low-frequency range. This extends the range where turbulence is detectable with LISA to lower frequencies, corresponding to higher energy scales than the assumed energy-carrying scale. Title: Helicity proxies from linear polarisation of solar active regions Authors: Prabhu, A.; Brandenburg, A.; Käpylä, M. J.; Lagg, A. Bibcode: 2020A&A...641A..46P Altcode: 2020arXiv200110884P Context. The α effect is believed to play a key role in the generation of the solar magnetic field. A fundamental test for its significance in the solar dynamo is to look for magnetic helicity of opposite signs both between the two hemispheres as well as between small and large scales. However, measuring magnetic helicity is compromised by the inability to fully infer the magnetic field vector from observations of solar spectra, caused by what is known as the π ambiguity of spectropolarimetric observations.
Aims: We decompose linear polarisation into parity-even and parity-odd E and B polarisations, which are not affected by the π ambiguity. Furthermore, we study whether the correlations of spatial Fourier spectra of B and parity-even quantities such as E or temperature T are a robust proxy for magnetic helicity of solar magnetic fields.
Methods: We analysed polarisation measurements of active regions observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics observatory. Theory predicts the magnetic helicity of active regions to have, statistically, opposite signs in the two hemispheres. We then computed the parity-odd EB and TB correlations and tested for a systematic preference of their sign based on the hemisphere of the active regions.
Results: We find that: (i) EB and TB correlations are a reliable proxy for magnetic helicity, when computed from linear polarisation measurements away from spectral line cores; and (ii) E polarisation reverses its sign close to the line core. Our analysis reveals that Faraday rotation does not have a significant influence on the computed parity-odd correlations.
Conclusions: The EB decomposition of linear polarisation appears to be a good proxy for magnetic helicity independent of the π ambiguity. This allows us to routinely infer magnetic helicity directly from polarisation measurements. Title: Hall Cascade with Fractional Magnetic Helicity in Neutron Star Crusts Authors: Brandenburg, Axel Bibcode: 2020ApJ...901...18B Altcode: 2020arXiv200612984B The ohmic decay of magnetic fields in the crusts of neutron stars is generally believed to be governed by Hall drift, which leads to what is known as a Hall cascade. Here we show that helical and fractionally helical magnetic fields undergo strong inverse cascading like in magnetohydrodynamics (MHD), but the magnetic energy decays more slowly with time t: $\propto \,{t}^{-2/5}$ instead of ∝t-2/3 in MHD. Even for a nonhelical magnetic field there is a certain degree of inverse cascading for sufficiently strong magnetic fields. The inertial range scaling with wavenumber k is compatible with earlier findings for the forced Hall cascade, i.e., proportional to k-7/3, but in the decaying cases, the subinertial range spectrum steepens to a novel k5 slope instead of the k4 slope in MHD. The energy of the large-scale magnetic field can increase quadratically in time through inverse cascading. For helical fields, the energy dissipation is found to be inversely proportional to the large-scale magnetic field and proportional to the fifth power of the rms magnetic field. For neutron star conditions with an rms magnetic field of a few times ${10}^{14}\,{\rm{G}}$ , the large-scale magnetic field might only be ${10}^{11}\,{\rm{G}}$ , while still producing magnetic dissipation of ${10}^{33}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ for thousands of years, which could manifest itself through X-ray emission. Finally, it is shown that the conclusions from local unstratified models agree rather well with those from stratified models with boundaries. Title: David Moss (1943-2020) Authors: Shukurov, Anvar; Brandenburg, Axel; Brooke, John; Sokoloff, Dmitry; Tavakol, Reza Bibcode: 2020A&G....61d4.12S Altcode: Anvar Shukurov and colleagues remember a theorist known for his work on stellar and galactic magnetism, who was also a prominent marine biologist. Title: On the Measurement of Handedness in Fermi Large Area Telescope Data Authors: Asplund, Julia; Jóhannesson, Guðlaugur.; Brandenburg, Axel Bibcode: 2020ApJ...898..124A Altcode: 2020arXiv200513065A A handedness in the arrival directions of high-energy photons from outside our Galaxy can be related to the helicity of an intergalactic magnetic field. Previous estimates by Tashiro et al. and Chen et al. showed a hint of a signal present in the photons observed by the Fermi Large Area Telescope (LAT). An update on the measurement of handedness in Fermi-LAT data is presented using more than 10 yr of observations. Simulations are performed to study the uncertainty of the measurements, taking into account the structure of the exposure caused by the energy-dependent instrument response and its observing profile, as well as the background from the interstellar medium. The simulations are required to accurately estimate the uncertainty and to show that previously the uncertainty was significantly underestimated. The apparent signal in the earlier analysis of Fermi-LAT data is rendered nonsignificant. Title: Application of a helicity proxy to edge-on galaxies Authors: Brandenburg, Axel; Furuya, Ray S. Bibcode: 2020MNRAS.496.4749B Altcode: 2020MNRAS.tmp.1992B; 2020arXiv200307284B We study the prospects of detecting magnetic helicity in galaxies by observing the dust polarization of the edge-on galaxy NGC 891. Our numerical results of mean-field dynamo calculations show that there should be a large-scale component of the rotationally invariant parity-odd B polarization that we predict to be negative in the first and third quadrants, and positive in the second and fourth quadrants. The large-scale parity-even E polarization is predicted to be negative near the axis and positive further away in the outskirts. These properties are shown to be mostly a consequence of the magnetic field being azimuthal and the polarized intensity being maximum at the centre of the galaxy and are not a signature of magnetic helicity. Title: Scientific usage of the Pencil Code Authors: Brandenburg, Axel Bibcode: 2020zndo...3466444B Altcode: A search using ADS https://ui.adsabs.harvard.edu lists the papers in which the Pencil Code is being quoted. In this document we present the papers that are making use of the code either for their own scientific work of those authors, or for code comparison purposes. We include conference proceedings, which make up 15-20% of all papers. We classify the references by year and by topic, although the topics are often overlapping. The primary application of the Pencil Code lies in astrophysics, in which case we classify the papers mostly by the field of research. Additional applications can also be found in meteorology and combustion. Title: Scientific usage of the Pencil Code Authors: Brandenburg, Axel Bibcode: 2020zndo...3947506B Altcode: A search using ADS https://ui.adsabs.harvard.edu lists the papers in which the Pencil Code is being quoted. In this document we present the papers that are making use of the code either for their own scientific work of those authors, or for code comparison purposes. We include conference proceedings, which make up 15-20% of all papers. We classify the references by year and by topic, although the topics are often overlapping. The primary application of the Pencil Code lies in astrophysics, in which case we classify the papers mostly by the field of research. Additional applications can also be found in meteorology and combustion. Title: Primordial magnetic helicity evolution with a homogeneous magnetic field from inflation Authors: Brandenburg, Axel; Durrer, Ruth; Huang, Yiwen; Kahniashvili, Tina; Mandal, Sayan; Mukohyama, Shinji Bibcode: 2020PhRvD.102b3536B Altcode: 2020arXiv200506449B Motivated by a scenario of magnetogenesis in which a homogeneous magnetic field is generated during inflation, we study the magnetohydrodynamic evolution of the primordial plasma motions for two kinds of initial conditions—(i) a spatially homogeneous field with an unlimited correlation length, and (ii) a zero flux scale-invariant statistically homogeneous magnetic field. In both cases, we apply, for a short initial time interval, monochromatic forcing at a certain wave number so that the correlation length is finite, but much smaller than the typical length scale of turbulence. In particular, we investigate the decay of nonhelical and helical hydromagnetic turbulence. We show that, in the presence of a homogeneous magnetic field, the decay of helical and nonhelical small-scale fields can occur rapidly. This is a special property of a system with a perfectly homogeneous magnetic field, which is sometimes considered as a local approximation to a slowly varying background field. It can never change and acts as an imposed magnetic field. This is in sharp contrast to the case of a statistically homogeneous magnetic field, where we recover familiar decay properties: a much slower decay of magnetic energy and a faster growth of the correlation length, especially in the case with magnetic helicity. The result suggests that a homogeneous magnetic field, if generated during inflation, should persist under the influence of small-scale fields and could be the origin of the large-scale magnetic field in the Universe. Title: Dynamo in Weakly Collisional Nonmagnetized Plasmas Impeded by Landau Damping of Magnetic Fields Authors: Pusztai, István; Juno, James; Brandenburg, Axel; TenBarge, Jason M.; Hakim, Ammar; Francisquez, Manaure; Sundström, Andréas Bibcode: 2020PhRvL.124y5102P Altcode: 2020arXiv200111929P We perform fully kinetic simulations of flows known to produce dynamo in magnetohydrodynamics (MHD), considering scenarios with low Reynolds number and high magnetic Prandtl number, relevant for galaxy cluster scale fluctuation dynamos. We find that Landau damping on the electrons leads to a rapid decay of magnetic perturbations, impeding the dynamo. This collisionless damping process operates on spatial scales where electrons are nonmagnetized, reducing the range of scales where the magnetic field grows in high magnetic Prandtl number fluctuation dynamos. When electrons are not magnetized down to the resistive scale, the magnetic energy spectrum is expected to be limited by the scale corresponding to magnetic Landau damping or, if smaller, the electron gyroradius scale, instead of the resistive scale. In simulations we thus observe decaying magnetic fields where resistive MHD would predict a dynamo. Title: Hemispheric Handedness in the Galactic Synchrotron Polarization Foreground Authors: Brandenburg, Axel; Brüggen, Marcus Bibcode: 2020ApJ...896L..14B Altcode: 2020arXiv200314178B The large-scale magnetic field of the Milky Way is thought to be created by an αΩ dynamo, which implies that it should have opposite handedness north and south of the Galactic midplane. Here we attempt to detect a variation in handedness using polarization data from the Wilkinson Microwave Anisotropy Probe. Previous analyzes of the parity-even and parity-odd parts of linear polarization of the global dust and synchrotron emission have focused on quadratic correlations in spectral space of, and between, these two components. Here, by contrast, we analyze the parity-odd polarization itself and show that it has, on average, opposite signs in northern and southern Galactic hemispheres. Comparison with a Galactic mean-field dynamo model shows broad qualitative agreement and reveals that the sign of the observed hemispheric dependence of the azimuthally averaged parity-odd polarization is not determined by the sign of α, but by the sense of differential rotation. Title: Karl-Heinz Rädler (1935-2020) Authors: Brandenburg, Axel; Rüdiger, Günther; Ruediger, Guenther; Ruediger Bibcode: 2020AN....341..365B Altcode: No abstract at ADS Title: Turbulent viscosity and magnetic Prandtl number from simulations of isotropically forced turbulence Authors: Käpylä, P. J.; Rheinhardt, M.; Brandenburg, A.; Käpylä, M. J. Bibcode: 2020A&A...636A..93K Altcode: 2019arXiv190100787K Context. Turbulent diffusion of large-scale flows and magnetic fields plays a major role in many astrophysical systems, such as stellar convection zones and accretion discs.
Aims: Our goal is to compute turbulent viscosity and magnetic diffusivity which are relevant for diffusing large-scale flows and magnetic fields, respectively. We also aim to compute their ratio, which is the turbulent magnetic Prandtl number, Pmt, for isotropically forced homogeneous turbulence.
Methods: We used simulations of forced turbulence in fully periodic cubes composed of isothermal gas with an imposed large-scale sinusoidal shear flow. Turbulent viscosity was computed either from the resulting Reynolds stress or from the decay rate of the large-scale flow. Turbulent magnetic diffusivity was computed using the test-field method for a microphysical magnetic Prandtl number of unity. The scale dependence of the coefficients was studied by varying the wavenumber of the imposed sinusoidal shear and test fields.
Results: We find that turbulent viscosity and magnetic diffusivity are in general of the same order of magnitude. Furthermore, the turbulent viscosity depends on the fluid Reynolds number (Re) and scale separation ratio of turbulence. The scale dependence of the turbulent viscosity is found to be well approximated by a Lorentzian. These results are similar to those obtained earlier for the turbulent magnetic diffusivity. The results for the turbulent transport coefficients appear to converge at sufficiently high values of Re and the scale separation ratio. However, a weak trend is found even at the largest values of Re, suggesting that the turbulence is not in the fully developed regime. The turbulent magnetic Prandtl number converges to a value that is slightly below unity for large Re. For small Re we find values between 0.5 and 0.6 but the data are insufficient to draw conclusions regarding asymptotics. We demonstrate that our results are independent of the correlation time of the forcing function.
Conclusions: The turbulent magnetic diffusivity is, in general, consistently higher than the turbulent viscosity, which is in qualitative agreement with analytic theories. However, the actual value of Pmt found from the simulations (≈0.9-0.95) at large Re and large scale separation ratio is higher than any of the analytic predictions (0.4-0.8). Title: The Turbulent Stress Spectrum in the Inertial and Subinertial Ranges Authors: Brandenburg, Axel; Boldyrev, Stanislav Bibcode: 2020ApJ...892...80B Altcode: 2019arXiv191207499B For velocity and magnetic fields, the turbulent pressure and, more generally, the squared fields such as the components of the turbulent stress tensor, play important roles in astrophysics. For both one and three dimensions, we derive the equations relating the energy spectra of the fields to the spectra of their squares. We solve the resulting integrals numerically and show that for turbulent energy spectra of Kolmogorov type, the spectral slope of the stress spectrum is also of Kolmogorov type. For shallower turbulence spectra, the slope of the stress spectrum quickly approaches that of white noise, regardless of how blue the spectrum of the field is. For fully helical fields, the stress spectrum is elevated by about a factor of two in the subinertial range, while that in the inertial range remains unchanged. We discuss possible implications for understanding the spectrum of primordial gravitational waves from causally generated magnetic fields during cosmological phase transitions in the early universe. We also discuss potential diagnostic applications to the interstellar medium, where polarization and scintillation measurements characterize the square of the magnetic field. Title: Chiral fermion asymmetry in high-energy plasma simulations Authors: Schober, J.; Brandenburg, A.; Rogachevskii, I. Bibcode: 2020GApFD.114..106S Altcode: The chiral magnetic effect (CME) is a quantum relativistic effect that describes the appearance of an additional electric current along a magnetic field. It is caused by an asymmetry between the number densities of left- and right-handed fermions, which can be maintained at high energies when the chirality flipping rate can be neglected, for example in the early Universe. The inclusion of the CME in the Maxwell equations leads to a modified set of magnetohydrodynamical (MHD) equations. The CME is studied here in numerical simulations with the PENCIL CODE. We discuss how the CME is implemented in the code and how the time step and the spatial resolution of a simulation need to be adjusted in presence of a chiral asymmetry. The CME plays a key role in the evolution of magnetic fields, since it results in a dynamo effect associated with an additional term in the induction equation. This term is formally similar to the α effect in classical mean-field MHD. However, the chiral dynamo can operate without turbulence and is associated with small spatial scales that can be, in the case of the early Universe, orders of magnitude below the Hubble radius. A chiral ? effect has also been identified in mean-field theory. It occurs in the presence of turbulence, but is not related to kinetic helicity. Depending on the plasma parameters, chiral dynamo instabilities can amplify magnetic fields over many orders of magnitude. These instabilities can potentially affect the propagation of MHD waves. Our numerical simulations demonstrate strong modifications of the dispersion relation for MHD waves for large chiral asymmetry. We also study the coupling between the evolution of the chiral chemical potential and the ordinary chemical potential, which is proportional to the sum of the number densities of left- and right-handed fermions. An important consequence of this coupling is the emergence of chiral magnetic waves (CMWs). We confirm numerically that linear CMWs and MHD waves are not interacting. Our simulations suggest that the chemical potential has only a minor effect on the non-linear evolution of the chiral dynamo. Title: The timestep constraint in solving the gravitational wave equations sourced by hydromagnetic turbulence Authors: Roper Pol, Alberto; Brandenburg, Axel; Kahniashvili, Tina; Kosowsky, Arthur; Mandal, Sayan Bibcode: 2020GApFD.114..130R Altcode: 2018arXiv180705479R Hydromagnetic turbulence produced during phase transitions in the early universe can be a powerful source of stochastic gravitational waves (GWs). GWs can be modelled by the linearised spatial part of the Einstein equations sourced by the Reynolds and Maxwell stresses. We have implemented two different GW solvers into the Pencil Code - a code which uses a third order timestep and sixth order finite differences. Using direct numerical integration of the GW equations, we study the appearance of a numerical degradation of the GW amplitude at the highest wavenumbers, which depends on the length of the timestep - even when the Courant-Friedrichs-Lewy condition is ten times below the stability limit. This degradation leads to a numerical error, which is found to scale with the third power of the timestep. A similar degradation is not seen in the magnetic and velocity fields. To mitigate numerical degradation effects, we alternatively use the exact solution of the GW equations under the assumption that the source is constant between subsequent timesteps. This allows us to use a much longer timestep, which cuts the computational cost by a factor of about ten. Title: The time step constraint in radiation hydrodynamics Authors: Brandenburg, Axel; Das, Upasana Bibcode: 2020GApFD.114..162B Altcode: 2019arXiv190106385B Explicit radiation hydrodynamic simulations of the atmospheres of massive stars and of convection in accretion discs around white dwarfs suffer from prohibitively short time steps due to radiation. This constraint is related to the cooling time rather than the radiative pressure, which also becomes important in hot stars and discs. We show that the radiative time step constraint is governed by the minimum of the sum of the optically thick and thin contributions rather than the smaller one of the two. In simulations with the PENCIL CODE, their weighting fractions are found empirically. In three-dimensional convective accretion disc simulations, the Deardorff term is found to be the main contributor to the enthalpy flux rather than the superadiabatic gradient. We conclude with a discussion of how the radiative time step problem could be mitigated in certain types of investigations. Title: Convergence properties of detonation simulations Authors: Qian, Chengeng; Wang, Cheng; Liu, JianNan; Brandenburg, Axel; Haugen, Nils E. L.; Liberman, Mikhael A. Bibcode: 2020GApFD.114...58Q Altcode: 2019arXiv190203816Q We present a high-resolution convergence study of detonation initiated by a temperature gradient in a stoichiometric hydrogen-oxygen mixture using the PENCIL CODE and compare with a code that employs a fifth order weighted essentially non-oscillating (WENO) scheme. With Mach numbers reaching 10-30, a certain amount of shock viscosity is needed in the PENCIL CODE to remove or reduce numerical pressure oscillations on the grid scale at the position of the shock. Detonation is found to occur for intermediate values of the shock viscosity parameter. At fixed values of this parameter, the numerical error associated with those small wiggles in the pressure profile is found to decrease with decreasing mesh width ? like ? down to ?. With the WENO scheme, solutions are smooth at ?, but no detonation is obtained for ?. This is argued to be an artifact of a decoupling between pressure and reaction fronts. Title: Sensitivity to luminosity, centrifugal force, and boundary conditions in spherical shell convection Authors: Käpylä, P. J.; Gent, F. A.; Olspert, N.; Käpylä, M. J.; Brandenburg, A. Bibcode: 2020GApFD.114....8K Altcode: 2018arXiv180709309K We test the sensitivity of hydrodynamic and magnetohydrodynamic turbulent convection simulations with respect to Mach number, thermal and magnetic boundary conditions, and the centrifugal force. We find that varying the luminosity, which also controls the Mach number, has only a minor effect on the large-scale dynamics. A similar conclusion can also be drawn from the comparison of two formulations of the lower magnetic boundary condition with either vanishing electric field or current density. The centrifugal force has an effect on the solutions, but only if its magnitude with respect to acceleration due to gravity is by two orders of magnitude greater than in the Sun. Finally, we find that the parameterisation of the photospheric physics, either by an explicit cooling term or enhanced radiative diffusion, is more important than the thermal boundary condition. In particular, runs with cooling tend to lead to more anisotropic convection and stronger deviations from the Taylor-Proudman state. In summary, the fully compressible approach taken here with the Pencil Code is found to be valid, while still allowing the disparate timescales to be taken into account. Title: Magnetism in the Early Universe Authors: Kahniashvili, Tina; Brandenburg, Axel; Kosowsky, Arthur; Mandal, Sayan; Roper Pol, Alberto Bibcode: 2020IAUGA..30..295K Altcode: 2018arXiv181011876K Blazar observations point toward the possible presence of magnetic fields over intergalactic scales of the order of up to ~1 Mpc, with strengths of at least ~10-16 G. Understanding the origin of these large-scale magnetic fields is a challenge for modern astrophysics. Here we discuss the cosmological scenario, focussing on the following questions: (i) How and when was this magnetic field generated? (ii) How does it evolve during the expansion of the universe? (iii) Are the amplitude and statistical properties of this field such that they can explain the strengths and correlation lengths of observed magnetic fields? We also discuss the possibility of observing primordial turbulence through direct detection of stochastic gravitational waves in the mHz range accessible to LISA. Title: Introduction Authors: Brandenburg, A.; Candelaresi, S.; Gent, F. A. Bibcode: 2020GApFD.114....1B Altcode: No abstract at ADS Title: f-mode strengthening from a localised bipolar subsurface magnetic field Authors: Singh, Nishant K.; Raichur, Harsha; Käpylä, Maarit J.; Rheinhardt, Matthias; Brandenburg, Axel; Käpylä, Petri J. Bibcode: 2020GApFD.114..196S Altcode: Recent numerical work in helioseismology has shown that a periodically varying subsurface magnetic field leads to a fanning of the f-mode, which emerges from a density jump at the surface. In an attempt to model a more realistic situation, we now modulate this periodic variation with an envelope, giving thus more emphasis on localised bipolar magnetic structures in the middle of the domain. Some notable findings are: (i) compared to the purely hydrodynamic case, the strength of the f-mode is significantly larger at high horizontal wavenumbers k, but the fanning is weaker for the localised subsurface magnetic field concentrations investigated here than the periodic ones studied earlier; (ii) when the strength of the magnetic field is enhanced at a fixed depth below the surface, the fanning of the f-mode in the ? diagram increases proportionally in such a way that the normalised f-mode strengths remain nearly the same in different such cases; (iii) the unstable Bloch modes reported previously in case of harmonically varying magnetic fields are now completely absent when more realistic localised magnetic field concentrations are imposed beneath the surface, thus suggesting that the Bloch modes are unlikely to be supported during most phases of the solar cycle; (iv) the f-mode strength appears to depend also on the depth of magnetic field concentrations such that it shows a relative decrement when the maximum of the magnetic field is moved to a deeper layer. We argue that detections of f-mode perturbations such as those being explored here could be effective tracers of solar magnetic fields below the photosphere before these are directly detectable as visible manifestations in terms of active regions or sunspots. Title: The nature of mean-field generation in three classes of optimal dynamos Authors: Brandenburg, Axel; Chen, Long Bibcode: 2020JPlPh..86a9010B Altcode: 2019arXiv191101712B In recent years, several optimal dynamos have been discovered. They minimize the magnetic energy dissipation or, equivalently, maximize the growth rate at a fixed magnetic Reynolds number. In the optimal dynamo of Willis (Phys. Rev. Lett., vol. 109, 2012, 251101), we find mean-field dynamo action for planar averages. One component of the magnetic field grows exponentially while the other decays in an oscillatory fashion near onset. This behaviour is different from that of an α2 dynamo, where the two non-vanishing components of the planar averages are coupled and have the same growth rate. For the Willis dynamo, we find that the mean field is excited by a negative turbulent magnetic diffusivity, which has a non-uniform spatial profile near onset. The temporal oscillations in the decaying component are caused by the corresponding component of the diffusivity tensor being complex when the mean field is decaying and, in this way, time dependent. The growing mean field can be modelled by a negative magnetic diffusivity combined with a positive magnetic hyperdiffusivity. In two other classes of optimal dynamos of Chen et al. (J. Fluid Mech., vol. 783, 2015, pp. 23-45), we find, to some extent, similar mean-field dynamo actions. When the magnetic boundary conditions are mixed, the two components of the planar averaged field grow at different rates when the dynamo is 15 % supercritical. When the mean magnetic field satisfies homogeneous boundary conditions (where the magnetic field is tangential to the boundary), mean-field dynamo action is found for one-dimensional averages, but not for planar averages. Despite having different spatial profiles, both dynamos show negative turbulent magnetic diffusivities. Our finding suggests that negative turbulent magnetic diffusivities may support a broader class of dynamos than previously thought, including these three optimal dynamos. Title: Landau damping of magnetic fluctuations inhibit the dynamo in weakly collisional nonmagnetized plasmas Authors: Pusztai, Istvan; Juno, James; Brandenburg, Axel; Tenbarge, Jason M.; Hakim, Ammar; Francisquez, Manaure; Sundström, Andréas Bibcode: 2020APS..DPPJ03001P Altcode: We perform fully kinetic simulations of flows known to produce dynamo in magnetohydrodynamics (MHD), considering scenarios with low Reynolds number and high magnetic Prandtl number, with relevance to fluctuation dynamos in galaxy clusters. We find that Landau damping on the electrons leads to a rapid decay of magnetic perturbations (apart from those corresponding to a current caused by the forcing of the flows), impeding the dynamo. The effect of the magnetic Landau damping is similar to that of a magnetic diffusivity that scales with the wave number of the perturbation. This collisionless damping process operates on spatial scales where electrons are nonmagnetized, reducing the range of scales where the magnetic field grows in high magnetic Prandtl number fluctuation dynamos. When electrons are not magnetized down to the resistive scale, such as galaxy clusters at typical Biermann battery seed fields, the magnetic energy spectrum is expected to be limited by the scale corresponding to magnetic Landau damping or, if smaller, the electron gyroradius scale, instead of the resistive scale, potentially reducing the total energy in magnetic fluctuations. In simulations we thus observe decaying magnetic fields where resistive MHD predicts a dynamo. Title: Magnetic field evolution in solar-type stars Authors: Brandenburg, Axel Bibcode: 2020IAUS..354..169B Altcode: 2020arXiv200400439B We discuss selected aspects regarding the magnetic field evolution of solar-type stars. Most of the stars with activity cycles are in the range where the normalized chromospheric Calcium emission increases linearly with the inverse Rossby number. For Rossby numbers below about a quarter of the solar value, the activity saturates and no cycles have been found. For Rossby numbers above the solar value, again no activity cycles have been found, but now the activity goes up again for a major fraction of the stars. Rapidly rotating stars show nonaxisymmetric large-scale magnetic fields, but there is disagreement between models and observations regarding the actual value of the Rossby number where this happens. We also discuss the prospects of detecting the sign of magnetic helicity using various linear polarization techniques both at the stellar surface using the parity-odd contribution to linear polarization and above the surface using Faraday rotation. Title: Magnetic Helicity Dissipation and Production in an Ideal MHD Code Authors: Brandenburg, Axel; Scannapieco, Evan Bibcode: 2020ApJ...889...55B Altcode: 2019arXiv191006074B We study a turbulent helical dynamo in a periodic domain by solving the ideal magnetohydrodynamic (MHD) equations with the FLASH code using the divergence-cleaning eight-wave method and compare our results with direct numerical simulations (DNS) using the Pencil Code. At low resolution, FLASH reproduces the DNS results qualitatively by developing the large-scale magnetic field expected from DNS, but at higher resolution, no large-scale magnetic field is obtained. In all those cases in which a large-scale magnetic field is generated, the ideal MHD results yield too little power at small scales. As a consequence, the small-scale current helicity is too small compared with that of the DNS. The resulting net current helicity has then always the wrong sign, and its statistical average also does not approach zero at late times, as expected from the DNS. Our results have implications for astrophysical dynamo simulations of stellar and galactic magnetism using ideal MHD codes. Title: A Global Two-scale Helicity Proxy from π-ambiguous Solar Magnetic Fields Authors: Brandenburg, Axel Bibcode: 2019ApJ...883..119B Altcode: 2019arXiv190603877B If the α effect plays a role in the generation of the Sun’s magnetic field, the field should show evidence of magnetic helicity of opposite signs at large and small length scales. Measuring this faces two challenges: (i) in weak-field regions, horizontal field measurements are unreliable because of the π ambiguity, and (ii) one needs a truly global approach to computing helicity spectra in the case where one expects a sign reversal across the equator at all wavenumbers. Here we develop such a method using spin-2 spherical harmonics to decompose the linear polarization in terms of the parity-even and parity-odd E and B polarizations, respectively. Using simple one- and two-dimensional models, we show that the product of the spectral decompositions of E and B, taken at spherical harmonic degrees that are shifted by one, can act as a proxy of the global magnetic helicity with a sign that represents that in the northern hemisphere. We then apply this method to the analysis of solar synoptic vector magnetograms, from which we extract a pseudo-polarization corresponding to a “π-ambiguated” magnetic field, i.e., a magnetic field vector that has no arrow. We find a negative sign of the global EB helicity proxy at spherical harmonic degrees of around 6. This could indicate a positive magnetic helicity at large length scales, but the spectrum fails to capture clear evidence of the well-known negative magnetic helicity at smaller scales. This method might also be applicable to stellar and Galactic polarization data. Title: Spectral Magnetic Helicity of Solar Active Regions between 2006 and 2017 Authors: Gosain, Sanjay; Brandenburg, Axel Bibcode: 2019ApJ...882...80G Altcode: 2019arXiv190211273G We compute magnetic helicity and energy spectra from about 2485 patches of about 100 Mm side length on the solar surface using data from Hinode during 2006-2017. An extensive database is assembled where we list the magnetic energy and helicity, large- and small-scale magnetic helicity, mean current helicity density, fractional magnetic helicity, and correlation length along with the Hinode map identification number (MapID), as well as the Carrington latitude and longitude for each MapID. While there are departures from the hemispheric sign rule for magnetic and current helicities, the weak trend reported here is in agreement with the previous results. This is argued to be a physical effect associated with the dominance of individual active regions that contribute more strongly in the better-resolved Hinode maps. In comparison with earlier work, the typical correlation length is found to be 6-8 {Mm}, while the length scale relating the magnetic and current helicities to each other is around 1.4 {Mm}. Title: Ambipolar diffusion in large Prandtl number turbulence Authors: Brandenburg, Axel Bibcode: 2019MNRAS.487.2673B Altcode: 2019arXiv190308976B; 2019MNRAS.tmp.1443B We study the effects of ambipolar diffusion (AD) on hydromagnetic turbulence. We consider the regime of large magnetic Prandtl number, relevant to the interstellar medium. In most of the cases, we use the single-fluid approximation where the drift velocity between charged and neutral particles is proportional to the Lorentz force. In two cases we also compare with the corresponding two-fluid model, where ionization and recombination are included in the continuity and momentum equations for the neutral and charged species. The magnetic field properties are found to be well represented by the single-fluid approximation. We quantify the effects of AD on total and spectral kinetic and magnetic energies, the ohmic and AD dissipation rates, the statistics of the magnetic field, the current density, and the linear polarization as measured by the rotationally invariant E and B mode polarizations. We show that the kurtosis of the magnetic field decreases with increasing AD. The E mode polarization changes its skewness from positive values for small AD to negative ones for large AD. Even when AD is weak, changes in AD have a marked effect on the skewness and kurtosis of E, and only a weak effect on those of B. These results open the possibility of employing E and B mode polarizations as diagnostic tools for characterizing turbulent properties of the interstellar medium. Title: Reversed Dynamo at Small Scales and Large Magnetic Prandtl Number Authors: Brandenburg, Axel; Rempel, Matthias Bibcode: 2019ApJ...879...57B Altcode: 2019arXiv190311869B We show that at large magnetic Prandtl numbers, the Lorentz force does work on the flow at small scales and drives fluid motions, whose energy is dissipated viscously. This situation is the opposite of that in a normal dynamo, where the flow does work against the Lorentz force. We compute the spectral conversion rates between kinetic and magnetic energies for several magnetic Prandtl numbers and show that normal (forward) dynamo action occurs on large scales over a progressively narrower range of wavenumbers as the magnetic Prandtl number is increased. At higher wavenumbers, reversed dynamo action occurs, i.e., magnetic energy is converted back into kinetic energy at small scales. We demonstrate this in both direct numerical simulations forced by volume stirring and in large eddy simulations (LESs) of solar convectively driven small-scale dynamos. Low-density plasmas such as stellar coronae tend to have large magnetic Prandtl numbers, i.e., the viscosity is large compared with the magnetic diffusivity. The regime in which viscous dissipation dominates over resistive dissipation for large magnetic Prandtl numbers was also previously found in LESs of the solar corona, i.e., our findings are a more fundamental property of MHD that is not just restricted to dynamos. Viscous energy dissipation is a consequence of positive Lorentz force work, which may partly correspond to particle acceleration in close-to-collisionless plasmas. This is, however, not modeled in the MHD approximation employed. By contrast, resistive energy dissipation on current sheets is expected to be unimportant in stellar coronae. Title: The Limited Roles of Autocatalysis and Enantiomeric Cross-Inhibition in Achieving Homochirality in Dilute Systems Authors: Brandenburg, Axel Bibcode: 2019OLEB...49...49B Altcode: 2019arXiv190307855B; 2019OLEB..tmp...17B To understand the effects of fluctuations on achieving homochirality, we employ a Monte-Carlo method where autocatalysis and enantiomeric cross-inhibition, as well as racemization and deracemization reactions are included. The results of earlier work either without autocatalysis or without cross-inhibition are reproduced. Bifurcation diagrams and the dependencies of the number of reaction steps on parameters are studied. In systems with 30,000 molecules, for example, up to a billion reaction steps may be needed to achieve homochirality without autocatalysis. Title: Learning about solar/stellar dynamo physics from the variability Authors: Brandenburg, Axel Bibcode: 2019shin.confE.220B Altcode: I will highlight three reasons where current simulations fail to reproduce the Sun, but I will also highlight three robust results, and finally, I will highlight three striking differences between simulations and observations. (A) Realistic solar/stellar convectively driven dynamo simulations suffer from three principle difficulties: (i) the tremendous stratification, the range of time and length scales, and the lack of realistic surface physics (radiation); (ii) a barely resolved near-surface shear layer, especially at higher latitudes; (iii) angular velocity contours that are still not as spoke-like as suggested by helioseismology; (B) Nevertheless, several robust results have emerged from such simulations: (i) at some rotation rate (Rossby number close to the solar value), there is a transition from solar-like to antisolar-like differential rotation for slower rotation; (ii) at a very similar rotation rate, there is another transition from axisymmetric to nonaxisymmetric (m=1) large-scale magnetic fields; (iii) the rotation to cycle period ratio decreases with increasing stellar activity or decreasing Rossby number. (C) Conflicts between observations and simulations include: (i) the presence of an intermediate solar-like branch where the period frequency ratio increases with increasing stellar activity. The transition to nonaxisymmetric large-scale magnetic fields would be to the right of this branch (larger activity), and the transition to anti solar differential rotation would be to the left, but in simulations the two transitions are found to appear at the same rotation rate, so this intermediate solar-like branch has disappeared. (ii) Both simulations and observations can show evidence for multiple periods. If this is real, it is unclear how the surface appearance of the magnetic field changes. Also, while some observational work has associated the longer periods with dynamo activity closer to the surface, different models show instead that longer periods may originate from deeper down in the convection zone. (iii) Variability in the sunspot data shows relatively nice cycles with a single grand minimum. Stellar cycles are never that clean, and simulations show surface patterns with additional significant variation away from the sunspot belts. Can these discrepancies simply be explained by sunspots being a threshold phenomenon, or is there more behind this difference. Title: Efficient quasi-kinematic large-scale dynamo as the small-scale dynamo saturates Authors: Bhat, Pallavi; Subramanian, Kandaswamy; Brandenburg, Axel Bibcode: 2019arXiv190508278B Altcode: Large-scale magnetic fields in stars and galaxies are thought to arise by mean-field dynamo action due to the combined influence of both helical turbulence and shear. Those systems are also highly conducting and the turbulence therein leads to a fluctuation (or small-scale) dynamo which more rapidly amplifies magnetic field fluctuations on the eddy scales and smaller. Will this then interfere with and suppress the mean (or large-scale) field growth? Using direct numerical simulations of helical turbulence (with and without shear), we identify a novel quasi-kinematic large-scale dynamo which operates as the small-scale dynamo saturates. Thus both dynamos operate efficiently, one after the other, and lead to the generation of significant large-scale fields. Title: Effects of a subadiabatic layer on convection and dynamos in spherical wedge simulations Authors: Käpylä, P. J.; Viviani, M.; Käpylä, M. J.; Brandenburg, A.; Spada, F. Bibcode: 2019GApFD.113..149K Altcode: 2018arXiv180305898K We consider the effect of a subadiabatic layer at the base of the convection zone on convection itself and the associated large-scale dynamos in spherical wedge geometry. We use a heat conduction prescription based on the Kramers opacity law which allows the depth of the convection zone to dynamically adapt to changes in the physical characteristics such as rotation rate and magnetic fields. We find that the convective heat transport is strongly concentrated towards the equatorial and polar regions in the cases without a substantial radiative layer below the convection zone. The presence of a stable layer below the convection zone significantly reduces the anisotropy of radial enthalpy transport. Furthermore, the dynamo solutions are sensitive to subtle changes in the convection zone structure. We find that the kinetic helicity changes sign in the deeper parts of the convection zone at high latitudes in all runs. This region expands progressively towards the equator in runs with a thicker stably stratified layer. Title: Energetics of turbulence generated by chiral MHD dynamos Authors: Schober, J.; Brandenburg, A.; Rogachevskii, I.; Kleeorin, N. Bibcode: 2019GApFD.113..107S Altcode: 2018arXiv180306350S An asymmetry in the number density of left- and right-handed fermions is known to give rise to a new term in the induction equation that can result in a dynamo instability. At high temperatures, when a chiral asymmetry can survive for long enough, this chiral dynamo instability can amplify magnetic fields efficiently, which in turn drive turbulence via the Lorentz force. While it has been demonstrated in numerical simulations that this chiral magnetically driven turbulence exists and strongly affects the dynamics of the magnetic field, the details of this process remain unclear. The goal of this paper is to analyse the energetics of chiral magnetically driven turbulence and its effect on the generation and dynamics of the magnetic field using direct numerical simulations. We study these effects for different initial conditions, including a variation of the initial chiral chemical potential and the magnetic Prandtl number, ? . In particular, we determine the ratio of kinetic to magnetic energy, ? , in chiral magnetically driven turbulence. Within the parameter space explored in this study, ? reaches a value of approximately 0.064-0.074-independently of the initial chiral asymmetry and for ? . Our simulations suggest, that ? decreases as a power law when increasing ? by decreasing the viscosity. While the exact scaling depends on the details of the fitting criteria and the Reynolds number regime, an approximate result of ? is reported. Using the findings from our numerical simulations, we analyse the energetics of chiral magnetically driven turbulence in the early Universe. Title: Dynamo effect in decaying helical turbulence Authors: Brandenburg, Axel; Kahniashvili, Tina; Mandal, Sayan; Pol, Alberto Roper; Tevzadze, Alexander G.; Vachaspati, Tanmay Bibcode: 2019PhRvF...4b4608B Altcode: 2017arXiv171001628B We show that in decaying hydromagnetic turbulence with initial kinetic helicity, a weak magnetic field eventually becomes fully helical. The sign of magnetic helicity is opposite to that of the kinetic helicity—regardless of whether the initial magnetic field was helical. The magnetic field undergoes inverse cascading with the magnetic energy decaying approximately like t−1 /2. This is even slower than in the fully helical case, where it decays like t−2 /3. In this parameter range, the product of magnetic energy and correlation length raised to a certain power slightly larger than unity is approximately constant. This scaling of magnetic energy persists over long timescales. At very late times and for domain sizes large enough to accommodate the growing spatial scales, we expect a crossover to the t−2 /3 decay law that is commonly observed for fully helical magnetic fields. Regardless of the presence or absence of initial kinetic helicity, the magnetic field experiences exponential growth during the first few turnover times, which is suggestive of small-scale dynamo action. Our results have applications to a wide range of experimental dynamos and astrophysical time-dependent plasmas, including primordial turbulence in the early universe. Title: Magnetic bipoles in rotating turbulence with coronal envelope Authors: Losada, I. R.; Warnecke, J.; Brandenburg, A.; Kleeorin, N.; Rogachevskii, I. Bibcode: 2019A&A...621A..61L Altcode: 2018arXiv180304446L Context. The formation mechanism of sunspots and starspots is not yet fully understood. It is a major open problem in astrophysics.
Aims: Magnetic flux concentrations can be produced by the negative effective magnetic pressure instability (NEMPI). This instability is strongly suppressed by rotation. However, the presence of an outer coronal envelope was previously found to strengthen the flux concentrations and make them more prominent. It also allows for the formation of bipolar regions (BRs). We aim to understand the important issue of whether the presence of an outer coronal envelope also changes the excitation conditions and the rotational dependence of NEMPI.
Methods: We have used direct numerical simulations and mean-field simulations. We adopted a simple two-layer model of turbulence that mimics the jump between the convective turbulent and coronal layers below and above the surface of a star, respectively. The computational domain is Cartesian and located at a certain latitude of a rotating sphere. We investigated the effects of rotation on NEMPI by changing the Coriolis number, the latitude, the strengths of the imposed magnetic field, and the box resolution.
Results: Rotation has a strong impact on the process of BR formation. Even rather slow rotation is found to suppress BR formation. However, increasing the imposed magnetic field strength also makes the structures stronger and alleviates the rotational suppression somewhat. The presence of a coronal layer itself does not significantly reduce the effects of rotational suppression. Title: E and B Polarizations from Inhomogeneous and Solar Surface Turbulence Authors: Brandenburg, Axel; Bracco, Andrea; Kahniashvili, Tina; Mandal, Sayan; Roper Pol, Alberto; Petrie, Gordon J. D.; Singh, Nishant K. Bibcode: 2019ApJ...870...87B Altcode: 2018arXiv180711457B Gradient- and curl-type or E- and B-type polarizations have been routinely analyzed to study the physics contributing to the cosmic microwave background polarization and galactic foregrounds. They characterize the parity-even and parity-odd properties of the underlying physical mechanisms, such as, for example, hydromagnetic turbulence in the case of dust polarization. Here, we study spectral correlation functions characterizing the parity-even and parity-odd parts of linear polarization for homogeneous and inhomogeneous turbulence to show that only the inhomogeneous helical case can give rise to a parity-odd polarization signal. We also study nonhelical turbulence and suggest that a strong non-vanishing (here negative) skewness of the E polarization is responsible for an enhanced ratio of the EE to the BB (quadratic) correlation in both the helical and nonhelical cases. This could explain the enhanced EE/BB ratio observed recently for dust polarization. We close with a preliminary assessment of using the linear polarization of the Sun to characterize its helical turbulence without being subjected to the π ambiguity that magnetic inversion techniques have to address. Title: Is there a left-handed magnetic field in the solar neighborhood?. Exploring helical magnetic fields in the interstellar medium through dust polarization power spectra Authors: Bracco, A.; Candelaresi, S.; Del Sordo, F.; Brandenburg, A. Bibcode: 2019A&A...621A..97B Altcode: 2018arXiv180710188B Context. The analysis of the full-sky Planck polarization data at 850 μm revealed unexpected properties of the E- and B-mode power spectra of dust emission in the interstellar medium (ISM). The positive cross-correlations over a wide range of angular scales between the total dust intensity, T, and both E and (most of all) B modes has raised new questions about the physical mechanisms that affect dust polarization, such as the Galactic magnetic field structure. This is key both to better understanding ISM dynamics and to accurately describing Galactic foregrounds to the polarization of the cosmic microwave background (CMB). In particular, in the quest to find primordial B modes of the CMB, the observed positive cross-correlation between T and B for interstellar dust requires further investigation towards parity-violating processes in the ISM.
Aims: In this theoretical paper we investigate the possibility that the observed cross-correlations in the dust polarization power spectra, and specifically the one between T and B, can be related to a parity-odd quantity in the ISM such as the magnetic helicity.
Methods: We produce synthetic dust polarization data, derived from 3D analytical toy models of density structures and helical magnetic fields, to compare with the E and B modes of observations. We present several models. The first is an ideal fully helical isotropic case, such as the Arnold-Beltrami-Childress field. Second, following the nowadays favored interpretation of the T-E signal in terms of the observed alignment between the magnetic field morphology and the filamentary density structure of the diffuse ISM, we design models for helical magnetic fields wrapped around cylindrical interstellar filaments. Lastly, focusing on the observed T-B correlation, we propose a new line of interpretation of the Planck observations advocating the presence of a large-scale helical component of the Galactic magnetic field in the solar neighborhood.
Results: Our analysis shows that: I) the sign of magnetic helicity does not affect E and B modes for isotropic magnetic-field configurations; II) helical magnetic fields threading interstellar filaments cannot reproduce the Planck results; and III) a weak helical left-handed magnetic field structure in the solar neighborhood may explain the T-B correlation seen in the Planck data. Such a magnetic-field configuration would also account for the observed large-scale T-E correlation.
Conclusions: This work suggests a new perspective for the interpretation of the dust polarization power spectra that supports the imprint of a large-scale structure of the Galactic magnetic field in the solar neighborhood. Title: Magnetic helicity and fluxes in an inhomogeneous alpha squared dynamo Authors: Brandenburg, A. Bibcode: 2019arXiv190107552B Altcode: Much work on turbulent three-dimensional dynamos has been done using triply periodic domains, in which there are no magnetic helicity fluxes. Here we present simulations where the turbulent intensity is still nearly homogeneous, but now there is a perfect conductor boundary condition on one end and a vertical field or pseudo-vacuum condition on the other. This leads to migratory dynamo waves. Good agreement with a corresponding analytically solvable alpha^2 dynamo is found. Magnetic helicity fluxes are studied in both types of models. It is found that at moderate magnetic Reynolds numbers, most of the magnetic helicity losses occur at large scales. Whether this changes at even larger magnetic Reynolds numbers, as required for alleviating the catastrophic dynamo quenching problem, remains still unclear. Title: Pencil Code Authors: Brandenburg, Axel Bibcode: 2018zndo...2315093B Altcode: This is the current version; see the "Scientific Usage of the Pencil Code" under http://pencil-code.nordita.org/highlights/ for the currently over 400 publications using the code. The code has received 29,502 commits since 2001. The latest version is available under https://github.com/pencil-code Title: Magnetic Helicity from Multipolar Regions on the Solar Surface Authors: Bourdin, Philippe-A.; Brandenburg, Axel Bibcode: 2018ApJ...869....3B Altcode: 2018arXiv180404160B The emergence of dipolar magnetic features on the solar surface is an idealization. Most of the magnetic flux emergence occurs in complex multipolar regions. Here, we show that the surface pattern of magnetic structures alone can reveal the sign of the underlying magnetic helicity in the nearly force-free coronal regions above. The sign of the magnetic helicity can be predicted to good accuracy by considering the three-dimensional position vectors of three spots on the sphere ordered by their relative strengths at the surface and compute from them the skew product. This product, which is a pseudoscalar, is shown to be a good proxy for the sign of the coronal magnetic helicity. Title: Magnetic Helicity Reversal in the Corona at Small Plasma Beta Authors: Bourdin, Philippe; Singh, Nishant K.; Brandenburg, Axel Bibcode: 2018ApJ...869....2B Altcode: 2018arXiv180404153B Solar and stellar dynamos shed small-scale and large-scale magnetic helicity of opposite signs. However, solar wind observations and simulations have shown that some distance above the dynamo both the small-scale and large-scale magnetic helicities have reversed signs. With realistic simulations of the solar corona above an active region now being available, we have access to the magnetic field and current density along coronal loops. We show that a sign reversal in the horizontal averages of the magnetic helicity occurs when the local maximum of the plasma beta drops below unity and the field becomes nearly fully force free. Hence, this reversal is expected to occur well within the solar corona and would not directly be accessible to in situ measurements with the Parker Solar Probe or SolarOrbiter. We also show that the reversal is associated with subtle changes in the relative dominance of structures with positive and negative magnetic helicity. Title: Cross-helically forced and decaying hydromagnetic turbulence Authors: Brandenburg, A.; Oughton, S. Bibcode: 2018AN....339..641B Altcode: 2019arXiv190105875B We study the evolution of kinetic and magnetic energy spectra in magnetohydrodynamic flows in the presence of strong cross helicity. For forced turbulence, we find a weak inverse transfer of kinetic energy toward the smallest wavenumber. This is plausibly explained by the finiteness of scale separation between the injection wavenumber and the smallest wavenumber of the domain, which here is a factor of 15. In the decaying case, there is a slight increase at the smallest wavenumber, which is probably explained by the dominance of kinetic energy over magnetic energy at the smallest wavenumbers. Within a range of wavenumbers covering almost an order of magnitude, the decay is purely exponential, which is argued to be a consequence of a suppression of nonlinearity due to the presence of strong cross helicity. Title: Magnetic helicity and fluxes in an inhomogeneous α2 dynamo Authors: Brandenburg, A. Bibcode: 2018AN....339..631B Altcode: Much work on turbulent three-dimensional dynamos has been done using triply periodic domains, in which there are no magnetic helicity fluxes. Here, we present simulations where the turbulent intensity is still nearly homogeneous, but now there is a perfect conductor boundary condition on one end and a vertical field or pseudovacuum conditions on the other. This leads to migratory dynamo waves. Good agreement with a corresponding analytically solvable α2 dynamo is found. Magnetic helicity fluxes are studied in both types of models. It is found that at moderate magnetic Reynolds numbers, most of the magnetic helicity losses occur on large scales. Whether this changes at even larger magnetic Reynolds numbers, as required for alleviating the catastrophic dynamo quenching problem, remains stillunclear. Title: Compressibility in turbulent magnetohydrodynamics and passive scalar transport: mean-field theory Authors: Rogachevskii, I.; Kleeorin, N.; Brandenburg, A. Bibcode: 2018JPlPh..84e7302R Altcode: 2018arXiv180101804R We develop a mean-field theory of compressibility effects in turbulent magnetohydrodynamics and passive scalar transport using the quasi-linear approximation and the spectral τ-approach. We find that compressibility decreases the α effect and the turbulent magnetic diffusivity both at small and large magnetic Reynolds numbers, Rm. Similarly, compressibility decreases the turbulent diffusivity for passive scalars both at small and large Péclet numbers, Pe. On the other hand, compressibility does not affect the effective pumping velocity of the magnetic field for large Rm, but it decreases it for small Rm. Density stratification causes turbulent pumping of passive scalars, but it is found to become weaker with increasing compressibility. No such pumping effect exists for magnetic fields. However, compressibility results in a new passive scalar pumping effect from regions of low to high turbulent intensity both for small and large Péclet numbers. It can be interpreted as compressible turbophoresis of non-inertial particles and gaseous admixtures, while the classical turbophoresis effect exists only for inertial particles and causes them to be pumped to regions with lower turbulent intensity. Title: Varying the forcing scale in low Prandtl number dynamos Authors: Brandenburg, A.; Haugen, N. E. L.; Li, Xiang-Yu; Subramanian, K. Bibcode: 2018MNRAS.479.2827B Altcode: 2018arXiv180501249B; 2018MNRAS.tmp.1491B Small-scale dynamos are expected to operate in all astrophysical fluids that are turbulent and electrically conducting, for example the interstellar medium, stellar interiors, and accretion discs, where they may also be affected by or competing with large-scale dynamos. However, the possibility of small-scale dynamos being excited at small and intermediate ratios of viscosity to magnetic diffusivity (the magnetic Prandtl number) has been debated, and the possibility of them depending on the large-scale forcing wavenumber has been raised. Here, we show, using four values of the forcing wavenumber, that the small-scale dynamo does not depend on the scale separation between the size of the simulation domain and the integral scale of the turbulence, i.e. the forcing scale. Moreover, the spectral bottleneck in turbulence, which has been implied as being responsible for raising the excitation conditions of small-scale dynamos, is found to be invariant under changing the forcing wavenumber. However, when forcing at the lowest few wavenumbers, the effective forcing wavenumber that enters in the definition of the magnetic Reynolds number is found to be about twice the minimum wavenumber of the domain. Our work is relevant to future studies of small-scale dynamos, of which several applications are being discussed. Title: Statistical properties of scale-invariant helical magnetic fields and applications to cosmology Authors: Brandenburg, Axel; Durrer, Ruth; Kahniashvili, Tina; Mandal, Sayan; Yin, Weichen Winston Bibcode: 2018JCAP...08..034B Altcode: 2018arXiv180401177B We investigate the statistical properties of isotropic, stochastic, Gaussian distributed, helical magnetic fields characterized by different shapes of the energy spectra at large length scales and study the associated realizability condition. We discuss smoothed magnetic fields that are commonly used when the primordial magnetic field is constrained by observational data. We are particularly interested in scale-invariant magnetic fields that can be generated during the inflationary stage by quantum fluctuations. We determine the correlation length of such magnetic fields and relate it to the infrared cutoff of perturbations produced during inflation. We show that this scale determines the observational signatures of the inflationary magnetic fields on the cosmic microwave background. At smaller scales, the scale-invariant spectrum changes with time. It becomes a steeper weak-turbulence spectrum at progressively larger scales. We show numerically that the critical length scale where this happens is the turbulent-diffusive scale, which increases with the square root of time. Title: Solar Kinetic Energy and Cross Helicity Spectra Authors: Zhang, Hongqi; Brandenburg, Axel Bibcode: 2018ApJ...862L..17Z Altcode: 2018arXiv180410321Z We develop a formalism that treats the calculation of solar kinetic energy and cross helicity spectra in an equal manner to that of magnetic energy and helicity spectra. The magnetic helicity spectrum is shown to be equal to the vertical part of the current helicity spectrum divided by the square of the wavenumber. For the cross helicity, we apply the recently developed two-scale approach globally over an entire active region to account for the sign change between the two polarities. Using vector magnetograms and Dopplergrams of NOAA 11158 and 12266, we show that kinetic and magnetic energy spectra have similar slopes at intermediate wavenumbers, where the contribution from the granulation velocity has been removed. At wavenumbers around 0.3 {Mm}}-1, the magnetic helicity is found to be close to its maximal value. The cross helicity spectra are found to be within about 10% of the maximum possible value. Using the two-scale method for NOAA 12266, the global cross helicity spectrum is found to be particularly steep, similarly to what has previously been found in theoretical models of spot generation. In the quiet Sun, by comparison, the cross helicity spectrum is found to be small. Title: Chiral fermion asymmetry in high-energy plasma simulations Authors: Schober, Jennifer; Brandenburg, Axel; Rogachevskii, Igor Bibcode: 2018arXiv180806624S Altcode: The chiral magnetic effect (CME) is a quantum relativistic effect that describes the appearance of an additional electric current along a magnetic field. It is caused by an asymmetry between the number densities of left- and right-handed fermions, which can be maintained at high energies when the chirality flipping rate can be neglected, for example in the early Universe. The inclusion of the CME in the Maxwell equations leads to a modified set of MHD equations. We discuss how the CME is implemented in the PENCIL CODE. The CME plays a key role in the evolution of magnetic fields since it results in a dynamo effect associated with an additional term in the induction equation. This term is formally similar to the $\alpha$ effect in classical mean-field MHD. However, the chiral dynamo can operate without turbulence and is associated with small spatial scales that can be, in the case of the early Universe, orders of magnitude below the Hubble radius. A chiral $\alpha_\mu$ effect has also been identified in mean-field theory. It occurs in the presence of turbulence but is not related to kinetic helicity. Depending on the plasma parameters, chiral dynamo instabilities can amplify magnetic fields over many orders of magnitude. These instabilities can affect the propagation of MHD waves, which is demonstrated by our DNS. We also study the coupling between the evolution of the chiral chemical potential and the ordinary chemical potential, which is proportional to the sum of the number densities of left- and right-handed fermions. An important consequence of this coupling is the emergence of chiral magnetic waves (CMWs). We confirm numerically that linear CMWs and MHD waves are not interacting. Our simulations suggest that the chemical potential has only a minor effect on the non-linear evolution of the chiral dynamo. Title: Advances in mean-field dynamo theory and applications to astrophysical turbulence Authors: Brandenburg, Axel Bibcode: 2018JPlPh..84d7304B Altcode: 2018arXiv180105384B Recent advances in mean-field theory are reviewed and applications to the Sun, late-type stars, accretion disks, galaxies and the early Universe are discussed. We focus particularly on aspects of spatio-temporal non-locality, which provided some of the main new qualitative and quantitative insights that emerged from applying the test-field method to magnetic fields of different length and time scales. We also review the status of nonlinear quenching and the relation to magnetic helicity, which is an important observational diagnostic of modern solar dynamo theory. Both solar and some stellar dynamos seem to operate in an intermediate regime that has not yet been possible to model successfully. This regime is bracketed by antisolar-like differential rotation on one end and stellar activity cycles belonging to the superactive stars on the other. The difficulty in modelling this regime may be related to shortcomings in simulating solar/stellar convection. On galactic and extragalactic length scales, the observational constraints on dynamo theory are still less stringent and more uncertain, but recent advances both in theory and observations suggest that more conclusive comparisons may soon be possible also here. The possibility of inversely cascading magnetic helicity in the early Universe is particularly exciting in explaining the recently observed lower limits of magnetic fields on cosmological length scales. Such magnetic fields may be helical with the same sign of magnetic helicity throughout the entire Universe. This would be a manifestation of parity breaking. Title: $f$-mode strengthening from a localized bipolar subsurface magnetic field Authors: Singh, Nishant K.; Raichur, Harsha; Käpylä, Maarit J.; Rheinhardt, Matthias; Brandenburg, Axel; Käpylä, Petri J. Bibcode: 2018arXiv180808904S Altcode: Recent numerical work in helioseismology has shown that a periodically varying subsurface magnetic field leads to a fanning of the $f$-mode, which emerges from the density jump at the surface. In an attempt to model a more realistic situation, we now modulate this periodic variation with an envelope, giving thus more emphasis on localized bipolar magnetic structures in the middle of the domain. Some notable findings are: (i) compared to the purely hydrodynamic case, the strength of the $f$-mode is significantly larger at high horizontal wavenumbers $k$, but the fanning is weaker for the localized subsurface magnetic field concentrations investigated here than the periodic ones studied earlier; (ii) when the strength of the magnetic field is enhanced at a fixed depth below the surface, the fanning of the $f$-mode in the $k\omega$ diagram increases proportionally in such a way that the normalized $f$-mode strengths remain nearly the same in different such cases; (iii) the unstable Bloch modes reported previously in case of harmonically varying magnetic fields are now completely absent when more realistic localized magnetic field concentrations are imposed beneath the surface, thus suggesting that the Bloch modes are unlikely to be supported during most phases of the solar cycle; (iv) the $f$-mode strength appears to depend also on the depth of magnetic field concentrations such that it shows a relative decrement when the maximum of the magnetic field is moved to a deeper layer. We argue that detections of $f$-mode perturbations such as those being explored here could be effective tracers of solar magnetic fields below the photosphere before these are directly detectable as visible manifestations in terms of active regions or sunspots. Title: Transition from axi- to nonaxisymmetric dynamo modes in spherical convection models of solar-like stars Authors: Viviani, M.; Warnecke, J.; Käpylä, M. J.; Käpylä, P. J.; Olspert, N.; Cole-Kodikara, E. M.; Lehtinen, J. J.; Brandenburg, A. Bibcode: 2018A&A...616A.160V Altcode: 2017arXiv171010222V Context. Both dynamo theory and observations of stellar large-scale magnetic fields suggest a change from nearly axisymmetric configurations at solar rotation rates to nonaxisymmetric configurations for rapid rotation.
Aims: We seek to understand this transition using numerical simulations.
Methods: We use three-dimensional simulations of turbulent magnetohydrodynamic convection in spherical shell wedges and considered rotation rates between 1 and 31 times the solar value.
Results: We find a transition from axi- to nonaxisymmetric solutions at around 1.8 times the solar rotation rate. This transition coincides with a change in the rotation profile from antisolar- to solar-like differential rotation with a faster equator and slow poles. In the solar-like rotation regime, the field configuration consists of an axisymmetric oscillatory field accompanied by an m = 1 azimuthal mode (two active longitudes), which also shows temporal variability. At slow (rapid) rotation, the axisymmetric (nonaxisymmetric) mode dominates. The axisymmetric mode produces latitudinal dynamo waves with polarity reversals, while the nonaxisymmetric mode often exhibits a slow drift in the rotating reference frame and the strength of the active longitudes changes cyclically over time between the different hemispheres. In the majority of cases we find retrograde waves, while prograde waves are more often found from observations. Most of the obtained dynamo solutions exhibit cyclic variability either caused by latitudinal or azimuthal dynamo waves. In an activity-period diagram, the cycle lengths normalized by the rotation period form two different populations as a function of rotation rate or magnetic activity level. The slowly rotating axisymmetric population lies close to what in observations is called the inactive branch, where the stars are believed to have solar-like differential rotation, while the rapidly rotating models are close to the superactive branch with a declining cycle to rotation frequency ratio and an increasing rotation rate.
Conclusions: We can successfully reproduce the transition from axi- to nonaxisymmetric dynamo solutions for high rotation rates, but high-resolution simulations are required to limit the effect of rotational quenching of convection at rotation rates above 20 times the solar value. Title: Bihelical Spectrum of Solar Magnetic Helicity and Its Evolution Authors: Singh, Nishant K.; Käpylä, Maarit J.; Brandenburg, Axel; Käpylä, Petri J.; Lagg, Andreas; Virtanen, Ilpo Bibcode: 2018ApJ...863..182S Altcode: 2018arXiv180404994S Using a recently developed two-scale formalism to determine the magnetic helicity spectrum, we analyze synoptic vector magnetograms built with data from the Vector Spectromagnetograph instrument on the Synoptic Optical Long-term Investigations of the Sun telescope during 2010 January-2016 July. In contrast to an earlier study using only three Carrington rotations (CRs), our analysis includes 74 synoptic CR maps. We recover here bihelical spectra at different phases of solar cycle 24, where the net magnetic helicity in the majority of the data is consistent with a large-scale dynamo with helical turbulence operating in the Sun. More than 20% of the analyzed maps, however, show violations of the expected sign rule. Title: Large-scale dynamos in rapidly rotating plane layer convection Authors: Bushby, P. J.; Käpylä, P. J.; Masada, Y.; Brandenburg, A.; Favier, B.; Guervilly, C.; Käpylä, M. J. Bibcode: 2018A&A...612A..97B Altcode: 2017arXiv171003174B Context. Convectively driven flows play a crucial role in the dynamo processes that are responsible for producing magnetic activity in stars and planets. It is still not fully understood why many astrophysical magnetic fields have a significant large-scale component.
Aims: Our aim is to investigate the dynamo properties of compressible convection in a rapidly rotating Cartesian domain, focusing upon a parameter regime in which the underlying hydrodynamic flow is known to be unstable to a large-scale vortex instability.
Methods: The governing equations of three-dimensional non-linear magnetohydrodynamics (MHD) are solved numerically. Different numerical schemes are compared and we propose a possible benchmark case for other similar codes.
Results: In keeping with previous related studies, we find that convection in this parameter regime can drive a large-scale dynamo. The components of the mean horizontal magnetic field oscillate, leading to a continuous overall rotation of the mean field. Whilst the large-scale vortex instability dominates the early evolution of the system, the large-scale vortex is suppressed by the magnetic field and makes a negligible contribution to the mean electromotive force that is responsible for driving the large-scale dynamo. The cycle period of the dynamo is comparable to the ohmic decay time, with longer cycles for dynamos in convective systems that are closer to onset. In these particular simulations, large-scale dynamo action is found only when vertical magnetic field boundary conditions are adopted at the upper and lower boundaries. Strongly modulated large-scale dynamos are found at higher Rayleigh numbers, with periods of reduced activity (grand minima-like events) occurring during transient phases in which the large-scale vortex temporarily re-establishes itself, before being suppressed again by the magnetic field. Title: Laminar and Turbulent Dynamos in Chiral Magnetohydrodynamics. II. Simulations Authors: Schober, Jennifer; Rogachevskii, Igor; Brandenburg, Axel; Boyarsky, Alexey; Fröhlich, Jürg; Ruchayskiy, Oleg; Kleeorin, Nathan Bibcode: 2018ApJ...858..124S Altcode: 2017arXiv171109733S Using direct numerical simulations (DNS), we study laminar and turbulent dynamos in chiral magnetohydrodynamics with an extended set of equations that accounts for an additional contribution to the electric current due to the chiral magnetic effect (CME). This quantum phenomenon originates from an asymmetry between left- and right-handed relativistic fermions in the presence of a magnetic field and gives rise to a chiral dynamo. We show that the magnetic field evolution proceeds in three stages: (1) a small-scale chiral dynamo instability, (2) production of chiral magnetically driven turbulence and excitation of a large-scale dynamo instability due to a new chiral effect (α μ effect), and (3) saturation of magnetic helicity and magnetic field growth controlled by a conservation law for the total chirality. The α μ effect becomes dominant at large fluid and magnetic Reynolds numbers and is not related to kinetic helicity. The growth rate of the large-scale magnetic field and its characteristic scale measured in the numerical simulations agree well with theoretical predictions based on mean-field theory. The previously discussed two-stage chiral magnetic scenario did not include stage (2), during which the characteristic scale of magnetic field variations can increase by many orders of magnitude. Based on the findings from numerical simulations, the relevance of the CME and the chiral effects revealed in the relativistic plasma of the early universe and of proto-neutron stars are discussed. Title: Enhanced Stellar Activity for Slow Antisolar Differential Rotation? Authors: Brandenburg, Axel; Giampapa, Mark S. Bibcode: 2018ApJ...855L..22B Altcode: 2018arXiv180208689B High-precision photometry of solar-like members of the open cluster M67 with Kepler/K2 data has recently revealed enhanced activity for stars with a large Rossby number, which is the ratio of rotation period to the convective turnover time. Contrary to the well established behavior for shorter rotation periods and smaller Rossby numbers, the chromospheric activity of the more slowly rotating stars of M67 was found to increase with increasing Rossby number. Such behavior has never been reported before, although it was theoretically predicted to emerge as a consequence of antisolar differential rotation (DR) for stars with Rossby numbers larger than that of the Sun, because in those models the absolute value of the DR was found to exceed that for solar-like DR. Using gyrochronological relations and an approximate age of 4 Gyr for the members of M67, we compare with computed rotation rates using just the B - V color. The resulting rotation-activity relation is found to be compatible with that obtained by employing the measured rotation rate. This provides additional support for the unconventional enhancement of activity at comparatively low rotation rates and the possible presence of antisolar differential rotation. Title: Small-scale dynamos in simulations of stratified turbulent convection Authors: Käpylä, P. J.; Käpylä, M. J.; Brandenburg, A. Bibcode: 2018AN....339..127K Altcode: 2018arXiv180209607K Small-scale dynamo action is often held responsible for the generation of quiet Sun magnetic fields. We aim to determine the excitation conditions and saturation level of small-scale dynamos in nonrotating turbulent convection at low magnetic Prandtl numbers. We use high-resolution direct numerical simulations of weakly stratified turbulent convection. We find that the critical magnetic Reynolds number for dynamo excitation increases as the magnetic Prandtl number is decreased, which might suggest that small-scale dynamo action is not automatically evident in bodies with small magnetic Prandtl numbers, such as the Sun. As a function of the magnetic Reynolds number (Rm), the growth rate of the dynamo is consistent with an Rm1/2 scaling. No evidence for a logarithmic increase of the growth rate with Rm is found. Title: Strong nonlocality variations in a spherical mean‑field dynamo Authors: Brandenburg, Axel; Chatterjee, Piyali Bibcode: 2018AN....339..118B Altcode: 2018arXiv180204231B To explain the large-scale magnetic field of the Sun and other bodies, mean-field dynamo theory is commonly applied where one solves the averaged equations for the mean magnetic field. However, the standard approach breaks down when the scale of the turbulent eddies becomes comparable to the scale of the variations of the mean magnetic field. Models showing sharp magnetic field structures have therefore been regarded as unreliable. Our aim is to look for new effects that occur when we relax the restrictions of the standard approach, which becomes particularly important at the bottom of the convection zone where the size of the turbulent eddies is comparable to the depth of the convection zone itself. We approximate the underlying integro-differential equation by a partial differential equation corresponding to a reaction-diffusion type equation for the mean electromotive force, making an approach that is nonlocal in space and time feasible under conditions where spherical geometry and nonlinearity are included. In agreement with earlier findings, spatio-temporal nonlocality lowers the excitation conditions of the dynamo. Sharp structures are now found to be absent. However, in the surface layers the field remains similar to before. Title: Turbulent transport coefficients in spherical wedge dynamo simulations of solar-like stars Authors: Warnecke, J.; Rheinhardt, M.; Tuomisto, S.; Käpylä, P. J.; Käpylä, M. J.; Brandenburg, A. Bibcode: 2018A&A...609A..51W Altcode: 2016arXiv160103730W
Aims: We investigate dynamo action in global compressible solar-like convective dynamos in the framework of mean-field theory.
Methods: We simulate a solar-type star in a wedge-shaped spherical shell, where the interplay between convection and rotation self-consistently drives a large-scale dynamo. To analyze the dynamo mechanism we apply the test-field method for azimuthally (φ) averaged fields to determine the 27 turbulent transport coefficients of the electromotive force, of which six are related to the α tensor. This method has previously been used either in simulations in Cartesian coordinates or in the geodynamo context and is applied here for the first time to fully compressible simulations of solar-like dynamos.
Results: We find that the φφ-component of the α tensor does not follow the profile expected from that of kinetic helicity. The turbulent pumping velocities significantly alter the effective mean flows acting on the magnetic field and therefore challenge the flux transport dynamo concept. All coefficients are significantly affected by dynamically important magnetic fields. Quenching as well as enhancement are being observed. This leads to a modulation of the coefficients with the activity cycle. The temporal variations are found to be comparable to the time-averaged values and seem to be responsible for a nonlinear feedback on the magnetic field generation. Furthermore, we quantify the validity of the Parker-Yoshimura rule for the equatorward propagation of the mean magnetic field in the present case. Title: The Global Solar Dynamo Authors: Cameron, R. H.; Dikpati, M.; Brandenburg, A. Bibcode: 2018smf..book..367C Altcode: No abstract at ADS Title: Spontaneous flux concentrations from the negative effective magnetic pressure instability beneath a radiative stellar surface Authors: Perri, B.; Brandenburg, A. Bibcode: 2018A&A...609A..99P Altcode: 2017arXiv170103018P Context. The formation of sunspots requires the concentration of magnetic flux near the surface. The negative effective magnetic pressure instability (NEMPI) might be a possible mechanism for accomplishing this, but it has mainly been studied in simple systems using an isothermal equation of state without a natural free surface.
Aims: We study NEMPI in a stratified Cartesian mean-field model where turbulence effects are parameterized. We use an ideal equation of state and include radiation transport, which establishes selfconsistently a free surface.
Methods: We use a Kramers-type opacity with adjustable exponents chosen such that the deeper layers are approximately isentropic. No convection is therefore possible in this model, allowing us to study NEMPI with radiation in isolation. We restrict ourselves to two-dimensional models. We use artificially enhanced mean-field coefficients to allow NEMPI to develop, thereby making it possible to study the reason why it is much harder to excite in the presence of radiation.
Results: NEMPI yields moderately strong magnetic flux concentrations a certain distance beneath the surface where the optical depth is unity. The instability is oscillatory and in the form of upward traveling waves. This seems to be a new effect that has not been found in earlier models without radiative transport. The horizontal wavelength is about ten times smaller than what has previously been found in more idealized isothermal models.
Conclusions: In our models, NEMPI saturates at field strengths too low to explain sunspots. Furthermore, the structures appear too narrow and too far beneath the surface to cause significant brightness variations at the radiative surface. We speculate that the failure to reproduce effects resembling sunspots may be related to the neglect of convection. Title: Evolution of hydromagnetic turbulence from the electroweak phase transition Authors: Brandenburg, Axel; Kahniashvili, Tina; Mandal, Sayan; Pol, Alberto Roper; Tevzadze, Alexander G.; Vachaspati, Tanmay Bibcode: 2017PhRvD..96l3528B Altcode: 2017arXiv171103804B We present new simulations of decaying hydromagnetic turbulence for a relativistic equation of state relevant to the early Universe. We compare helical and nonhelical cases either with kinetically or magnetically dominated initial fields. Both kinetic and magnetic initial helicities lead to maximally helical magnetic fields after some time, but with different temporal decay laws. Both are relevant to the early Universe, although no mechanisms have yet been identified that produce magnetic helicity with strengths comparable to the big bang nucleosynthesis limit at scales comparable to the Hubble horizon at the electroweak phase transition. Nonhelical magnetically dominated fields could still produce picoGauss magnetic fields under most optimistic conditions. Only helical magnetic fields can potentially have nanoGauss strengths at scales up to 30 kpc today. Title: Scale-invariant helical magnetic field evolution and the duration of inflation Authors: Kahniashvili, Tina; Brandenburg, Axel; Durrer, Ruth; Tevzadze, Alexander G.; Yin, Winston Bibcode: 2017JCAP...12..002K Altcode: 2016arXiv161003139K We consider a scale-invariant helical magnetic field generated during inflation. We show that, if the mean magnetic helicity density of such a field is measured, it can be used to determine a lower bound on the duration of inflation. Even if we just have upper bounds on the helicity, these can be used to derive constraints on the minimal duration if one assumes that the magnetic field generated during inflation is helical. Using three-dimensional simulations, we show that an initially scale-invariant field develops, which is similar both with and without magnetic helicity. In the fully helical case, however, the magnetic field appears to have a more pronounced folded structure. Title: Enhancement of Small-scale Turbulent Dynamo by Large-scale Shear Authors: Singh, Nishant K.; Rogachevskii, Igor; Brandenburg, Axel Bibcode: 2017ApJ...850L...8S Altcode: 2016arXiv161007215S Small-scale dynamos (SSDs) are ubiquitous in a broad range of turbulent flows with large-scale shear, ranging from solar and galactic magnetism to accretion disks, cosmology, and structure formation. Using high-resolution direct numerical simulations, we show that in non-helically forced turbulence with zero mean magnetic field, large-scale shear supports SSD action, I.e., the dynamo growth rate increases with shear and shear enhances or even produces turbulence, which, in turn, further increases the growth rate. When the production rates of turbulent kinetic energy due to shear and forcing are comparable, we find scalings for the growth rate γ of the SSD and the turbulent rms velocity {u}{rms} with shear rate S that are independent of the magnetic Prandtl number: γ \propto | S| and {u}{rms}\propto | S{| }2/3. For large fluid and magnetic Reynolds numbers, γ, normalized by its shear-free value, depends only on shear. Having compensated for shear-induced effects on turbulent velocity, we find that the normalized growth rate of the SSD exhibits the scaling, \widetilde{γ }\propto | S{| }2/3, arising solely from the induction equation for a given velocity field. Title: A new look at sunspot formation using theory and observations Authors: Losada, I. R.; Warnecke, J.; Glogowski, K.; Roth, M.; Brandenburg, A.; Kleeorin, N.; Rogachevskii, I. Bibcode: 2017IAUS..327...46L Altcode: 2017arXiv170404062L Sunspots are of basic interest in the study of the Sun. Their relevance ranges from them being an activity indicator of magnetic fields to being the place where coronal mass ejections and flares erupt. They are therefore also an important ingredient of space weather. Their formation, however, is still an unresolved problem in solar physics. Observations utilize just 2D surface information near the spot, but it is debatable how to infer deep structures and properties from local helioseismology. For a long time, it was believed that flux tubes rising from the bottom of the convection zone are the origin of the bipolar sunspot structure seen on the solar surface. However, this theory has been challenged, in particular recently by new surface observation, helioseismic inversions, and numerical models of convective dynamos. In this article we discuss another theoretical approach to the formation of sunspots: the negative effective magnetic pressure instability. This is a large-scale instability, in which the total (kinetic plus magnetic) turbulent pressure can be suppressed in the presence of a weak large-scale magnetic field, leading to a converging downflow, which eventually concentrates the magnetic field within it. Numerical simulations of forced stratified turbulence have been able to produce strong super-equipartition flux concentrations, similar to sunspots at the solar surface. In this framework, sunspots would only form close to the surface due to the instability constraints on stratification and rotation. Additionally, we present some ideas from local helioseismology, where we plan to use the Hankel analysis to study the pre-emergence phase of a sunspot and to constrain its deep structure and formation mechanism. Title: The Global Solar Dynamo Authors: Cameron, R. H.; Dikpati, M.; Brandenburg, A. Bibcode: 2017SSRv..210..367C Altcode: 2016arXiv160201754C; 2016SSRv..tmp....5C A brief summary of the various observations and constraints that underlie solar dynamo research are presented. The arguments that indicate that the solar dynamo is an alpha-omega dynamo of the Babcock-Leighton type are then shortly reviewed. The main open questions that remain are concerned with the subsurface dynamics, including why sunspots emerge at preferred latitudes as seen in the familiar butterfly wings, why the cycle is about 11 years long, and why the sunspot groups emerge tilted with respect to the equator (Joy's law). Next, we turn to magnetic helicity, whose conservation property has been identified with the decline of large-scale magnetic fields found in direct numerical simulations at large magnetic Reynolds numbers. However, magnetic helicity fluxes through the solar surface can alleviate this problem and connect theory with observations, as will be discussed. Title: Laminar and Turbulent Dynamos in Chiral Magnetohydrodynamics. I. Theory Authors: Rogachevskii, Igor; Ruchayskiy, Oleg; Boyarsky, Alexey; Fröhlich, Jürg; Kleeorin, Nathan; Brandenburg, Axel; Schober, Jennifer Bibcode: 2017ApJ...846..153R Altcode: 2017arXiv170500378R The magnetohydrodynamic (MHD) description of plasmas with relativistic particles necessarily includes an additional new field, the chiral chemical potential associated with the axial charge (I.e., the number difference between right- and left-handed relativistic fermions). This chiral chemical potential gives rise to a contribution to the electric current density of the plasma (chiral magnetic effect). We present a self-consistent treatment of the chiral MHD equations, which include the back-reaction of the magnetic field on a chiral chemical potential and its interaction with the plasma velocity field. A number of novel phenomena are exhibited. First, we show that the chiral magnetic effect decreases the frequency of the Alfvén wave for incompressible flows, increases the frequencies of the Alfvén wave and of the fast magnetosonic wave for compressible flows, and decreases the frequency of the slow magnetosonic wave. Second, we show that, in addition to the well-known laminar chiral dynamo effect, which is not related to fluid motions, there is a dynamo caused by the joint action of velocity shear and chiral magnetic effect. In the presence of turbulence with vanishing mean kinetic helicity, the derived mean-field chiral MHD equations describe turbulent large-scale dynamos caused by the chiral alpha effect, which is dominant for large fluid and magnetic Reynolds numbers. The chiral alpha effect is due to an interaction of the chiral magnetic effect and fluctuations of the small-scale current produced by tangling magnetic fluctuations (which are generated by tangling of the large-scale magnetic field by sheared velocity fluctuations). These dynamo effects may have interesting consequences in the dynamics of the early universe, neutron stars, and the quark-gluon plasma. Title: Extended Subadiabatic Layer in Simulations of Overshooting Convection Authors: Käpylä, Petri J.; Rheinhardt, Matthias; Brandenburg, Axel; Arlt, Rainer; Käpylä, Maarit J.; Lagg, Andreas; Olspert, Nigul; Warnecke, Jörn Bibcode: 2017ApJ...845L..23K Altcode: 2017arXiv170306845K We present numerical simulations of hydrodynamic overshooting convection in local Cartesian domains. We find that a substantial fraction of the lower part of the convection zone (CZ) is stably stratified according to the Schwarzschild criterion while the enthalpy flux is outward directed. This occurs when the heat conduction profile at the bottom of the CZ is smoothly varying, based either on a Kramers-like opacity prescription as a function of temperature and density or a static profile of a similar shape. We show that the subadiabatic layer arises due to nonlocal energy transport by buoyantly driven downflows in the upper parts of the CZ. Analysis of the force balance of the upflows and downflows confirms that convection is driven by cooling at the surface. We find that the commonly used prescription for the convective enthalpy flux being proportional to the negative entropy gradient does not hold in the stably stratified layers where the flux is positive. We demonstrate the existence of a non-gradient contribution to the enthalpy flux, which is estimated to be important throughout the convective layer. A quantitative analysis of downflows indicates a transition from a tree-like structure where smaller downdrafts merge into larger ones in the upper parts to a structure in the deeper parts where a height-independent number of strong downdrafts persist. This change of flow topology occurs when a substantial subadiabatic layer is present in the lower part of the CZ. Title: The Turbulent Chiral Magnetic Cascade in the Early Universe Authors: Brandenburg, Axel; Schober, Jennifer; Rogachevskii, Igor; Kahniashvili, Tina; Boyarsky, Alexey; Fröhlich, Jürg; Ruchayskiy, Oleg; Kleeorin, Nathan Bibcode: 2017ApJ...845L..21B Altcode: 2017arXiv170703385B The presence of asymmetry between fermions of opposite handedness in plasmas of relativistic particles can lead to exponential growth of a helical magnetic field via a small-scale chiral dynamo instability known as the chiral magnetic effect. Here, we show, using dimensional arguments and numerical simulations, that this process produces through the Lorentz force chiral magnetically driven turbulence. A {k}-2 magnetic energy spectrum emerges via inverse transfer over a certain range of wavenumbers k. The total chirality (magnetic helicity plus normalized chiral chemical potential) is conserved in this system. Therefore, as the helical magnetic field grows, most of the total chirality gets transferred into magnetic helicity until the chiral magnetic effect terminates. Quantitative results for height, slope, and extent of the spectrum are obtained. Consequences of this effect for cosmic magnetic fields are discussed. Title: Compensating Faraday Depolarization by Magnetic Helicity in the Solar Corona Authors: Brandenburg, Axel; Ashurova, Mohira B.; Jabbari, Sarah Bibcode: 2017ApJ...845L..15B Altcode: 2017arXiv170609540B A turbulent dynamo in spherical geometry with an outer corona is simulated to study the sign of magnetic helicity in the outer parts. In agreement with earlier studies, the sign in the outer corona is found to be opposite to that inside the dynamo. Line-of-sight observations of polarized emission are synthesized to explore the feasibility of using the local reduction of Faraday depolarization to infer the sign of helicity of magnetic fields in the solar corona. This approach was previously identified as an observational diagnostic in the context of galactic magnetic fields. Based on our simulations, we show that this method can be successful in the solar context if sufficient statistics are gathered by using averages over ring segments in the corona separately for the regions north and south of the solar equator. Title: Evolution of Co-existing Long and Short Period Stellar Activity Cycles Authors: Brandenburg, Axel; Mathur, Savita; Metcalfe, Travis S. Bibcode: 2017ApJ...845...79B Altcode: 2017arXiv170409009B The magnetic activity of the Sun becomes stronger and weaker over roughly an 11 year cycle, modulating the radiation and charged particle environment experienced by the Earth as “space weather.” Decades of observations from the Mount Wilson Observatory have revealed that other stars also show regular activity cycles in their Ca II H+K line emission, and identified two different relationships between the length of the cycle and the rotation rate of the star. Recent observations at higher cadence have allowed the discovery of shorter cycles with periods between 1{--}3 {years}. Some of these shorter cycles coexist with longer cycle periods, suggesting that two underlying dynamos can operate simultaneously. We combine these new observations with previous data, and show that the longer and shorter cycle periods agree remarkably well with those expected from an earlier analysis based on the mean activity level and the rotation period. The relative turbulent length scales associated with the two branches of cyclic behavior suggest that a near-surface dynamo may be the dominant mechanism that drives cycles in more active stars, whereas a dynamo operating in deeper layers may dominate in less active stars. However, several examples of equally prominent long and short cycles have been found at all levels of activity of stars younger than 2.3 Gyr. Deviations from the expected cycle periods show no dependence on the depth of the convection zone or on the metallicity. For some stars that exhibit longer cycles, we compute the periods of shorter cycles that might be detected with future high-cadence observations. Title: The contribution of kinetic helicity to turbulent magnetic diffusivity Authors: Brandenburg, A.; Schober, J.; Rogachevskii, I. Bibcode: 2017AN....338..790B Altcode: 2017arXiv170603421B Using numerical simulations of forced turbulence with and without mean kinetic helicity, we show that for magnetic Reynolds numbers larger than unity, that is, beyond the regime of quasilinear theory, the turbulent magnetic diffusivity attains an additional negative contribution that is quadratic in the kinetic helicity. In particular, for large magnetic Reynolds numbers, the turbulent magnetic diffusivity without helicity is about twice the value with helicity. Such a contribution was not previously anticipated, but, as we discuss, it turns out to be important when accurate estimates of the turbulent magnetic diffusivity are needed. Title: Sharp magnetic structures from dynamos with density stratification Authors: Jabbari, Sarah; Brandenburg, Axel; Kleeorin, Nathan; Rogachevskii, Igor Bibcode: 2017MNRAS.467.2753J Altcode: 2017MNRAS.467.1507J; 2017MNRAS.tmp..163J; 2016arXiv160708897J Recent direct numerical simulations (DNS) of large-scale turbulent dynamos in strongly stratified layers have resulted in surprisingly sharp bipolar structures at the surface. Here, we present new DNS of helically and non-helically forced turbulence with and without rotation and compare with corresponding mean-field simulations (MFS) to show that these structures are a generic outcome of a broader class of dynamos in density-stratified layers. The MFS agree qualitatively with the DNS, but the period of oscillations tends to be longer in the DNS. In both DNS and MFS, the sharp structures are produced by converging flows at the surface and might be driven in non-linear stage of evolution by the Lorentz force associated with the large-scale dynamo-driven magnetic field if the dynamo number is at least 2.5 times supercritical. Title: Convection-driven spherical shell dynamos at varying Prandtl numbers Authors: Käpylä, P. J.; Käpylä, M. J.; Olspert, N.; Warnecke, J.; Brandenburg, A. Bibcode: 2017A&A...599A...4K Altcode: 2016arXiv160505885K Context. Stellar convection zones are characterized by vigorous high-Reynolds number turbulence at low Prandtl numbers.
Aims: We study the dynamo and differential rotation regimes at varying levels of viscous, thermal, and magnetic diffusion.
Methods: We perform three-dimensional simulations of stratified fully compressible magnetohydrodynamic convection in rotating spherical wedges at various thermal and magnetic Prandtl numbers (from 0.25 to 2 and from 0.25 to 5, respectively). Differential rotation and large-scale magnetic fields are produced self-consistently.
Results: We find that for high thermal diffusivity, the rotation profiles show a monotonically increasing angular velocity from the bottom of the convection zone to the top and from the poles toward the equator. For sufficiently rapid rotation, a region of negative radial shear develops at mid-latitudes as the thermal diffusivity is decreased, corresponding to an increase of the Prandtl number. This coincides with and results in a change of the dynamo mode from poleward propagating activity belts to equatorward propagating ones. Furthermore, the clearly cyclic solutions disappear at the highest magnetic Reynolds numbers and give way to irregular sign changes or quasi-stationary states. The total (mean and fluctuating) magnetic energy increases as a function of the magnetic Reynolds number in the range studied here (5-151), but the energies of the mean magnetic fields level off at high magnetic Reynolds numbers. The differential rotation is strongly affected by the magnetic fields and almost vanishes at the highest magnetic Reynolds numbers. In some of our most turbulent cases, however, we find that two regimes are possible, where either differential rotation is strong and mean magnetic fields are relatively weak, or vice versa.
Conclusions: Our simulations indicate a strong nonlinear feedback of magnetic fields on differential rotation, leading to qualitative changes in the behaviors of large-scale dynamos at high magnetic Reynolds numbers. Furthermore, we do not find indications of the simulations approaching an asymptotic regime where the results would be independent of diffusion coefficients in the parameter range studied here. Title: Classes of Hydrodynamic and Magnetohydrodynamic Turbulent Decay Authors: Brandenburg, Axel; Kahniashvili, Tina Bibcode: 2017PhRvL.118e5102B Altcode: 2016arXiv160701360B We perform numerical simulations of decaying hydrodynamic and magnetohydrodynamic turbulence. We classify our time-dependent solutions by their evolutionary tracks in parametric plots between instantaneous scaling exponents. We find distinct classes of solutions evolving along specific trajectories toward points on a line of self-similar solutions. These trajectories are determined by the underlying physics governing individual cases, while the infrared slope of the initial conditions plays only a limited role. In the helical case, even for a scale-invariant initial spectrum (inversely proportional to wave number k ), the solution evolves along the same trajectory as for a Batchelor spectrum (proportional to k4). Title: Two-scale Analysis of Solar Magnetic Helicity Authors: Brandenburg, Axel; Petrie, Gordon J. D.; Singh, Nishant K. Bibcode: 2017ApJ...836...21B Altcode: 2016arXiv161005410B We develop a two-scale formalism to determine global magnetic helicity spectra in systems where the local magnetic helicity has opposite signs on both sides of the equator, giving rise to cancellation with conventional methods. We verify this approach using first a synthetic one-dimensional magnetic field and then two-dimensional slices from a three-dimensional α effect-type dynamo-generated magnetic field, with forced turbulence of opposite helicity above and below the midplane of the domain. We then apply this formalism to global solar synoptic vector magnetograms. To improve the statistics, data from three consecutive Carrington rotations (2161-2163) are combined into a single map. We find that the spectral magnetic helicity representative of the northern hemisphere is negative at all wavenumbers and peaks at ≈ 0.06 {{Mm}}-1 (scales around 100 {Mm}). There is no evidence of bihelical magnetic fields that are found in three-dimensional turbulence simulations of helicity-driven α effect-type dynamos. Title: Analytic solution of an oscillatory migratory α2 stellar dynamo Authors: Brandenburg, A. Bibcode: 2017A&A...598A.117B Altcode: 2016arXiv161102671B Context. Analytic solutions of the mean-field induction equation predict a nonoscillatory dynamo for homogeneous helical turbulence or constant α effect in unbounded or periodic domains. Oscillatory dynamos are generally thought impossible for constant α.
Aims: We present an analytic solution for a one-dimensional bounded domain resulting in oscillatory solutions for constant α, but different (Dirichlet and von Neumann or perfect conductor and vacuum) boundary conditions on the two boundaries.
Methods: We solve a second order complex equation and superimpose two independent solutions to obey both boundary conditions.
Results: The solution has time-independent energy density. On one end where the function value vanishes, the second derivative is finite, which would not be correctly reproduced with sine-like expansion functions where a node coincides with an inflection point. The field always migrates away from the perfect conductor boundary toward the vacuum boundary, independently of the sign of α.
Conclusions: The obtained solution may serve as a benchmark for numerical dynamo experiments and as a pedagogical illustration that oscillatory migratory dynamos are possible with constant α. Title: High-wavenumber Solar f-mode Strengthening Prior to Active Region Formation Authors: Singh, Nishant K.; Raichur, Harsha; Brandenburg, Axel Bibcode: 2016ApJ...832..120S Altcode: 2016arXiv160100629S We report a systematic strengthening of the local solar surface or fundamental f-mode one to two days prior to the emergence of an active region (AR) in the same (corotating) location. Except for a possibly related increase in the kurtosis of the magnetic field, no indication can be seen in the magnetograms at that time. Our study is motivated by earlier numerical findings of Singh et al., which showed that, in the presence of a nonuniform magnetic field that is concentrated a few scale heights below the surface, the f-mode fans out in the diagnostic kω diagram at high wavenumbers. Here we explore this possibility using data from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory and show for six isolated ARs, 11130, 11158, 11242, 11105, 11072, and 11768, that at large latitudinal wavenumbers (corresponding to horizontal scales of around 3000 {km}), the f-mode displays strengthening about two days prior to AR formation and thus provides a new precursor for AR formation. Furthermore, we study two ARs, 12051 and 11678, apart from a magnetically quiet patch lying next to AR 12529, to demonstrate the challenges in extracting such a precursor signal when a newly forming AR emerges in a patch that lies in close proximity to one or several already existing ARs, which are expected to pollute neighboring patches. We then discuss plausible procedures for extracting precursor signals from regions with crowded environments. The idea that the f-mode is perturbed days before any visible magnetic activity occurs at the surface can be important in constraining dynamo models aimed at understanding the global magnetic activity of the Sun. Title: Magnetic concentrations in stratified turbulence: the negative effective magnetic pressure instability Authors: Brandenburg, Axel; Rogachevskii, Igor; Kleeorin, Nathan Bibcode: 2016NJPh...18l5011B Altcode: 2016arXiv161003459B In the presence of strong density stratification, hydromagnetic turbulence attains qualitatively new properties: the formation of magnetic flux concentrations. We review here the theoretical foundations of this mechanism in terms of what is now called the negative effective magnetic pressure instability. We also present direct numerical simulations of forced turbulence in strongly stratified layers and discuss the qualitative and quantitative similarities with corresponding mean-field simulations. Finally, the relevance to sunspot formation is discussed. Title: Influence of a coronal envelope as a free boundary to global convective dynamo simulations Authors: Warnecke, J.; Käpylä, P. J.; Käpylä, M. J.; Brandenburg, A. Bibcode: 2016A&A...596A.115W Altcode: 2015arXiv150305251W
Aims: We explore the effects of an outer stably stratified coronal envelope on rotating turbulent convection, differential rotation, and large-scale dynamo action in spherical wedge models of the Sun.
Methods: We solve the compressible magnetohydrodynamic equations in a two-layer model with unstable stratification below the surface, representing the convection zone, and a stably stratified coronal envelope above. The interface represents a free surface. We compare our model to models that have no coronal envelope.
Results: The presence of a coronal envelope is found to modify the Reynolds stress and the Λ effect resulting in a weaker and non-cylindrical differential rotation. This is related to the reduced latitudinal temperature variations that are caused by and dependent on the angular velocity. Some simulations develop a near-surface shear layer that we can relate to a sign change in the meridional Reynolds stress term in the thermal wind balance equation. Furthermore, the presence of a free surface changes the magnetic field evolution since the toroidal field is concentrated closer to the surface. In all simulations, however, the migration direction of the mean magnetic field can be explained by the Parker-Yoshimura rule, which is consistent with earlier findings.
Conclusions: A realistic treatment of the upper boundary in spherical dynamo simulations is crucial for the dynamics of the flow and magnetic field evolution. Title: Stellar Mixing Length Theory with Entropy Rain Authors: Brandenburg, Axel Bibcode: 2016ApJ...832....6B Altcode: 2015arXiv150403189B The effects of a non-gradient flux term originating from the motion of convective elements with entropy perturbations of either sign are investigated and incorporated into a modified version of stellar mixing length theory (MLT). Such a term, first studied by Deardorff in the meteorological context, might represent the effects of cold intense downdrafts caused by the rapid cooling in the granulation layer at the top of the convection zone of late-type stars. These intense downdrafts were first seen in the strongly stratified simulations of Stein & Nordlund in the late 1980s. These downdrafts transport heat nonlocally, a phenomenon referred to as entropy rain. Moreover, the Deardorff term can cause upward enthalpy transport even in a weakly Schwarzschild-stably stratified layer. In that case, no giant cell convection would be excited. This is interesting in view of recent observations, which could be explained if the dominant flow structures were of small scale even at larger depths. To study this possibility, three distinct flow structures are examined: one in which convective structures have similar size and mutual separation at all depths, one in which the separation increases with depth, but their size is still unchanged, and one in which both size and separation increase with depth, which is the standard flow structure. It is concluded that the third possibility with fewer and thicker downdrafts in deeper layers remains the most plausible, but it may be unable to explain the suspected absence of large-scale flows with speeds and scales expected from MLT. Title: Robustness of oscillatory α2 dynamos in spherical wedges Authors: Cole, E.; Brandenburg, A.; Käpylä, P. J.; Käpylä, M. J. Bibcode: 2016A&A...593A.134C Altcode: 2016arXiv160105246C Context. Large-scale dynamo simulations are sometimes confined to spherical wedge geometries by imposing artificial boundary conditions at high latitudes. This may lead to spatio-temporal behaviours that are not representative of those in full spherical shells.
Aims: We study the connection between spherical wedge and full spherical shell geometries using simple mean-field dynamos.
Methods: We solve the equations for one-dimensional time-dependent α2 and α2Ω mean-field dynamos with only latitudinal extent to examine the effects of varying the polar angle θ0 between the latitudinal boundaries and the poles in spherical coordinates.
Results: In the case of constant α and ηt profiles, we find oscillatory solutions only with the commonly used perfect conductor boundary condition in a wedge geometry, while for full spheres all boundary conditions produce stationary solutions, indicating that perfect conductor conditions lead to unphysical solutions in such a wedge setup. To search for configurations in which this problem can be alleviated we choose a profile of the turbulent magnetic diffusivity that decreases toward the poles, corresponding to high conductivity there. Oscillatory solutions are now achieved with models extending to the poles, but the magnetic field is strongly concentrated near the poles and the oscillation period is very long. By changing both the turbulent magnetic diffusivity and α profiles so that both effects are more concentrated toward the equator, we see oscillatory dynamos with equatorward drift, shorter cycles, and magnetic fields distributed over a wider range of latitudes. Those profiles thus remove the sensitive and unphysical dependence on θ0. When introducing radial shear, we again see oscillatory dynamos, and the direction of drift follows the Parker-Yoshimura rule.
Conclusions: A reduced α effect near the poles with a turbulent diffusivity concentrated toward the equator yields oscillatory dynamos with equatorward migration and reproduces best the solutions in spherical wedges. For weak shear, oscillatory solutions are obtained only for perfect conductor field conditions and negative shear. Oscillatory solutions become preferred at sufficiently strong shear. Recent three-dimensional dynamo simulations producing solar-like magnetic activity are expected to lie in this range. Title: Two-scale Analysis of Solar Magnetic Helicity Authors: Brandenburg, Axel; Petrie, Gordon; Singh, Nishant Bibcode: 2016usc..confE.110B Altcode: The solar magnetic helicity has opposite signs not only in the two hemispheres, but also at large and small length scales. The latter can be detected by computing magnetic helicity spectra, but this must be done separately in each hemisphere. Here we utilize a two-scale method from mean-field dynamo theory that allows us to compute magnetic helicity spectra as a function of two different wavenumbers: one corresponding to rapidly varying scale and one corresponding to a slowly varying one. We generalize this method to spherical harmonics and compute in that way global magnetic helicity spectra for that part of the field that shows a global dipolar symmetry. We present results from simple one-dimensional model calculations, three-dimensional dynamo simulations, and the two-dimensional magnetic field from synaptic vector magnetograms. Title: The evolution of primordial magnetic fields since their generation Authors: Kahniashvili, Tina; Brandenburg, Axel; Tevzadze, Alexander G. Bibcode: 2016PhyS...91j4008K Altcode: 2015arXiv150700510K We study the evolution of primordial magnetic fields in an expanding cosmic plasma. For this purpose we present a comprehensive theoretical model to consider the evolution of MHD turbulence that can be used over a wide range of physical conditions, including cosmological and astrophysical applications. We model different types of decaying cosmic MHD turbulence in the expanding Universe and characterize the large-scale magnetic fields in such a medium. Direct numerical simulations of freely decaying MHD turbulence are performed for different magnetogenesis scenarios: magnetic fields generated during cosmic inflation as well as electroweak and QCD phase transitions in the early Universe. Magnetic fields and fluid motions are strongly coupled due to the high Reynolds number in the early Universe. Hence, we abandon the simple adiabatic dilution model to estimate magnetic field amplitudes in the expanding Universe and include turbulent mixing effects on the large-scale magnetic field evolution. Numerical simulations have been carried out for non-helical and helical magnetic field configurations. The numerical results show the possibility of inverse transfer of energy in magnetically dominated non-helical MHD turbulence. On the other hand, decay properties of helical turbulence depend on whether the turbulent magnetic field is in a weakly or a fully helical state. Our results show that primordial magnetic fields can be considered as a seed for the observed large-scale magnetic fields in galaxies and clusters. Bounds on the magnetic field strength are obtained and are consistent with the upper and lower limits set by observations of extragalactic magnetic fields. Title: A unified large/small-scale dynamo in helical turbulence Authors: Bhat, Pallavi; Subramanian, Kandaswamy; Brandenburg, Axel Bibcode: 2016MNRAS.461..240B Altcode: 2015arXiv150802706B We use high resolution direct numerical simulations (DNS) to show that helical turbulence can generate significant large-scale fields even in the presence of strong small-scale dynamo action. During the kinematic stage, the unified large/small-scale dynamo grows fields with a shape-invariant eigenfunction, with most power peaked at small scales or large k, as in Subramanian & Brandenburg. Nevertheless, the large-scale field can be clearly detected as an excess power at small k in the negatively polarized component of the energy spectrum for a forcing with positively polarized waves. Its strength overline{B}, relative to the total rms field Brms, decreases with increasing magnetic Reynolds number, ReM. However, as the Lorentz force becomes important, the field generated by the unified dynamo orders itself by saturating on successively larger scales. The magnetic integral scale for the positively polarized waves, characterizing the small-scale field, increases significantly from the kinematic stage to saturation. This implies that the small-scale field becomes as coherent as possible for a given forcing scale, which averts the ReM-dependent quenching of overline{B}/B_rms. These results are obtained for 10243 DNS with magnetic Prandtl numbers of PrM = 0.1 and 10. For PrM = 0.1, overline{B}/B_rms grows from about 0.04 to about 0.4 at saturation, aided in the final stages by helicity dissipation. For PrM = 10, overline{B}/B_rms grows from much less than 0.01 to values of the order the 0.2. Our results confirm that there is a unified large/small-scale dynamo in helical turbulence. Title: Turbulent reconnection of magnetic bipoles in stratified turbulence Authors: Jabbari, S.; Brandenburg, A.; Mitra, Dhrubaditya; Kleeorin, N.; Rogachevskii, I. Bibcode: 2016MNRAS.459.4046J Altcode: 2016MNRAS.tmp..680J; 2016arXiv160108167J We consider strongly stratified forced turbulence in a plane-parallel layer with helicity and corresponding large-scale dynamo action in the lower part and non-helical turbulence in the upper. The magnetic field is found to develop strongly concentrated bipolar structures near the surface. They form elongated bands with a sharp interface between opposite polarities. Unlike earlier experiments with imposed magnetic field, the inclusion of rotation does not strongly suppress the formation of these structures. We perform a systematic numerical study of this phenomenon by varying magnetic Reynolds number, scale-separation ratio, and Coriolis number. We focus on the formation of a current sheet between bipolar regions where reconnection of oppositely oriented field lines occurs. We determine the reconnection rate by measuring either the inflow velocity in the vicinity of the current sheet or by measuring the electric field in the reconnection region. We demonstrate that for large Lundquist numbers, S > 103, the reconnection rate is nearly independent of S in agreement with results of recent numerical simulations performed by other groups in simpler settings. Title: High-wavenumber solar f-mode strengthening prior to active region formation Authors: Singh, Nishant; Raichur, Harsha; Brandenburg, Axel Bibcode: 2016SPD....47.0711S Altcode: We report a systematic strengthening of the local solar surface mode, i.e. the f-mode, 1-2 days prior to the emergence of an active region (AR) in the same (corotating) location while no indication can yet be seen in the magnetograms. Our study is motivated by earlier numerical findings of Singh et al. (2014) which showed that, in the presence of a nonuniform magnetic field that is concentrated a few scale heights below the surface, the f-mode fans out in the diagnostic kΩ diagram at high wavenumbers. Here we explore this possibility using data from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, and show for four ARs 11130, 11158, 11768, and 12051, that at large latitudinal wavenumbers (corresponding to horizontal scales of around 3000 km), the f-mode displays strengthening about two days prior to AR formation and thus provides a new precursor for AR formation. The idea that the f-mode is perturbed days before any visible magnetic activity occurs on the surface can be important in constraining dynamo models aimed at understanding the global magnetic activity of the Sun. Title: The magnetic helicity spectrum from solar vector magnetograms Authors: Brandenburg, Axel; Zhang, Hongqi; Sokoloff, Dmitry Bibcode: 2016SPD....4720103B Altcode: The gauge-invariant (or relative) magnetic helicity is often measured to characterize the degree of magnetic complexity of active regions. However, magnetic helicity is expected to have different signs on different length scales that can be identified with the large- and small-scale fields used in dynamo theory. To address this, it is important to determine magnetic helicity spectra as functions of wavenumber. These spectra are defined such that the integral over all wavenumbers gives the usual magnetic helicity density in a particular patch of interest. Using vector magnetograms from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory for active region NOAA 11515, which was on the southern hemisphere, we show that the magnetic helicity spectrum has positive sign on scales below 30 Mm, but negative sign on larger scales. This active region was rather complex and its magnetic helicity was within 26% of its theoretical maximum value. This is much more than that of NOAA 11158, which was also rather complex, but only within 5% of its theoretical maximum value. Since the contribution of larger length scales turned out to be important in the case of NOAA 11515, its total magnetic helicity is dominated by the negative values from large length scales, which explains the unusual sign for the southern hemisphere. Measuring magnetic helicity spectra with DKIST may become an important tool to learn about the workings of the underlying dynamo. Title: Bipolar region formation in stratified two-layer turbulence Authors: Warnecke, J.; Losada, I. R.; Brandenburg, A.; Kleeorin, N.; Rogachevskii, I. Bibcode: 2016A&A...589A.125W Altcode: 2015arXiv150203799W
Aims: This work presents an extensive study of the previously discovered formation of bipolar flux concentrations in a two-layer model. We interpret the formation process in terms of negative effective magnetic pressure instability (NEMPI), which is a possible mechanism to explain the origin of sunspots.
Methods: In our simulations, we use a Cartesian domain of isothermal stratified gas that is divided into two layers. In the lower layer, turbulence is forced with transverse nonhelical random waves, whereas in the upper layer no flow is induced. A weak uniform magnetic field is imposed in the entire domain at all times. In most cases, it is horizontal, but a vertical and an inclined field are also considered. In this study we vary the stratification by changing the gravitational acceleration, magnetic Reynolds number, strength of the imposed magnetic field, and size of the domain to investigate their influence on the formation process.
Results: Bipolar magnetic structure formation takes place over a large range of parameters. The magnetic structures become more intense for higher stratification until the density contrast becomes around 100 across the turbulent layer. For the fluid Reynolds numbers considered, magnetic flux concentrations are generated at magnetic Prandtl number between 0.1 and 1. The magnetic field in bipolar regions increases with higher imposed field strength until the field becomes comparable to the equipartition field strength of the turbulence. A larger horizontal extent enables the flux concentrations to become stronger and more coherent. The size of the bipolar structures turns out to be independent of the domain size. A small imposed horizontal field component is necessary to generate bipolar structures. In the case of bipolar region formation, we find an exponential growth of the large-scale magnetic field, which is indicative of a hydromagnetic instability. Additionally, the flux concentrations are correlated with strong large-scale downward and converging flows. These findings imply that NEMPI is responsible for magnetic flux concentrations. Title: The structure and evolution of boundary layers in stratified convection Authors: Anders, Evan H.; Brown, Benjamin; Brandenburg, Axel; Rast, Mark Bibcode: 2016SPD....47.0712A Altcode: Solar convection is highly stratified, and the density in the Sun increases by many orders of magnitude from the photosphere to the base of the convection zone. The photosphere is an important boundary layer, and interactions between the surface convection and deep convection may lie at the root of the solar convection conundrum, where observed large-scale velocities are much lower than predicted by full numerical simulations. Here, we study the structure and time evolution of boundary layers in numerical stratified convection. We study fully compressible convection within plane-parallel layers using the Dedalus pseudospectral framework. Within the context of polytropic stratification, we study flows from low (1e-3) to moderately high (0.1) Mach number, and at moderate to high Rayleigh number to study both laminar and turbulent convective transport. We aim to characterize the thickness and time variation of velocity and thermal (entropy) boundary layers at the top and bottom boundaries of the domain. Title: Multiple dynamo modes as a mechanism for long-term solar activity variations Authors: Käpylä, M. J.; Käpylä, P. J.; Olspert, N.; Brandenburg, A.; Warnecke, J.; Karak, B. B.; Pelt, J. Bibcode: 2016A&A...589A..56K Altcode: 2015arXiv150705417K Context. Solar magnetic activity shows both smooth secular changes, such as the modern Grand Maximum, and quite abrupt drops that are denoted as grand minima, such as the Maunder Minimum. Direct numerical simulations (DNS) of convection-driven dynamos offer one way of examining the mechanisms behind these events.
Aims: In this work, we analyze a solution of a solar-like DNS that was evolved for roughly 80 magnetic cycles of 4.9 years and where epochs of irregular behavior are detected. The emphasis of our analysis is to find physical causes for such behavior.
Methods: The DNS employed is a semi-global (wedge-shaped) magnetoconvection model. For the data analysis tasks we use Ensemble Empirical Mode Decomposition and phase dispersion methods, as they are well suited for analyzing cyclic (non-periodic) signals.
Results: A special property of the DNS is the existence of multiple dynamo modes at different depths and latitudes. The dominant mode is solar-like (equatorward migration at low latitudes and poleward at high latitudes). This mode is accompanied by a higher frequency mode near the surface and at low latitudes, showing poleward migration, and a low-frequency mode at the bottom of the convection zone. The low-frequency mode is almost purely antisymmetric with respect to the equator, while the dominant mode has strongly fluctuating mixed parity. The overall behavior of the dynamo solution is extremely complex, exhibiting variable cycle lengths, epochs of disturbed and even ceased surface activity, and strong short-term hemispherical asymmetries. Surprisingly, the most prominent suppressed surface activity epoch is actually a global magnetic energy maximum; during this epoch the bottom toroidal magnetic field obtains a maximum, demonstrating that the interpretation of grand minima-type events is non-trivial. The hemispherical asymmetries are seen only in the magnetic field, while the velocity field exhibits considerably weaker asymmetry.
Conclusions: We interpret the overall irregular behavior as being due to the interplay of the different dynamo modes showing different equatorial symmetries, especially the smoother part of the irregular variations being related to the variations of the mode strengths, evolving with different and variable cycle lengths. The abrupt low-activity epoch in the dominant dynamo mode near the surface is related to a strong maximum of the bottom toroidal field strength, which causes abrupt disturbances especially in the differential rotation profile via the suppression of the Reynolds stresses. Title: Magnetic flux concentrations from turbulent stratified convection Authors: Käpylä, P. J.; Brandenburg, A.; Kleeorin, N.; Käpylä, M. J.; Rogachevskii, I. Bibcode: 2016A&A...588A.150K Altcode: 2015arXiv151103718K Context. The formation of magnetic flux concentrations within the solar convection zone leading to sunspot formation is unexplained.
Aims: We study the self-organization of initially uniform sub-equipartition magnetic fields by highly stratified turbulent convection.
Methods: We perform simulations of magnetoconvection in Cartesian domains representing the uppermost 8.5-24 Mm of the solar convection zone with the horizontal size of the domain varying between 34 and 96 Mm. The density contrast in the 24 Mm deep models is more than 3 × 103 or eight density scale heights, corresponding to a little over 12 pressure scale heights. We impose either a vertical or a horizontal uniform magnetic field in a convection-driven turbulent flow in set-ups where no small-scale dynamos are present. In the most highly stratified cases we employ the reduced sound speed method to relax the time step constraint arising from the high sound speed in the deep layers. We model radiation via the diffusion approximation and neglect detailed radiative transfer in order to concentrate on purely magnetohydrodynamic effects.
Results: We find that super-equipartition magnetic flux concentrations are formed near the surface in cases with moderate and high density stratification, corresponding to domain depths of 12.5 and 24 Mm. The size of the concentrations increases as the box size increases and the largest structures (20 Mm horizontally near the surface) are obtained in the models that are 24 Mm deep. The field strength in the concentrations is in the range of 3-5 kG, almost independent of the magnitude of the imposed field. The amplitude of the concentrations grows approximately linearly in time. The effective magnetic pressure measured in the simulations is positive near the surface and negative in the bulk of the convection zone. Its derivative with respect to the mean magnetic field, however, is positive in most of the domain, which is unfavourable for the operation of the negative effective magnetic pressure instability (NEMPI). Simulations in which a passive vector field is evolved do not show a noticeable difference from magnetohydrodynamic runs in terms of the growth of the structures. Furthermore, we find that magnetic flux is concentrated in regions of converging flow corresponding to large-scale supergranulation convection pattern.
Conclusions: The linear growth of large-scale flux concentrations implies that their dominant formation process is a tangling of the large-scale field rather than an instability. One plausible mechanism that can explain both the linear growth and the concentration of the flux in the regions of converging flow pattern is flux expulsion. A possible reason for the absence of NEMPI is that the derivative of the effective magnetic pressure with respect to the mean magnetic field has an unfavourable sign. Furthermore, there may not be sufficient scale separation, which is required for NEMPI to work.

Movies associated to Figs. 4 and 5 are available in electronic form at http://www.aanda.org Title: Commission 12: Solar Radiation and Structure Authors: Cauzzi, Gianna; Shchukina, Nataliya; Kosovichev, Alexander; Bianda, Michele; Brandenburg, Axel; Chou, Dean-Yi; Dasso, Sergio; Ding, Ming-De; Jefferies, Stuart; Krivova, Natalie; Kuznetsov, Vladimir D.; Moreno-Insertis, Fernando Bibcode: 2016IAUTA..29..278C Altcode: Commission 12 of the International Astronomical Union encompasses investigations of the internal structure and dynamics of the Sun, the quiet solar atmosphere, solar radiation and its variability, and the nature of relatively stable magnetic structures like sunspots, faculae and the magnetic network. The Commission sees participation of over 300 scientists worldwide. Title: Evolution of Magnetic Helicity and Energy Spectra of Solar Active Regions Authors: Zhang, Hongqi; Brandenburg, Axel; Sokoloff, D. D. Bibcode: 2016ApJ...819..146Z Altcode: 2015arXiv150300846Z We adopt an isotropic representation of the Fourier-transformed two-point correlation tensor of the magnetic field to estimate the magnetic energy and helicity spectra as well as current helicity spectra of two individual active regions (NOAA 11158 and NOAA 11515) and the change of the spectral indices during their development as well as during the solar cycle. The departure of the spectral indices of magnetic energy and current helicity from 5/3 are analyzed, and it is found that it is lower than the spectral index of the magnetic energy spectrum. Furthermore, the fractional magnetic helicity tends to increase when the scale of the energy-carrying magnetic structures increases. The magnetic helicity of NOAA 11515 violates the expected hemispheric sign rule, which is interpreted as an effect of enhanced field strengths at scales larger than 30-60 Mm with opposite signs of helicity. This is consistent with the general cycle dependence, which shows that around the solar maximum the magnetic energy and helicity spectra are steeper, emphasizing the large-scale field. Title: Large-scale flow generation by inhomogeneous helicity Authors: Yokoi, N.; Brandenburg, A. Bibcode: 2016PhRvE..93c3125Y Altcode: 2015arXiv151108983Y The effect of kinetic helicity (velocity-vorticity correlation) on turbulent momentum transport is investigated. The turbulent kinetic helicity (pseudoscalar) enters the Reynolds stress (mirror-symmetric tensor) expression in the form of a helicity gradient as the coupling coefficient for the mean vorticity and/or the angular velocity (axial vector), which suggests the possibility of mean-flow generation in the presence of inhomogeneous helicity. This inhomogeneous helicity effect, which was previously confirmed at the level of a turbulence- or closure-model simulation, is examined with the aid of direct numerical simulations of rotating turbulence with nonuniform helicity sustained by an external forcing. The numerical simulations show that the spatial distribution of the Reynolds stress is in agreement with the helicity-related term coupled with the angular velocity, and that a large-scale flow is generated in the direction of angular velocity. Such a large-scale flow is not induced in the case of homogeneous turbulent helicity. This result confirms the validity of the inhomogeneous helicity effect in large-scale flow generation and suggests that a vortex dynamo is possible even in incompressible turbulence where there is no baroclinicity effect. Title: Hydraulic effects in a radiative atmosphere with ionization Authors: Bhat, P.; Brandenburg, A. Bibcode: 2016A&A...587A..90B Altcode: 2014arXiv1411.6610B Context. In his 1978 paper, Eugene Parker postulated the need for hydraulic downward motion to explain magnetic flux concentrations at the solar surface. A similar process has also recently been seen in simplified (e.g., isothermal) models of flux concentrations from the negative effective magnetic pressure instability (NEMPI).
Aims: We study the effects of partial ionization near the radiative surface on the formation of these magnetic flux concentrations.
Methods: We first obtain one-dimensional (1D) equilibrium solutions using either a Kramers-like opacity or the H- opacity. The resulting atmospheres are then used as initial conditions in two-dimensional (2D) models where flows are driven by an imposed gradient force that resembles a localized negative pressure in the form of a blob. To isolate the effects of partial ionization and radiation, we ignore turbulence and convection.
Results: Because of partial ionization, an unstable stratification always forms near the surface. We show that the extrema in the specific entropy profiles correspond to the extrema in the degree of ionization. In the 2D models without partial ionization, strong flux concentrations form just above the height where the blob is placed. Interestingly, in models with partial ionization, such flux concentrations always form at the surface well above the blob. This is due to the corresponding negative gradient in specific entropy. Owing to the absence of turbulence, the downflows reach transonic speeds.
Conclusions: We demonstrate that, together with density stratification, the imposed source of negative pressure drives the formation of flux concentrations. We find that the inclusion of partial ionization affects the entropy profile dramatically, causing strong flux concentrations to form closer to the surface. We speculate that turbulence effects are needed to limit the strength of flux concentrations and homogenize the specific entropy to a stratification that is close to marginal. Title: A New Twist in Simulating Solar Flares Authors: Brandenburg, Axel Bibcode: 2016PhyOJ...9...26B Altcode: 2016arXiv160301917B Simulations show for the first time how the magnetic fields that produce solar flares can extend out of the Sun by acquiring a twist. Title: Is the Small-scale Magnetic Field Correlated with the Dynamo Cycle? Authors: Karak, Bidya Binay; Brandenburg, Axel Bibcode: 2016ApJ...816...28K Altcode: 2015arXiv150506632K The small-scale magnetic field is ubiquitous at the solar surface—even at high latitudes. From observations we know that this field is uncorrelated (or perhaps even weakly anticorrelated) with the global sunspot cycle. Our aim is to explore the origin, and particularly the cycle dependence, of such a phenomenon using three-dimensional dynamo simulations. We adopt a simple model of a turbulent dynamo in a shearing box driven by helically forced turbulence. Depending on the dynamo parameters, large-scale (global) and small-scale (local) dynamos can be excited independently in this model. Based on simulations in different parameter regimes, we find that, when only the large-scale dynamo is operating in the system, the small-scale magnetic field generated through shredding and tangling of the large-scale magnetic field is positively correlated with the global magnetic cycle. However, when both dynamos are operating, the small-scale field is produced from both the small-scale dynamo and the tangling of the large-scale field. In this situation, when the large-scale field is weaker than the equipartition value of the turbulence, the small-scale field is almost uncorrelated with the large-scale magnetic cycle. On the other hand, when the large-scale field is stronger than the equipartition value, we observe an anticorrelation between the small-scale field and the large-scale magnetic cycle. This anticorrelation can be interpreted as a suppression of the small-scale dynamo. Based on our studies we conclude that the observed small-scale magnetic field in the Sun is generated by the combined mechanisms of a small-scale dynamo and tangling of the large-scale field. Title: Large-Eddy Simulations of Magnetohydrodynamic Turbulence in Heliophysics and Astrophysics Authors: Miesch, Mark; Matthaeus, William; Brandenburg, Axel; Petrosyan, Arakel; Pouquet, Annick; Cambon, Claude; Jenko, Frank; Uzdensky, Dmitri; Stone, James; Tobias, Steve; Toomre, Juri; Velli, Marco Bibcode: 2015SSRv..194...97M Altcode: 2015arXiv150501808M; 2015SSRv..tmp...83M We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and most challenging of these problems is turbulence. Yet, despite these advances, the extreme parameter regimes encountered in space physics and astrophysics (as in atmospheric and oceanic physics) still preclude direct numerical simulation. Numerical models must take a Large Eddy Simulation (LES) approach, explicitly computing only a fraction of the active dynamical scales. The success of such an approach hinges on how well the model can represent the subgrid-scales (SGS) that are not explicitly resolved. In addition to the parameter regime, heliophysical and astrophysical applications must also face an equally daunting challenge: magnetism. The presence of magnetic fields in a turbulent, electrically conducting fluid flow can dramatically alter the coupling between large and small scales, with potentially profound implications for LES/SGS modeling. In this review article, we summarize the state of the art in LES modeling of turbulent magnetohydrodynamic (MHD) flows. After discussing the nature of MHD turbulence and the small-scale processes that give rise to energy dissipation, plasma heating, and magnetic reconnection, we consider how these processes may best be captured within an LES/SGS framework. We then consider several specific applications in heliophysics and astrophysics, assessing triumphs, challenges, and future directions. Title: Magnetohydrodynamics of the Sun Authors: Brandenburg, Axel Bibcode: 2015GApFD.109..615B Altcode: No abstract at ADS Title: Negative Magnetic Eddy Diffusivities from the Test-field Method and Multiscale Stability Theory Authors: Andrievsky, Alexander; Brandenburg, Axel; Noullez, Alain; Zheligovsky, Vladislav Bibcode: 2015ApJ...811..135A Altcode: 2015arXiv150104465A The generation of a large-scale magnetic field in the kinematic regime in the absence of an α-effect is investigated by following two different approaches: the test-field method and the multiscale stability theory relying on the homogenization technique. Our computations of the magnetic eddy diffusivity tensor of the parity-invariant flow IV of G. O. Roberts and the modified Taylor-Green flow confirm the findings of previous studies and also explain some of their apparent contradictions. The two flows have large symmetry groups; this is used to considerably simplify the eddy diffusivity tensor. Finally, a new analytic result is presented: upon expressing the eddy diffusivity tensor in terms of solutions to auxiliary problems for the adjoint operator, we derive relations between the magnetic eddy diffusivity tensors that arise for mutually reverse small-scale flows {\boldsymbol{v}}(x) and -{\boldsymbol{v}}(x). Title: Division II: Commission 12: Solar Radiation and Structure Authors: Kosovichev, Alexander; Cauzzi, Gianna; Martinez Pillet, Valentin; Asplund, Martin; Brandenburg, Axel; Chou, Dean-Yi; Christensen-Dalsgaard, Jorgen; Gan, Weiqun; Kuznetsov, Vladimir D.; Rovira, Marta G.; Shchukina, Nataliya; Venkatakrishnan, P. Bibcode: 2015IAUTB..28..109K Altcode: The President of C12, Alexander Kosovichev, presented the status of the Commission and its working Group(s). Primary activities included organization of international meetings (IAU Symposia, Special Sessions and Joint Discussion); review and support of proposals for IAU sponsored meetings; organization of working groups on the Commission topics to promote the international cooperation; preparation of triennial report on the organizational and science activities of Commission members. Commission 12 broadly encompasses topics of solar research which include studies of the Sun's internal structure, composition, dynamics and magnetism (through helioseismology and other techniques), studies of the quiet photosphere, chromosphere and corona, and also research of the mechanisms of solar radiation, and its variability on various time scales. Some overlap with topics covered by Commission 10 Solar Activity is unavoidable, and many activities are sponsored jointly by these two commissions. The Commission website can be found at http://sun.stanford.edu/IAU-Com12/, with information about related IAU Symposiums and activities, and links to appropriate web sites. Title: Posters: Dust from impacts on exoplanets Authors: Cataldi, G.; Brandeker, A.; Thebault, P.; Singer, K.; Ahmed, E.; Brandenburg, A.; Olofsson, G.; de Vries, B. Bibcode: 2015pthp.confE..49C Altcode: No abstract at ADS Title: Bipolar Magnetic Spots from Dynamos in Stratified Spherical Shell Turbulence Authors: Jabbari, Sarah; Brandenburg, Axel; Kleeorin, Nathan; Mitra, Dhrubaditya; Rogachevskii, Igor Bibcode: 2015ApJ...805..166J Altcode: 2014arXiv1411.4912J Recent work by Mitra et al. (2014) has shown that in strongly stratified forced two-layer turbulence with helicity and corresponding large-scale dynamo action in the lower layer, and nonhelical turbulence in the upper, a magnetic field occurs in the upper layer in the form of sharply bounded bipolar magnetic spots. Here we extend this model to spherical wedge geometry covering the northern hemisphere up to 75° latitude and an azimuthal extent of 180°. The kinetic helicity and therefore also the large-scale magnetic field are strongest at low latitudes. For moderately strong stratification, several bipolar spots form that eventually fill the full longitudinal extent. At early times, the polarity of spots reflects the orientation of the underlying azimuthal field, as expected from Parker’s Ω-shaped flux loops. At late times their tilt changes such that there is a radial field of opposite orientation at different latitudes separated by about 10°. Our model demonstrates the spontaneous formation of spots of sizes much larger than the pressure scale height. Their tendency to produce filling factors close to unity is argued to be reminiscent of highly active stars. We confirm that strong stratification and strong scale separation are essential ingredients behind magnetic spot formation, which appears to be associated with downflows at larger depths. Title: Hysteresis between Distinct Modes of Turbulent Dynamos Authors: Karak, Bidya Binay; Kitchatinov, Leonid L.; Brandenburg, Axel Bibcode: 2015ApJ...803...95K Altcode: 2014arXiv1411.0485K Nonlinear mean-field models of the solar dynamo show long-term variability, which may be relevant to different states of activity inferred from long-term radiocarbon data. This paper is aimed at probing the dynamo hysteresis predicted by the recent mean-field models of Kitchatinov & Olemskoy with direct numerical simulations. We perform three-dimensional (3D) simulations of large-scale dynamos in a shearing box with helically forced turbulence. As an initial condition, we either take a weak random magnetic field or we start from a snapshot of an earlier simulation. Two quasi-stable states are found to coexist in a certain range of parameters close to the onset of the large-scale dynamo. The simulations converge to one of these states depending on the initial conditions. When either the fractional helicity or the magnetic Prandtl number is increased between successive runs above the critical value for onset of the dynamo, the field strength jumps to a finite value. However, when the fractional helicity or the magnetic Prandtl number is then decreased again, the field strength stays at a similar value (strong field branch) even below the original onset. We also observe intermittent decaying phases away from the strong field branch close to the point where large-scale dynamo action is just possible. The dynamo hysteresis seen previously in mean-field models is thus reproduced by 3D simulations. Its possible relation to distinct modes of solar activity such as grand minima is discussed. Title: Magnetically controlled stellar differential rotation near the transition from solar to anti-solar profiles Authors: Karak, B. B.; Käpylä, P. J.; Käpylä, M. J.; Brandenburg, A.; Olspert, N.; Pelt, J. Bibcode: 2015A&A...576A..26K Altcode: 2014arXiv1407.0984K Context. Late-type stars rotate differentially owing to anisotropic turbulence in their outer convection zones. The rotation is called solar-like (SL) when the equator rotates fastest and anti-solar (AS) otherwise. Hydrodynamic simulations show a transition from SL to AS rotation as the influence of rotation on convection is reduced, but the opposite transition occurs at a different point in the parameter space. The system is bistable, i.e., SL and AS rotation profiles can both be stable.
Aims: We study the effect of a dynamo-generated magnetic field on the large-scale flows, particularly on the possibility of bistable behaviour of differential rotation.
Methods: We solve the hydromagnetic equations numerically in a rotating spherical shell that typically covers ± 75° latitude (wedge geometry) for a set of different radiative conductivities controlling the relative importance of convection. We analyse the resulting differential rotation, meridional circulation, and magnetic field and compare the corresponding modifications of the Reynolds and Maxwell stresses.
Results: In agreement with earlier findings, our models display SL rotation profiles when the rotational influence on convection is strong and a transition to AS when the rotational influence decreases. We find that dynamo-generated magnetic fields help to produce SL differential rotation compared to the hydrodynamic simulations. We do not observe any bistable states of differential rotation. In the AS cases we find coherent single-cell meridional circulation, whereas in SL cases we find multi-cellular patterns. In both cases, we obtain poleward circulation near the surface with a magnitude close to that observed in the Sun. In the slowly rotating cases, we find activity cycles, but no clear polarity reversals, whereas in the more rapidly rotating cases irregular variations are obtained. Moreover, both differential rotation and meridional circulation have significant temporal variations that are similar in strength to those of the Sun.
Conclusions: Purely hydrodynamic simulations of differential rotation and meridional circulation are shown to be of limited relevance as magnetic fields, self-consistently generated by dynamo action, significantly affect the flows. Title: Properties of p and f modes in hydromagnetic turbulence Authors: Singh, Nishant K.; Brandenburg, Axel; Chitre, S. M.; Rheinhardt, Matthias Bibcode: 2015MNRAS.447.3708S Altcode: 2014arXiv1404.3246S With the ultimate aim of using the fundamental or f mode to study helioseismic aspects of turbulence-generated magnetic flux concentrations, we use randomly forced hydromagnetic simulations of a piecewise isothermal layer in two dimensions with reflecting boundaries at top and bottom. We compute numerically diagnostic wavenumber-frequency diagrams of the vertical velocity at the interface between the denser gas below and the less dense gas above. For an Alfvén-to-sound speed ratio of about 0.1, a 5 per cent frequency increase of the f mode can be measured when kxHp = 3-4, where kx is the horizontal wavenumber and Hp is the pressure scaleheight at the surface. Since the solar radius is about 2000 times larger than Hp, the corresponding spherical harmonic degree would be 6000-8000. For weaker fields, a kx-dependent frequency decrease by the turbulent motions becomes dominant. For vertical magnetic fields, the frequency is enhanced for kxHp ≈ 4, but decreased relative to its nonmagnetic value for kxHp ≈ 9. Title: Nonhelical Inverse Transfer of a Decaying Turbulent Magnetic Field Authors: Brandenburg, Axel; Kahniashvili, Tina; Tevzadze, Alexander G. Bibcode: 2015PhRvL.114g5001B Altcode: 2014arXiv1404.2238B In the presence of magnetic helicity, inverse transfer from small to large scales is well known in magnetohydrodynamic (MHD) turbulence and has applications in astrophysics, cosmology, and fusion plasmas. Using high resolution direct numerical simulations of magnetically dominated self-similarly decaying MHD turbulence, we report a similar inverse transfer even in the absence of magnetic helicity. We compute for the first time spectral energy transfer rates to show that this inverse transfer is about half as strong as with helicity, but in both cases the magnetic gain at large scales results from velocity at similar scales interacting with smaller-scale magnetic fields. This suggests that both inverse transfers are a consequence of universal mechanisms for magnetically dominated turbulence. Possible explanations include inverse cascading of the mean squared vector potential associated with local near two dimensionality and the shallower k2 subinertial range spectrum of kinetic energy forcing the magnetic field with a k4 subinertial range to attain larger-scale coherence. The inertial range shows a clear k-2 spectrum and is the first example of fully isotropic magnetically dominated MHD turbulence exhibiting weak turbulence scaling. Title: Simulations of Galactic Dynamos Authors: Brandenburg, Axel Bibcode: 2015ASSL..407..529B Altcode: 2014arXiv1402.0212B We review our current understanding of galactic dynamo theory, paying particular attention to numerical simulations both of the mean-field equations and the original three-dimensional equations relevant to describing the magnetic field evolution for a turbulent flow. We emphasize the theoretical difficulties in explaining non-axisymmetric magnetic fields in galaxies and discuss the observational basis for such results in terms of rotation measure analysis. Next, we discuss nonlinear theory, the role of magnetic helicity conservation and magnetic helicity fluxes. This leads to the possibility that galactic magnetic fields may be bi-helical, with opposite signs of helicity and large and small length scales. We discuss their observational signatures and close by discussing the possibilities of explaining the origin of primordial magnetic fields. Title: Dynamical quenching with non-local α and downward pumping Authors: Brandenburg, A.; Hubbard, A. Käpylä, P. J. Bibcode: 2015AN....336...91B Altcode: 2014arXiv1412.0997B In light of new results, the one-dimensional mean-field dynamo model of Brandenburg & Käpylä (2007) with dynamical quenching and a nonlocal Babcock-Leighton \alpha effect is re-examined for the solar dynamo. We extend the one-dimensional model to include the effects of turbulent downward pumping (Kitchatinov & Olemskoy 2011), and to combine dynamical quenching with shear. We use both the conventional dynamical quenching model of Kleeorin & Ruzmaikin (1982) and the alternate one of Hubbard & Brandenburg (2011), and confirm that with varying levels of non-locality in the \alpha effect, and possibly shear as well, the saturation field strength can be independent of the magnetic Reynolds number. Title: Traces of large-scale dynamo action in the kinematic stage Authors: Subramanian, Kandaswamy; Brandenburg, Axel Bibcode: 2014MNRAS.445.2930S Altcode: 2014arXiv1408.4416S Using direct numerical simulations (DNS), we verify that in the kinematic regime, a turbulent helical dynamo grows in such a way that the magnetic energy spectrum remains to high-precision shape-invariant, i.e. at each wavenumber k the spectrum grows with the same growth rate. Signatures of large-scale dynamo action can be identified through the excess of magnetic energy at small k, of one of the two oppositely polarized constituents. Also a suitably defined planar average of the magnetic field can be chosen such that its rms value isolates the strength of the mean field. However, these different means of analysis suggest that the strength of the large-scale field diminishes with increasing magnetic Reynolds number ReM like Re_M^{-1/2} for intermediate values and like Re_M^{-3/4} for larger ones. Both an analysis from the Kazantsev model including helicity and the DNS show that this arises due to the magnetic energy spectrum still peaking at resistive scales, even when helicity is present. As expected, the amplitude of the large-scale field increases with increasing fractional helicity, enabling us to determine the onset of large-scale dynamo action and distinguishing it from that of the small-scale dynamo. Our DNS show that, contrary to earlier results for smaller scale separation (only 1.5 instead of now 4), the small-scale dynamo can still be excited at magnetic Prandtl numbers of 0.1 and only moderate values of the magnetic Reynolds numbers (∼160). Title: Magnetic Flux Concentrations in Stratified Turbulent Plasma Due to Negative Effective Magnetic Pressure Instability Authors: Jabbari, S.; Brandenburg, A. Bibcode: 2014AGUFMSH41B4131J Altcode: Recent studies have suggested a new mechanism that can be used to explain the formation of magnetic spots or bipolar regions in highly stratified turbulent plasmas. According to this model, a large-scale magnetic field suppresses the turbulent pressure, which leads to a negative contribution of turbulence to the effective magnetic pressure. Direct numerical simulations (DNS) have confirmed that the negative contribution is large enough so that the effective magnetic pressure becomes negative and leads to a large-scale instability, which we refer to as negative effective magnetic pressure Instability (NEMPI). NEMPI was used to explain the formation of active regions and sunspots on the solar surface. One step toward improving this model was to combine dynamo in- stability with NEMPI. The dynamo is known to be responsible for the solar large-scale magnetic field and to play a role in solar activity. In this context, we studied stratified turbulent plasmas in spherical geometry, where the background field was generated by alpha squared dynamo. For NEMPI to be excited, the initial magnetic field should be in a proper range, so we used quenching function for alpha. Using the Pencil Code and mean field simulations (MFS), we showed that in the presence of dynamo-generated magnetic fields, we deal with a coupled system, where both instabilities, dynamo and NEMPI, work together and lead to the formation of magnetic structures (Jabbari et al. 2013). We also studied a similar system in plane geometry in the presence of rotation and confirmed that for slow rotation NEMPI works, but as the Coriolis number increases, the rotation suppresses NEMPI. By increasing the Coriolis number even further, the combination of fast rotation and high stratification excites a dynamo, which leads again to a coupled system of dynamo and NEMPI (Jabbari et al. 2014). Another important finding concerning NEMPI is the case where the instability is excited by a vertical magnetic field (Brandenburg et al. 2013). When the field is vertical, the resulting magnetic flux concentrations lead to the magnetic spots and can be of equipartition field strength. DNS, MFS, and implicit large eddy simulations (ILES) confirm that in a proper parameter regime, vertical imposed fields lead to the formation of circular magnetic spots (Brandenburg et al. 2014). Title: Near-polytropic stellar simulations with a radiative surface Authors: Barekat, A.; Brandenburg, A. Bibcode: 2014A&A...571A..68B Altcode: 2013arXiv1308.1660B Context. Studies of solar and stellar convection often employ simple polytropic setups using the diffusion approximation instead of solving the proper radiative transfer equation. This allows one to control separately the polytropic index of the hydrostatic reference solution, the temperature contrast between top and bottom, and the Rayleigh and Péclet numbers.
Aims: Here we extend such studies by including radiative transfer in the gray approximation using a Kramers-like opacity with freely adjustable coefficients. We study the properties of such models and compare them with results from the diffusion approximation.
Methods: We use the Pencil code, which is a high-order finite difference code where radiation is treated using the method of long characteristics. The source function is given by the Planck function. The opacity is written as κ = κ0ρaTb, where a = 1 in most cases, b is varied from -3.5 to + 5, and κ0 is varied by four orders of magnitude. We adopt a perfect monatomic gas. We consider sets of one-dimensional models and perform a comparison with the diffusion approximation in one- and two-dimensional models.
Results: Except for the case where b = 5, we find one-dimensional hydrostatic equilibria with a nearly polytropic stratification and a polytropic index close to n = (3 - b)/(1 + a), covering both convectively stable (n> 3/2) and unstable (n< 3/2) cases. For b = 3 and a = -1, the value of n is undefined a priori and the actual value of n depends then on the depth of the domain. For large values of κ0, the thermal adjustment time becomes long, the Péclet and Rayleigh numbers become large, and the temperature contrast increases and is thus no longer an independent input parameter, unless the Stefan-Boltzmann constant is considered adjustable.
Conclusions: Proper radiative transfer with Kramers-like opacities provides a useful tool for studying stratified layers with a radiative surface in ways that are more physical than what is possible with polytropic models using the diffusion approximation.

Appendices are available in electronic form at http://www.aanda.org Title: Intense bipolar structures from stratified helical dynamos Authors: Mitra, Dhrubaditya; Brandenburg, A.; Kleeorin, N.; Rogachevskii, I. Bibcode: 2014MNRAS.445..761M Altcode: 2014arXiv1404.3194M We perform direct numerical simulations of the equations of magnetohydrodynamics with external random forcing and in the presence of gravity. The domain is divided into two parts: a lower layer where the forcing is helical and an upper layer where the helicity of the forcing is zero with a smooth transition in between. At early times, a large-scale helical dynamo develops in the bottom layer. At later times the dynamo saturates, but the vertical magnetic field continues to develop and rises to form dynamic bipolar structures at the top, which later disappear and reappear. Some of the structures look similar to δ spots observed in the Sun. This is the first example of magnetic flux concentrations, owing to strong density stratification, from self-consistent dynamo simulations that generate bipolar, super-equipartition strength, magnetic structures whose energy density can exceeds the turbulent kinetic energy by even a factor of 10. Title: On The Cause of Solar-like Equatorward Migration in Global Convective Dynamo Simulations Authors: Warnecke, Jörn; Käpylä, Petri J.; Käpylä, Maarit J.; Brandenburg, Axel Bibcode: 2014ApJ...796L..12W Altcode: 2014arXiv1409.3213W We present results from four convectively driven stellar dynamo simulations in spherical wedge geometry. All of these simulations produce cyclic and migrating mean magnetic fields. Through detailed comparisons, we show that the migration direction can be explained by an αΩ dynamo wave following the Parker-Yoshimura rule. We conclude that the equatorward migration in this and previous work is due to a positive (negative) α effect in the northern (southern) hemisphere and a negative radial gradient of Ω outside the inner tangent cylinder of these models. This idea is supported by a strong correlation between negative radial shear and toroidal field strength in the region of equatorward propagation. Title: Fanning Out of the Solar f-mode in the Presence of Non-uniform Magnetic Fields? Authors: Singh, Nishant K.; Brandenburg, Axel; Rheinhardt, Matthias Bibcode: 2014ApJ...795L...8S Altcode: 2014arXiv1407.0356S We show that in the presence of a magnetic field that is varying harmonically in space, the fundamental mode, or f-mode, in a stratified layer is altered in such a way that it fans out in the diagnostic kω diagram, with mode power also within the fan. In our simulations, the surface is defined by a temperature and density jump in a piecewise isothermal layer. Unlike our previous work (Singh et al. 2014), where a uniform magnetic field was considered, here we employ a non-uniform magnetic field together with hydromagnetic turbulence at length scales much smaller than those of the magnetic field. The expansion of the f-mode is stronger for fields confined to the layer below the surface. In some of those cases, the kω diagram also reveals a new class of low-frequency vertical stripes at multiples of twice the horizontal wavenumber of the background magnetic field. We argue that the study of the f-mode expansion might be a new and sensitive tool to determine subsurface magnetic fields with azimuthal or other horizontal periodicity. Title: Quenching and Anisotropy of Hydromagnetic Turbulent Transport Authors: Karak, Bidya Binay; Rheinhardt, Matthias; Brandenburg, Axel; Käpylä, Petri J.; Käpylä, Maarit J. Bibcode: 2014ApJ...795...16K Altcode: 2014arXiv1406.4521K Hydromagnetic turbulence affects the evolution of large-scale magnetic fields through mean-field effects like turbulent diffusion and the α effect. For stronger fields, these effects are usually suppressed or quenched, and additional anisotropies are introduced. Using different variants of the test-field method, we determine the quenching of the turbulent transport coefficients for the forced Roberts flow, isotropically forced non-helical turbulence, and rotating thermal convection. We see significant quenching only when the mean magnetic field is larger than the equipartition value of the turbulence. Expressing the magnetic field in terms of the equipartition value of the quenched flows, we obtain for the quenching exponents of the turbulent magnetic diffusivity about 1.3, 1.1, and 1.3 for Roberts flow, forced turbulence, and convection, respectively. However, when the magnetic field is expressed in terms of the equipartition value of the unquenched flows, these quenching exponents become about 4, 1.5, and 2.3, respectively. For the α effect, the exponent is about 1.3 for the Roberts flow and 2 for convection in the first case, but 4 and 3, respectively, in the second. In convection, the quenching of turbulent pumping follows the same power law as turbulent diffusion, while for the coefficient describing the {\boldsymbolΩ} × \boldsymbol {{J}} effect nearly the same quenching exponent is obtained as for α. For forced turbulence, turbulent diffusion proportional to the second derivative along the mean magnetic field is quenched much less, especially for larger values of the magnetic Reynolds number. However, we find that in corresponding axisymmetric mean-field dynamos with dominant toroidal field the quenched diffusion coefficients are the same for the poloidal and toroidal field constituents. Title: Confirmation of bistable stellar differential rotation profiles Authors: Käpylä, P. J.; Käpylä, M. J.; Brandenburg, A. Bibcode: 2014A&A...570A..43K Altcode: 2014arXiv1401.2981K Context. Solar-like differential rotation is characterized by a rapidly rotating equator and slower poles. However, theoretical models and numerical simulations can also result in a slower equator and faster poles when the overall rotation is slow.
Aims: We study the critical rotational influence under which differential rotation flips from solar-like (fast equator, slow poles) to an anti-solar one (slow equator, fast poles). We also estimate the non-diffusive (Λ effect) and diffusive (turbulent viscosity) contributions to the Reynolds stress.
Methods: We present the results of three-dimensional numerical simulations of mildly turbulent convection in spherical wedge geometry. Here we apply a fully compressible setup which would suffer from a prohibitive time step constraint if the real solar luminosity was used. To avoid this problem while still representing the same rotational influence on the flow as in the Sun, we increase the luminosity by a factor of roughly 106 and the rotation rate by a factor of 102. We regulate the convective velocities by varying the amount of heat transported by thermal conduction, turbulent diffusion, and resolved convection.
Results: Increasing the efficiency of resolved convection leads to a reduction of the rotational influence on the flow and a sharp transition from solar-like to anti-solar differential rotation for Coriolis numbers around 1.3. We confirm the recent finding of a large-scale flow bistability: contrasted with running the models from an initial condition with unprescribed differential rotation, the initialization of the model with certain kind of rotation profile sustains the solution over a wider parameter range. The anti-solar profiles are found to be more stable against perturbations in the level of convective turbulent velocity than the solar-type solutions.
Conclusions: Our results may have implications for real stars that start their lives as rapid rotators implying solar-like rotation in the early main-sequence evolution. As they slow down, they might be able to retain solar-like rotation for lower Coriolis numbers, and thus longer in time, before switching to anti-solar rotation. This could partially explain the puzzling findings of anti-solar rotation profiles for models in the solar parameter regime. Title: Superflare Occurrence and Energies on G-, K-, and M-type Dwarfs Authors: Candelaresi, S.; Hillier, A.; Maehara, H.; Brandenburg, A.; Shibata, K. Bibcode: 2014ApJ...792...67C Altcode: 2014arXiv1405.1453C Kepler data from G-, K-, and M-type stars are used to study conditions that lead to superflares with energies above 1034 erg. From the 117,661 stars included, 380 show superflares with a total of 1690 such events. We study whether parameters, like effective temperature or rotation rate, have any effect on the superflare occurrence rate or energy. With increasing effective temperature we observe a decrease in the superflare rate, which is analogous to the previous findings of a decrease in dynamo activity with increasing effective temperature. For slowly rotating stars, we find a quadratic increase of the mean occurrence rate with the rotation rate up to a critical point, after which the rate decreases linearly. Motivated by standard dynamo theory, we study the behavior of the relative starspot coverage, approximated as the relative brightness variation. For faster rotating stars, an increased fraction of stars shows higher spot coverage, which leads to higher superflare rates. A turbulent dynamo is used to study the dependence of the Ohmic dissipation as a proxy of the flare energy on the differential rotation or shear rate. The resulting statistics of the dissipation energy as a function of dynamo number is similar to the observed flare statistics as a function of the inverse Rossby number and shows similarly strong fluctuations. This supports the idea that superflares might well be possible for solar-type G stars. Title: Magnetic Prandtl Number Dependence of the Kinetic-to-magnetic Dissipation Ratio Authors: Brandenburg, Axel Bibcode: 2014ApJ...791...12B Altcode: 2014arXiv1404.6964B Using direct numerical simulations of three-dimensional hydromagnetic turbulence, either with helical or non-helical forcing, we show that the kinetic-to-magnetic energy dissipation ratio always increases with the magnetic Prandtl number, i.e., the ratio of kinematic viscosity to magnetic diffusivity. This dependence can always be approximated by a power law, but the exponent is not the same in all cases. For non-helical turbulence, the exponent is around 1/3, while for helical turbulence it is between 0.6 and 2/3. In the statistically steady state, the rate of energy conversion from kinetic into magnetic by the dynamo must be equal to the Joule dissipation rate. We emphasize that for both small-scale and large-scale dynamos, the efficiency of the energy conversion depends sensitively on the magnetic Prandtl number, and thus on the microphysical dissipation process. To understand this behavior, we also study shell models of turbulence and one-dimensional passive and active scalar models. We conclude that the magnetic Prandtl number dependence is qualitatively best reproduced in the one-dimensional model as a result of dissipation via localized Alfvén kinks. Title: Coronal influence on dynamos Authors: Warnecke, Jörn; Brandenburg, Axel Bibcode: 2014IAUS..302..134W Altcode: 2013arXiv1310.0787W We report on turbulent dynamo simulations in a spherical wedge with an outer coronal layer. We apply a two-layer model where the lower layer represents the convection zone and the upper layer the solar corona. This setup is used to study the coronal influence on the dynamo action beneath the surface. Increasing the radial coronal extent gradually to three times the solar radius and changing the magnetic Reynolds number, we find that dynamo action benefits from the additional coronal extent in terms of higher magnetic energy in the saturated stage. The flux of magnetic helicity can play an important role in this context. Title: Magnetic flux concentrations from dynamo-generated fields Authors: Jabbari, S.; Brandenburg, A.; Losada, I. R.; Kleeorin, N.; Rogachevskii, I. Bibcode: 2014A&A...568A.112J Altcode: 2014arXiv1401.6107J Context. The mean-field theory of magnetized stellar convection gives rise to two distinct instabilities: the large-scale dynamo instability, operating in the bulk of the convection zone and a negative effective magnetic pressure instability (NEMPI) operating in the strongly stratified surface layers. The latter might be important in connection with magnetic spot formation. However, as follows from theoretical analysis, the growth rate of NEMPI is suppressed with increasing rotation rates. On the other hand, recent direct numerical simulations (DNS) have shown a subsequent increase in the growth rate.
Aims: We examine quantitatively whether this increase in the growth rate of NEMPI can be explained by an α2 mean-field dynamo, and whether both NEMPI and the dynamo instability can operate at the same time.
Methods: We use both DNS and mean-field simulations (MFS) to solve the underlying equations numerically either with or without an imposed horizontal field. We use the test-field method to compute relevant dynamo coefficients.
Results: DNS show that magnetic flux concentrations are still possible up to rotation rates above which the large-scale dynamo effect produces mean magnetic fields. The resulting DNS growth rates are quantitatively reproduced with MFS. As expected for weak or vanishing rotation, the growth rate of NEMPI increases with increasing gravity, but there is a correction term for strong gravity and large turbulent magnetic diffusivity.
Conclusions: Magnetic flux concentrations are still possible for rotation rates above which dynamo action takes over. For the solar rotation rate, the corresponding turbulent turnover time is about 5 h, with dynamo action commencing in the layers beneath. Title: Quantifying the effect of turbulent magnetic diffusion on the growth rate of the magneto-rotational instability Authors: Väisälä, M. S.; Brandenburg, A.; Mitra, D.; Käpylä, P. J.; Mantere, M. J. Bibcode: 2014A&A...567A.139V Altcode: 2013arXiv1310.3157V Context. In astrophysics, turbulent diffusion is often used in place of microphysical diffusion to avoid resolving the small scales. However, we expect this approach to break down when time and length scales of the turbulence become comparable with other relevant time and length scales in the system. Turbulent diffusion has previously been applied to the magneto-rotational instability (MRI), but no quantitative comparison of growth rates at different turbulent intensities has been performed.
Aims: We investigate to what extent turbulent diffusion can be used to model the effects of small-scale turbulence on the kinematic growth rates of the MRI, and how this depends on angular velocity and magnetic field strength.
Methods: We use direct numerical simulations in three-dimensional shearing boxes with periodic boundary conditions in the spanwise direction and additional random plane-wave volume forcing to drive a turbulent flow at a given length scale. We estimate the turbulent diffusivity using a mixing length formula and compare with results obtained with the test-field method.
Results: It turns out that the concept of turbulent diffusion is remarkably accurate in describing the effect of turbulence on the growth rate of the MRI. No noticeable breakdown of turbulent diffusion has been found, even when time and length scales of the turbulence become comparable with those imposed by the MRI itself. On the other hand, quenching of turbulent magnetic diffusivity by the magnetic field is found to be absent.
Conclusions: Turbulence reduces the growth rate of the MRI in the same way as microphysical magnetic diffusion does.

Appendix A is available in electronic form at http://www.aanda.org Title: Mean-field dynamo action from delayed transport Authors: Rheinhardt, Matthias; Devlen, Ebru; Rädler, Karl-Heinz; Brandenburg, Axel Bibcode: 2014MNRAS.441..116R Altcode: 2014arXiv1401.5026R We analyse the nature of dynamo action that enables growing horizontally averaged magnetic fields in two particular flows that were studied by Roberts in 1972, namely his flows II and III. They have zero kinetic helicity either pointwise (flow II), or on average (flow III). Using direct numerical simulations, we determine the onset conditions for dynamo action at moderate values of the magnetic Reynolds number. Using the test-field method, we show that the turbulent magnetic diffusivity is then positive for both flows. However, we demonstrate that for both flows large-scale dynamo action occurs through delayed transport. Mathematically speaking, the magnetic field at earlier times contributes to the electromotive force through the off-diagonal components of the α tensor such that a zero mean magnetic field becomes unstable to dynamo action. This represents a qualitatively new mean-field dynamo mechanism not previously described. Title: Faraday Signature of Magnetic Helicity from Reduced Depolarization Authors: Brandenburg, Axel; Stepanov, Rodion Bibcode: 2014ApJ...786...91B Altcode: 2014arXiv1401.4102B Using one-dimensional models, we show that a helical magnetic field with an appropriate sign of helicity can compensate the Faraday depolarization resulting from the superposition of Faraday-rotated polarization planes from a spatially extended source. For radio emission from a helical magnetic field, the polarization as a function of the square of the wavelength becomes asymmetric with respect to zero. Mathematically speaking, the resulting emission occurs then either at observable or at unobservable (imaginary) wavelengths. We demonstrate that rotation measure (RM) synthesis allows for the reconstruction of the underlying Faraday dispersion function in the former case, but not in the latter. The presence of positive magnetic helicity can thus be detected by observing positive RM in highly polarized regions in the sky and negative RM in weakly polarized regions. Conversely, negative magnetic helicity can be detected by observing negative RM in highly polarized regions and positive RM in weakly polarized regions. The simultaneous presence of two magnetic constituents with opposite signs of helicity is shown to possess signatures that can be quantified through polarization peaks at specific wavelengths and the gradient of the phase of the Faraday dispersion function. Similar polarization peaks can tentatively also be identified for the bi-helical magnetic fields that are generated self-consistently by a dynamo from helically forced turbulence, even though the magnetic energy spectrum is then continuous. Finally, we discuss the possibility of detecting magnetic fields with helical and non-helical properties in external galaxies using the Square Kilometre Array. Title: Particle energization through time-periodic helical magnetic fields Authors: Mitra, Dhrubaditya; Brandenburg, Axel; Dasgupta, Brahmananda; Niklasson, Eyvind; Ram, Abhay Bibcode: 2014PhRvE..89d2919M Altcode: 2013arXiv1306.0151M We solve for the motion of charged particles in a helical time-periodic ABC (Arnold-Beltrami-Childress) magnetic field. The magnetic field lines of a stationary ABC field with coefficients A =B=C=1 are chaotic, and we show that the motion of a charged particle in such a field is also chaotic at late times with positive Lyapunov exponent. We further show that in time-periodic ABC fields, the kinetic energy of a charged particle can increase indefinitely with time. At late times the mean kinetic energy grows as a power law in time with an exponent that approaches unity. For an initial distribution of particles, whose kinetic energy is uniformly distributed within some interval, the probability density function of kinetic energy is, at late times, close to a Gaussian but with steeper tails. Title: Magnetic flux concentrations in a polytropic atmosphere Authors: Losada, I. R.; Brandenburg, A.; Kleeorin, N.; Rogachevskii, I. Bibcode: 2014A&A...564A...2L Altcode: 2013arXiv1307.4945L Context. Strongly stratified hydromagnetic turbulence has recently been identified as a candidate for explaining the spontaneous formation of magnetic flux concentrations by the negative effective magnetic pressure instability (NEMPI). Much of this work has been done for isothermal layers, in which the density scale height is constant throughout.
Aims: We now want to know whether earlier conclusions regarding the size of magnetic structures and their growth rates carry over to the case of polytropic layers, in which the scale height decreases sharply as one approaches the surface.
Methods: To allow for a continuous transition from isothermal to polytropic layers, we employ a generalization of the exponential function known as the q-exponential. This implies that the top of the polytropic layer shifts with changing polytropic index such that the scale height is always the same at some reference height. We used both mean-field simulations (MFS) and direct numerical simulations (DNS) of forced stratified turbulence to determine the resulting flux concentrations in polytropic layers. Cases of both horizontal and vertical applied magnetic fields were considered.
Results: Magnetic structures begin to form at a depth where the magnetic field strength is a small fraction of the local equipartition field strength with respect to the turbulent kinetic energy. Unlike the isothermal case where stronger fields can give rise to magnetic flux concentrations at larger depths, in the polytropic case the growth rate of NEMPI decreases for structures deeper down. Moreover, the structures that form higher up have a smaller horizontal scale of about four times their local depth. For vertical fields, magnetic structures of super-equipartition strengths are formed, because such fields survive downward advection that causes NEMPI with horizontal magnetic fields to reach premature nonlinear saturation by what is called the "potato-sack" effect. The horizontal cross-section of such structures found in DNS is approximately circular, which is reproduced with MFS of NEMPI using a vertical magnetic field.
Conclusions: Results based on isothermal models can be applied locally to polytropic layers. For vertical fields, magnetic flux concentrations of super-equipartition strengths form, which supports suggestions that sunspot formation might be a shallow phenomenon. Title: Magnetic Helicity and Energy Spectra of a Solar Active Region Authors: Zhang, Hongqi; Brandenburg, Axel; Sokoloff, D. D. Bibcode: 2014ApJ...784L..45Z Altcode: 2013arXiv1311.2432Z We compute for the first time the magnetic helicity and energy spectra of the solar active region NOAA 11158 during 2011 February 11-15 at 20° southern heliographic latitude using observational photospheric vector magnetograms. We adopt the isotropic representation of the Fourier-transformed two-point correlation tensor of the magnetic field. The sign of the magnetic helicity turns out to be predominantly positive at all wavenumbers. This sign is consistent with what is theoretically expected for the southern hemisphere. The magnetic helicity normalized to its theoretical maximum value, here referred to as relative helicity, is around 4% and strongest at intermediate wavenumbers of k ≈ 0.4 Mm-1, corresponding to a scale of 2π/k ≈ 16 Mm. The same sign and a similar value are also found for the relative current helicity evaluated in real space based on the vertical components of magnetic field and current density. The modulus of the magnetic helicity spectrum shows a k -11/3 power law at large wavenumbers, which implies a k -5/3 spectrum for the modulus of the current helicity. A k -5/3 spectrum is also obtained for the magnetic energy. The energy spectra evaluated separately from the horizontal and vertical fields agree for wavenumbers below 3 Mm-1, corresponding to scales above 2 Mm. This gives some justification to our assumption of isotropy and places limits resulting from possible instrumental artifacts at small scales. Title: α effect in a turbulent liquid-metal plane Couette flow Authors: Rüdiger, G.; Brandenburg, A. Bibcode: 2014PhRvE..89c3009R Altcode: 2012arXiv1201.0652R We calculate the mean electromotive force in plane Couette flows of a nonrotating conducting fluid under the influence of a large-scale magnetic field for driven turbulence. A vertical stratification of the turbulence intensity results in an α effect owing to the presence of horizontal shear. Here we discuss the possibility of an experimental determination of the components of the α tensor using both quasilinear theory and nonlinear numerical simulations. For magnetic Prandtl numbers of the order of unity, we find that in the high-conductivity limit the α effect in the direction of the flow clearly exceeds the component in spanwise direction. In this limit, α runs linearly with the magnetic Reynolds number Rm , while in the low-conductivity limit it runs with the product Rm .Re, where Re is the kinetic Reynolds number, so that for a given Rm the α effect grows with decreasing magnetic Prandtl number. For the small magnetic Prandtl numbers of liquid metals, a common value for the horizontal elements of the α tensor appears, which makes it unimportant whether the α effect is measured in the spanwise or the streamwise directions. The resulting effect should lead to an observable voltage of about 0.5 mV in both directions for magnetic fields of 1 kG and velocity fluctuations of about 1 m/s in a channel of 50-cm height (independent of its width). Title: Mean-field and direct numerical simulations of magnetic flux concentrations from vertical field Authors: Brandenburg, A.; Gressel, O.; Jabbari, S.; Kleeorin, N.; Rogachevskii, I. Bibcode: 2014A&A...562A..53B Altcode: 2013arXiv1309.3547B Context. Strongly stratified hydromagnetic turbulence has previously been found to produce magnetic flux concentrations if the domain is large enough compared with the size of turbulent eddies. Mean-field simulations (MFS) using parameterizations of the Reynolds and Maxwell stresses show a large-scale negative effective magnetic pressure instability and have been able to reproduce many aspects of direct numerical simulations (DNS) regarding growth rate, shape of the resulting magnetic structures, and their height as a function of magnetic field strength. Unlike the case of an imposed horizontal field, for a vertical one, magnetic flux concentrations of equipartition strength with the turbulence can be reached, resulting in magnetic spots that are reminiscent of sunspots.
Aims: We determine under what conditions magnetic flux concentrations with vertical field occur and what their internal structure is.
Methods: We use a combination of MFS, DNS, and implicit large-eddy simulations (ILES) to characterize the resulting magnetic flux concentrations in forced isothermal turbulence with an imposed vertical magnetic field.
Results: Using DNS, we confirm earlier results that in the kinematic stage of the large-scale instability the horizontal wavelength of structures is about 10 times the density scale height. At later times, even larger structures are being produced in a fashion similar to inverse spectral transfer in helically driven turbulence. Using ILES, we find that magnetic flux concentrations occur for Mach numbers between 0.1 and 0.7. They occur also for weaker stratification and larger turbulent eddies if the domain is wide enough. Using MFS, the size and aspect ratio of magnetic structures are determined as functions of two input parameters characterizing the parameterization of the effective magnetic pressure. DNS, ILES, and MFS show magnetic flux tubes with mean-field energies comparable to the turbulent kinetic energy. These tubes can reach a length of about eight density scale heights. Despite being ≤1% equipartition strength, it is important that their lower part is included within the computational domain to achieve the full strength of the instability.
Conclusions: The resulting vertical magnetic flux tubes are being confined by downflows along the tubes and corresponding inflow from the sides, which keep the field concentrated. Application to sunspots remains a viable possibility. Title: Astrophysical Hydromagnetic Turbulence Authors: Brandenburg, A.; Lazarian, A. Bibcode: 2014mpcp.book...87B Altcode: 2014mcp..book...87B Recent progress in astrophysical hydromagnetic turbulence is being reviewed. The physical ideas behind the now widely accepted Goldreich-Sridhar model and its extension to compressible magnetohydrodynamic turbulence are introduced. Implications for cosmic ray diffusion and acceleration is being discussed. Dynamo-generated magnetic fields with and without helicity are contrasted against each other. Certain turbulent transport processes are being modified and often suppressed by anisotropy and inhomogeneities of the turbulence, while others are being produced by such properties, which can lead to new large-scale instabilities of the turbulent medium. Applications of various such processes to astrophysical systems are being considered. Title: Microphysics of Cosmic Ray Driven Plasma Instabilities Authors: Bykov, A. M.; Brandenburg, A.; Malkov, M. A.; Osipov, S. M. Bibcode: 2014mpcp.book..125B Altcode: 2014mcp..book..125B Energetic nonthermal particles (cosmic rays, CRs) are accelerated in supernova remnants, relativistic jets and other astrophysical objects. The CR energy density is typically comparable with that of the thermal components and magnetic fields. In this review we discuss mechanisms of magnetic field amplification due to instabilities induced by CRs. We derive CR kinetic and magnetohydrodynamic equations that govern cosmic plasma systems comprising the thermal background plasma, comic rays and fluctuating magnetic fields to study CR-driven instabilities. Both resonant and non-resonant instabilities are reviewed, including the Bell short-wavelength instability, and the firehose instability. Special attention is paid to the longwavelength instabilities driven by the CR current and pressure gradient. The helicity production by the CR current-driven instabilities is discussed in connection with the dynamo mechanisms of cosmic magnetic field amplification. Title: An Azimuthal Dynamo Wave in Spherical Shell Convection Authors: Cole, Elizabeth; Käpylä, Petri J.; Mantere, Maarit J.; Brandenburg, Axel Bibcode: 2014ApJ...780L..22C Altcode: 2013arXiv1309.6802C We report the discovery of an azimuthal dynamo wave of a low-order (m = 1) mode in direct numerical simulations (DNS) of turbulent convection in spherical shells. Such waves are predicted by mean-field dynamo theory and have been obtained previously in mean-field models. An azimuthal dynamo wave has been proposed as a possible explanation for the persistent drifts of spots observed on several rapidly rotating stars, as revealed through photometry and Doppler imaging. However, this has been judged unlikely because evidence for such waves from DNS has been lacking. Here we present DNS of large-scale magnetic fields showing a retrograde m = 1 mode. Its pattern speed is nearly independent of latitude and does not reflect the speed of the differential rotation at any depth. The extrema of magnetic m = 1 structures coincide reasonably well with the maxima of m = 2 structures of the temperature. These results provide direct support for the observed drifts being due to an azimuthal dynamo wave. Title: Spoke-like Differential Rotation in a Convective Dynamo with a Coronal Envelope Authors: Warnecke, Jörn; Käpylä, Petri J.; Mantere, Maarit J.; Brandenburg, Axel Bibcode: 2013ApJ...778..141W Altcode: 2013arXiv1301.2248W We report on the results of four convective dynamo simulations with an outer coronal layer. The magnetic field is self-consistently generated by the convective motions beneath the surface. Above the convection zone, we include a polytropic layer that extends to 1.6 solar radii. The temperature increases in this region to ≈8 times the value at the surface, corresponding to ≈1.2 times the value at the bottom of the spherical shell. We associate this region with the solar corona. We find solar-like differential rotation with radial contours of constant rotation rate, together with a near-surface shear layer. This non-cylindrical rotation profile is caused by a non-zero latitudinal entropy gradient that offsets the Taylor-Proudman balance through the baroclinic term. The meridional circulation is multi-cellular with a solar-like poleward flow near the surface at low latitudes. In most of the cases, the mean magnetic field is oscillatory with equatorward migration in two cases. In other cases, the equatorward migration is overlaid by stationary or even poleward migrating mean fields. Title: Effects of Enhanced Stratification on Equatorward Dynamo Wave Propagation Authors: Käpylä, Petri J.; Mantere, Maarit J.; Cole, Elizabeth; Warnecke, Jörn; Brandenburg, Axel Bibcode: 2013ApJ...778...41K Altcode: 2013arXiv1301.2595K We present results from simulations of rotating magnetized turbulent convection in spherical wedge geometry representing parts of the latitudinal and longitudinal extents of a star. Here we consider a set of runs for which the density stratification is varied, keeping the Reynolds and Coriolis numbers at similar values. In the case of weak stratification, we find quasi-steady dynamo solutions for moderate rotation and oscillatory ones with poleward migration of activity belts for more rapid rotation. For stronger stratification, the growth rate tends to become smaller. Furthermore, a transition from quasi-steady to oscillatory dynamos is found as the Coriolis number is increased, but now there is an equatorward migrating branch near the equator. The breakpoint where this happens corresponds to a rotation rate that is about three to seven times the solar value. The phase relation of the magnetic field is such that the toroidal field lags behind the radial field by about π/2, which can be explained by an oscillatory α2 dynamo caused by the sign change of the α-effect about the equator. We test the domain size dependence of our results for a rapidly rotating run with equatorward migration by varying the longitudinal extent of our wedge. The energy of the axisymmetric mean magnetic field decreases as the domain size increases and we find that an m = 1 mode is excited for a full 2π azimuthal extent, reminiscent of the field configurations deduced from observations of rapidly rotating late-type stars. Title: Bipolar Magnetic Structures Driven by Stratified Turbulence with a Coronal Envelope Authors: Warnecke, Jörn; Losada, Illa R.; Brandenburg, Axel; Kleeorin, Nathan; Rogachevskii, Igor Bibcode: 2013ApJ...777L..37W Altcode: 2013arXiv1308.1080W We report the spontaneous formation of bipolar magnetic structures in direct numerical simulations of stratified forced turbulence with an outer coronal envelope. The turbulence is forced with transverse random waves only in the lower (turbulent) part of the domain. Our initial magnetic field is either uniform in the entire domain or confined to the turbulent layer. After about 1-2 turbulent diffusion times, a bipolar magnetic region of vertical field develops with two coherent circular structures that live during one turbulent diffusion time, and then decay during 0.5 turbulent diffusion times. The resulting magnetic field strengths inside the bipolar region are comparable to the equipartition value with respect to the turbulent kinetic energy. The bipolar magnetic region forms a loop-like structure in the upper coronal layer. We associate the magnetic structure formation with the negative effective magnetic pressure instability in the two-layer model. Title: Self-assembly of Shallow Magnetic Spots through Strongly Stratified Turbulence Authors: Brandenburg, Axel; Kleeorin, Nathan; Rogachevskii, Igor Bibcode: 2013ApJ...776L..23B Altcode: 2013arXiv1306.4915B Recent studies have demonstrated that in fully developed turbulence, the effective magnetic pressure of a large-scale field (non-turbulent plus turbulent contributions) can become negative. In the presence of strongly stratified turbulence, this was shown to lead to a large-scale instability that produces spontaneous magnetic flux concentrations. Furthermore, using a horizontal magnetic field, elongated flux concentrations with a strength of a few percent of the equipartition value were found. Here we show that a uniform vertical magnetic field leads to circular magnetic spots of equipartition field strengths. This could represent a minimalistic model of sunspot formation and highlights the importance of two critical ingredients: turbulence and strong stratification. Radiation, ionization, and supergranulation may be important for realistic simulations, but are not critical at the level of a minimalistic model of magnetic spot formation. Title: Microphysics of Cosmic Ray Driven Plasma Instabilities Authors: Bykov, A. M.; Brandenburg, A.; Malkov, M. A.; Osipov, S. M. Bibcode: 2013SSRv..178..201B Altcode: 2013SSRv..tmp...61B; 2013arXiv1304.7081B Energetic nonthermal particles (cosmic rays, CRs) are accelerated in supernova remnants, relativistic jets and other astrophysical objects. The CR energy density is typically comparable with that of the thermal components and magnetic fields. In this review we discuss mechanisms of magnetic field amplification due to instabilities induced by CRs. We derive CR kinetic and magnetohydrodynamic equations that govern cosmic plasma systems comprising the thermal background plasma, comic rays and fluctuating magnetic fields to study CR-driven instabilities. Both resonant and non-resonant instabilities are reviewed, including the Bell short-wavelength instability, and the firehose instability. Special attention is paid to the longwavelength instabilities driven by the CR current and pressure gradient. The helicity production by the CR current-driven instabilities is discussed in connection with the dynamo mechanisms of cosmic magnetic field amplification. Title: Active Region Formation through the Negative Effective Magnetic Pressure Instability Authors: Kemel, Koen; Brandenburg, Axel; Kleeorin, Nathan; Mitra, Dhrubaditya; Rogachevskii, Igor Bibcode: 2013SoPh..287..293K Altcode: 2012arXiv1203.1232K; 2012SoPh..tmp..154K The negative effective magnetic-pressure instability operates on scales encompassing many turbulent eddies, which correspond to convection cells in the Sun. This instability is discussed here in connection with the formation of active regions near the surface layers of the Sun. This instability is related to the negative contribution of turbulence to the mean magnetic pressure that causes the formation of large-scale magnetic structures. For an isothermal layer, direct numerical simulations and mean-field simulations of this phenomenon are shown to agree in many details, for example the onset of the instability occurs at the same depth. This depth increases with increasing field strength, such that the growth rate of this instability is independent of the field strength, provided the magnetic structures are fully contained within the domain. A linear stability analysis is shown to support this finding. The instability also leads to a redistribution of turbulent intensity and gas pressure that could provide direct observational signatures. Title: Astrophysical Hydromagnetic Turbulence Authors: Brandenburg, A.; Lazarian, A. Bibcode: 2013SSRv..178..163B Altcode: 2013arXiv1307.5496B; 2013SSRv..tmp...83B Recent progress in astrophysical hydromagnetic turbulence is being reviewed. The physical ideas behind the now widely accepted Goldreich-Sridhar model and its extension to compressible magnetohydrodynamic turbulence are introduced. Implications for cosmic ray diffusion and acceleration is being discussed. Dynamo-generated magnetic fields with and without helicity are contrasted against each other. Certain turbulent transport processes are being modified and often suppressed by anisotropy and inhomogeneities of the turbulence, while others are being produced by such properties, which can lead to new large-scale instabilities of the turbulent medium. Applications of various such processes to astrophysical systems are being considered. Title: Can Planetesimals Form by Collisional Fusion? Authors: Mitra, Dhrubaditya; Wettlaufer, J. S.; Brandenburg, Axel Bibcode: 2013ApJ...773..120M Altcode: 2013arXiv1306.3672M As a test bed for the growth of protoplanetary bodies in a turbulent circumstellar disk, we examine the fate of a boulder using direct numerical simulations of particle seeded gas flowing around it. We provide an accurate description of the flow by imposing no-slip and non-penetrating boundary conditions on the boulder surface using the immersed boundary method pioneered by Peskin. Advected by the turbulent disk flow, the dust grains collide with the boulder and we compute the probability density function of the normal component of the collisional velocity. Through this examination of the statistics of collisional velocities, we test the recently developed concept of collisional fusion which provides a physical basis for a range of collisional velocities exhibiting perfect sticking. A boulder can then grow sufficiently rapidly to settle into a Keplerian orbit on disk evolution timescales. Title: Surface flux concentrations in a spherical α2 dynamo Authors: Jabbari, S.; Brandenburg, A.; Kleeorin, N.; Mitra, D.; Rogachevskii, I. Bibcode: 2013A&A...556A.106J Altcode: 2013arXiv1302.5841J Context. In the presence of strong density stratification, turbulence can lead to the large-scale instability of a horizontal magnetic field if its strength is in a suitable range (around a few percent of the turbulent equipartition value). This instability is related to a suppression of the turbulent pressure so that the turbulent contribution to the mean magnetic pressure becomes negative. This results in the excitation of a negative effective magnetic pressure instability (NEMPI). This instability has so far only been studied for an imposed magnetic field.
Aims: We want to know how NEMPI works when the mean magnetic field is generated self-consistently by an α2 dynamo, whether it is affected by global spherical geometry, and whether it can influence the properties of the dynamo itself.
Methods: We adopt the mean-field approach, which has previously been shown to provide a realistic description of NEMPI in direct numerical simulations. We assume axisymmetry and solve the mean-field equations with the Pencil Code for an adiabatic stratification at a total density contrast in the radial direction of ≈4 orders of magnitude.
Results: NEMPI is found to work when the dynamo-generated field is about 4% of the equipartition value, which is achieved through strong α quenching. This instability is excited in the top 5% of the outer radius, provided the density contrast across this top layer is at least 10. NEMPI is found to occur at lower latitudes when the mean magnetic field is stronger. For weaker fields, NEMPI can make the dynamo oscillatory with poleward migration.
Conclusions: NEMPI is a viable mechanism for producing magnetic flux concentrations in a strongly stratified spherical shell in which a magnetic field is generated by a strongly quenched α effect dynamo. Title: Data assimilation for stratified convection Authors: Svedin, Andreas; Cuéllar, Milena C.; Brandenburg, Axel Bibcode: 2013MNRAS.433.2278S Altcode: 2012arXiv1207.7314S; 2013MNRAS.tmp.1606S We show how the 3DVAR data assimilation methodology can be used in the astrophysical context of a two-dimensional convection flow. We study the way in which this variational approach finds best estimates of the current state of the flow from a weighted average of model states and observations. We use numerical simulations to generate synthetic observations of a vertical two-dimensional slice of the outer part of the solar convection zone for varying noise levels, and implement 3DVAR when the covariance matrices are diagonal and proportional to the identity matrix. Our simulation results demonstrate the capability of 3DVAR to produce error estimates of system states that can be more than two orders of magnitude below the original noise level present in the observations. This work illustrates the importance of applying data to obtain accurate model estimates given a set of observations. It also exemplifies how data assimilation techniques can be applied to simulations of stratified convection. Title: Coherent structures and the saturation of a nonlinear dynamo Authors: Rempel, Erico L.; Chian, Abraham C. -L.; Brandenburg, Axel; Muñoz, Pablo R.; Shadden, Shawn C. Bibcode: 2013JFM...729..309R Altcode: 2012arXiv1210.6637R Eulerian and Lagrangian tools are used to detect coherent structures in the velocity and magnetic fields of a mean--field dynamo, produced by direct numerical simulations of the three--dimensional compressible magnetohydrodynamic equations with an isotropic helical forcing and moderate Reynolds number. Two distinct stages of the dynamo are studied, the kinematic stage, where a seed magnetic field undergoes exponential growth, and the saturated regime. It is shown that the Lagrangian analysis detects structures with greater detail, besides providing information on the chaotic mixing properties of the flow and the magnetic fields. The traditional way of detecting Lagrangian coherent structures using finite--time Lyapunov exponents is compared with a recently developed method called function M. The latter is shown to produce clearer pictures which readily permit the identification of hyperbolic regions in the magnetic field, where chaotic transport/dispersion of magnetic field lines is highly enhanced. Title: Competition of rotation and stratification in flux concentrations Authors: Losada, I. R.; Brandenburg, A.; Kleeorin, N.; Rogachevskii, I. Bibcode: 2013A&A...556A..83L Altcode: 2012arXiv1212.4077L Context. In a strongly stratified turbulent layer, a uniform horizontal magnetic field can become unstable and spontaneously form local flux concentrations due to a negative contribution of turbulence to the large-scale (mean-field) magnetic pressure. This mechanism, which is called negative effective magnetic pressure instability (NEMPI), is of interest in connection with dynamo scenarios in which most of the magnetic field resides in the bulk of the convection zone and not at the bottom, as is often assumed. Recent work using mean-field hydromagnetic equations has shown that NEMPI becomes suppressed at rather low rotation rates with Coriolis numbers as low as 0.1.
Aims: Here we extend these earlier investigations by studying the effects of rotation both on the development of NEMPI and on the effective magnetic pressure. We also quantify the kinetic helicity resulting from direct numerical simulations (DNS) with Coriolis numbers and strengths of stratification comparable to values near the solar surface and compare it with earlier work at smaller scale separation ratios. Further, we estimate the expected observable signals of magnetic helicity at the solar surface.
Methods: To calculate the rotational effect on the effective magnetic pressure we consider both DNS and analytical studies using the τ approach. To study the effects of rotation on the development of NEMPI we use both DNS and mean-field calculations of the three-dimensional hydromagnetic equations in a Cartesian domain.
Results: We find that the growth rates of NEMPI from earlier mean-field calculations are well reproduced with DNS, provided the Coriolis number is below 0.06. In that case, kinetic and magnetic helicities are found to be weak and the rotational effect on the effective magnetic pressure is negligible as long as the production of flux concentrations is not inhibited by rotation. For faster rotation, dynamo action becomes possible. However, there is an intermediate range of rotation rates where dynamo action on its own is not yet possible, but the rotational suppression of NEMPI is being alleviated.
Conclusions: Production of magnetic flux concentrations through the suppression of turbulent pressure appears to be possible only in the uppermost layers of the Sun, where the convective turnover time is less than two hours. Title: Solar-like differential rotation and equatorward migration in a convective dynamo with a coronal envelope Authors: Warnecke, J.; Käpylä, P. J.; Mantere, M. J.; Brandenburg, A. Bibcode: 2013IAUS..294..307W Altcode: 2012arXiv1211.0452W We present results of convective turbulent dynamo simulations including a coronal layer in a spherical wedge. We find an equatorward migration of the radial and azimuthal fields similar to the behavior of sunspots during the solar cycle. The migration of the field coexist with a spoke-like differential rotation and anti-solar (clockwise) meridional circulation. Even though the migration extends over the whole convection zone, the mechanism causing this is not yet fully understood. Title: Non-linear and chaotic dynamo regimes Authors: Brandenburg, Axel Bibcode: 2013IAUS..294..387B Altcode: 2013arXiv1305.1952B An update is given on the current status of solar and stellar dynamos. At present, it is still unclear why stellar cycle frequencies increase with rotation frequency in such a way that their ratio increases with stellar activity. The small-scale dynamo is expected to operate in spite of a small value of the magnetic Prandtl number in stars. Whether or not the global magnetic activity in stars is a shallow or deeply rooted phenomenon is another open question. Progress in demonstrating the presence and importance of magnetic helicity fluxes in dynamos is briefly reviewed, and finally the role of nonlocality is emphasized in modeling stellar dynamos using the mean-field approach. On the other hand, direct numerical simulations have now come to the point where the models show solar-like equatorward migration that can be compared with observations and that need to be understood theoretically. Title: Topological constraints on magnetic field relaxation Authors: Candelaresi, Simon; Brandenburg, Axel Bibcode: 2013IAUS..294..353C Altcode: 2012arXiv1212.0879C Magnetic field relaxation is determined by both the field's geometry and its topology. For relaxation processes, however, it turns out that its topology is a much more stringent constraint. As quantifier for the topology we use magnetic helicity and test whether it is a stronger condition than the linking of field lines. Further, we search for evidence of other topological invariants, which give rise to further restrictions in the field's relaxation. We find that magnetic helicity is the sole determinant in most cases. Nevertheless, we see evidence for restrictions not captured through magnetic helicity. Title: Non-uniformity effects in the negative effective magnetic pressure instability Authors: Kemel, K.; Brandenburg, A.; Kleeorin, N.; Rogachevskii, I. Bibcode: 2013PhST..155a4027K Altcode: 2012arXiv1208.0517K In direct numerical simulations of strongly stratified turbulence we have previously studied the development of large scale magnetic structures starting from a uniform background field. This is caused by an instability resulting from a negative contribution of small-scale turbulence to the effective (mean-field) magnetic pressure, and was qualitatively reproduced in mean-field simulations (MFS) where this pressure reduction was modeled as a function of the mean magnetic field normalized by the equipartition field. We now investigate the effect of mean current density on the turbulent pressure reduction. In our MFS, such currents are associated with sharp gradients of the growing structures. We find that an enhanced mean current density increases the suppression of the turbulent pressure. Title: Flux concentrations in turbulent convection Authors: Käpylä, Petri J.; Brandenburg, Axel; Kleeorin, Nathan; Mantere, Maarit J.; Rogachevskii, Igor Bibcode: 2013IAUS..294..283K Altcode: 2012arXiv1211.2962K We present preliminary results from high resolution magneto-convection simulations where we find the formation of flux concentrations from an initially uniform magnetic field. The structures appear in roughly ten convective turnover times and live close to a turbulent diffusion time. The time scales are compatible with the negative effective magnetic pressure instability (NEMPI), although structure formation is not restricted to regions where the effective magnetic pressure is negative. Title: A mean field dynamo from negative eddy diffusivity Authors: Devlen, Ebru; Brandenburg, Axel; Mitra, Dhrubaditya Bibcode: 2013MNRAS.432.1651D Altcode: 2013MNRAS.tmp.1243D; 2012arXiv1212.2626D Using direct numerical simulations, we verify that Roberts-IV flow exhibits dynamo action dominated by horizontally averaged large-scale magnetic field. With the test-field method, we compute the turbulent magnetic diffusivity and find that it is negative and overcomes the molecular diffusivity, thus explaining quantitatively the large-scale dynamo for magnetic Reynolds numbers above ≈8. As expected for a dynamo of this type, but contrary to α-effect dynamos, the two horizontal field components grow independently of each other and have arbitrary amplitude ratios and phase differences. Small length-scales of the mean magnetic field are shown to be stabilized by the turbulent magnetic diffusivity becoming positive at larger wavenumbers. Oscillatory decaying or growing solutions have also been found in certain wavenumber intervals and sufficiently large values of the magnetic Reynolds number. For magnetic Reynolds numbers below ≈0.5, the turbulent magnetic diffusivity is confirmed to be positive, as expected for all incompressible flows. Earlier claims of a dynamo driven by a modified Taylor-Green flow through negative eddy diffusivity could not be confirmed. Title: Evolution of primordial magnetic fields from phase transitions Authors: Kahniashvili, Tina; Tevzadze, Alexander G.; Brandenburg, Axel; Neronov, Andrii Bibcode: 2013PhRvD..87h3007K Altcode: 2012arXiv1212.0596K We consider the evolution of primordial magnetic fields generated during cosmological, electroweak, or QCD phase transitions. We assume that the magnetic field generation can be described as an injection of magnetic energy to cosmological plasma at a given scale determined by the moment of magnetic field generation. A high Reynolds number ensures strong coupling between the magnetic field and fluid motions. The subsequent evolution of the magnetic field is governed by decaying hydromagnetic turbulence. Both our numerical simulations and a phenomenological description allow us to recover “universal” laws for the decay of magnetic energy and the growth of magnetic correlation length in the turbulent (low-viscosity) regime. In particular, we show that during the radiation-dominated epoch, the energy and correlation length of nonhelical magnetic fields scale as conformal time to the powers -1/2 and +1/2, respectively. For helical magnetic fields, the energy and correlation length scale as conformal time to the powers -1/3 and +2/3, respectively. The universal decay law of the magnetic field implies that the strength of the magnetic field generated during the QCD phase transition could reach ∼10-9G with the present-day correlation length ∼50kpc. The fields generated at the electroweak phase transition could be as strong as ∼10-10G with correlation lengths reaching ∼0.3kpc. These values of the magnetic fields are consistent with the lower bounds of the extragalactic magnetic fields. Title: Kinetic helicity needed to drive large-scale dynamos Authors: Candelaresi, Simon; Brandenburg, Axel Bibcode: 2013PhRvE..87d3104C Altcode: 2012arXiv1208.4529C Magnetic field generation on scales that are large compared with the scale of the turbulent eddies is known to be possible via the so-called α effect when the turbulence is helical and if the domain is large enough for the α effect to dominate over turbulent diffusion. Using three-dimensional turbulence simulations, we show that the energy of the resulting mean magnetic field of the saturated state increases linearly with the product of normalized helicity and the ratio of domain scale to eddy scale, provided this product exceeds a critical value of around unity. This implies that large-scale dynamo action commences when the normalized helicity is larger than the inverse scale ratio. Our results show that the emergence of small-scale dynamo action does not have any noticeable effect on the large-scale dynamo. Recent findings by Pietarila Graham [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.85.066406 85, 066406 (2012)] of a smaller minimal helicity may be an artifact due to the onset of small-scale dynamo action at large magnetic Reynolds numbers. However, the onset of large-scale dynamo action is difficult to establish when the kinetic helicity is small. Instead of random forcing, they used an ABC flow with time-dependent phases. We show that such dynamos saturate prematurely in a way that is reminiscent of inhomogeneous dynamos with internal magnetic helicity fluxes. Furthermore, even for very low fractional helicities, such dynamos display large-scale fields that change direction, which is uncharacteristic of turbulent dynamos. Title: Oscillatory large-scale dynamos from Cartesian convection simulations Authors: Käpylä, P. J.; Mantere, M. J.; Brandenburg, A. Bibcode: 2013GApFD.107..244K Altcode: 2011arXiv1111.6894K We present results from compressible Cartesian convection simulations with and without imposed shear. In the former case the dynamo is expected to be of α2 Ω type, which is generally expected to be relevant for the Sun, whereas the latter case refers to α2 dynamos that are more likely to occur in more rapidly rotating stars whose differential rotation is small. We perform a parameter study where the shear flow and the rotational influence are varied to probe the relative importance of both types of dynamos. Oscillatory solutions are preferred both in the kinematic and saturated regimes when the negative ratio of shear to rotation rates, q ≡ -S/Ω, is between 1.5 and 2, i.e. when shear and rotation are of comparable strengths. Other regions of oscillatory solutions are found with small values of q, i.e. when shear is weak in comparison to rotation, and in the regime of large negative qs, when shear is very strong in comparison to rotation. However, exceptions to these rules also appear so that for a given ratio of shear to rotation, solutions are non-oscillatory for small and large shear, but oscillatory in the intermediate range. Changing the boundary conditions from vertical field to perfect conductor ones changes the dynamo mode from oscillatory to quasi-steady. Furthermore, in many cases an oscillatory solution exists only in the kinematic regime whereas in the nonlinear stage the mean fields are stationary. However, the cases with rotation and no shear are always oscillatory in the parameter range studied here and the dynamo mode does not depend on the magnetic boundary conditions. The strengths of total and large-scale components of the magnetic field in the saturated state, however, are sensitive to the chosen boundary conditions. Title: Introduction Authors: Brandenburg, Axel; Rogachevskii, Igor Bibcode: 2013GApFD.107....1B Altcode: No abstract at ADS Title: Yoshizawa's cross-helicity effect and its quenching Authors: Brandenburg, A.; Rädler, K. -H. Bibcode: 2013GApFD.107..207B Altcode: 2011arXiv1112.1237B A central quantity in mean-field magnetohydrodynamics is the mean electromotive force overlineBE, which in general depends on the mean magnetic field. It may however also have a part independent of the mean magnetic field. Here we study an example of a rotating conducting body of turbulent fluid with non-zero cross-helicity, in which a contribution to overlineBE proportional to the angular velocity occurs (Yoshizawa, A., Self-consistent turbulent dynamo modeling of reversed field pinches and planetary magnetic fields. Phys. Fluids B 1990, 2, 1589-1600). If the forcing is helical, it also leads to an α effect, and large-scale magnetic fields can be generated. For not too rapid rotation, the field configuration is such that Yoshizawa's contribution to overlineBE is considerably reduced compared to the case without α effect. In that case, large-scale flows are also found to be generated. Title: Turbulent dynamos with advective magnetic helicity flux Authors: Del Sordo, F.; Guerrero, G.; Brandenburg, A. Bibcode: 2013MNRAS.429.1686D Altcode: 2012arXiv1205.3502D; 2012MNRAS.tmp..344D Many astrophysical bodies harbour magnetic fields that are thought to be sustained by a dynamo process. However, it has been argued that the production of large-scale magnetic fields by mean-field dynamo action is strongly suppressed at large magnetic Reynolds numbers owing to the conservation of magnetic helicity. This phenomenon is known as catastrophic quenching. Advection of magnetic fields by stellar and galactic winds towards the outer boundaries and away from the dynamo is expected to alleviate such quenching. Here we explore the relative roles played by advective and turbulent-diffusive fluxes of magnetic helicity in the dynamo. In particular, we study how the dynamo is affected by advection. We do this by performing direct numerical simulations of a turbulent dynamo of α2 type driven by forced turbulence in a Cartesian domain in the presence of a flow away from the equator where helicity changes sign. Our results indicate that in the presence of advection, the dynamo, otherwise stationary, becomes oscillatory. We confirm an earlier result for turbulent-diffusive magnetic helicity fluxes that for small magnetic Reynolds numbers (Rm ≲ 100...200, based on the wavenumber of the energy-carrying eddies) the magnetic helicity flux scales less strongly with magnetic Reynolds number (Rm-1/2) than the term describing magnetic helicity destruction by resistivity (Rm-1). Our new results now suggest that for larger Rm the former becomes approximately independent of Rm, while the latter falls off more slowly. We show for the first time that both for weak and stronger winds, the magnetic helicity flux term becomes comparable to the resistive term for Rm ≳ 1000, which is necessary for alleviating catastrophic quenching. Title: Current Status of Turbulent Dynamo Theory Authors: Brandenburg, Axel; Sokoloff, Dmitry; Subramanian, Kandaswamy Bibcode: 2013lsmf.book..371B Altcode: No abstract at ADS Title: New Scaling for the Alpha Effect in Slowly Rotating Turbulence Authors: Brandenburg, A.; Gressel, O.; Käpylä, P. J.; Kleeorin, N.; Mantere, M. J.; Rogachevskii, I. Bibcode: 2013ApJ...762..127B Altcode: 2012arXiv1208.5004B Using simulations of slowly rotating stratified turbulence, we show that the α effect responsible for the generation of astrophysical magnetic fields is proportional to the logarithmic gradient of kinetic energy density rather than that of momentum, as was previously thought. This result is in agreement with a new analytic theory developed in this paper for large Reynolds numbers and slow rotation. Thus, the contribution of density stratification is less important than that of turbulent velocity. The α effect and other turbulent transport coefficients are determined by means of the test-field method. In addition to forced turbulence, we also investigate supernova-driven turbulence and stellar convection. In some cases (intermediate rotation rate for forced turbulence, convection with intermediate temperature stratification, and supernova-driven turbulence), we find that the contribution of density stratification might be even less important than suggested by the analytic theory. Title: Rotational effects on the negative magnetic pressure instability Authors: Losada, I. R.; Brandenburg, A.; Kleeorin, N.; Mitra, D.; Rogachevskii, I. Bibcode: 2012A&A...548A..49L Altcode: 2012arXiv1207.5392L Context. The surface layers of the Sun are strongly stratified. In the presence of turbulence with a weak mean magnetic field, a large-scale instability resulting in the formation of nonuniform magnetic structures, can be excited on the scale of many (more than ten) turbulent eddies (or convection cells). This instability is caused by a negative contribution of turbulence to the effective (mean-field) magnetic pressure and has previously been discussed in connection with the formation of active regions.
Aims: We want to understand the effects of rotation on this instability in both two and three dimensions.
Methods: We use mean-field magnetohydrodynamics in a parameter regime in which the properties of the negative effective magnetic pressure instability have previously been found to agree with properties of direct numerical simulations.
Results: We find that the instability is already suppressed for relatively slow rotation with Coriolis numbers (i.e. inverse Rossby numbers) around 0.2. The suppression is strongest at the equator. In the nonlinear regime, we find traveling wave solutions with propagation in the prograde direction at the equator with additional poleward migration away from the equator.
Conclusions: We speculate that the prograde rotation of the magnetic pattern near the equator might be a possible explanation for the faster rotation speed of magnetic tracers relative to the plasma velocity on the Sun. In the bulk of the domain, kinetic and current helicities are negative in the northern hemisphere and positive in the southern. Title: Magnetic Fields from QCD Phase Transitions Authors: Tevzadze, Alexander G.; Kisslinger, Leonard; Brandenburg, Axel; Kahniashvili, Tina Bibcode: 2012ApJ...759...54T Altcode: 2012arXiv1207.0751T We study the evolution of QCD phase transition-generated magnetic fields (MFs) in freely decaying MHD turbulence of the expanding universe. We consider an MF generation model that starts from basic non-perturbative QCD theory and predicts stochastic MFs with an amplitude of the order of 0.02 μG and small magnetic helicity. We employ direct numerical simulations to model the MHD turbulence decay and identify two different regimes: a "weakly helical" turbulence regime, when magnetic helicity increases during decay, and "fully helical" turbulence, when maximal magnetic helicity is reached and an inverse cascade develops. The results of our analysis show that in the most optimistic scenario the magnetic correlation length in the comoving frame can reach 10 kpc with the amplitude of the effective MF being 0.007 nG. We demonstrate that the considered model of magnetogenesis can provide the seed MF for galaxies and clusters. Title: Evolution of inflation-generated magnetic field through phase transitions Authors: Kahniashvili, Tina; Brandenburg, Axel; Campanelli, Leonardo; Ratra, Bharat; Tevzadze, Alexander G. Bibcode: 2012PhRvD..86j3005K Altcode: 2012arXiv1206.2428K We study the evolution of an inflation-generated magnetic field, due to its coupling to fluid motions, during cosmological phase transitions. We find that the magnetic field stays almost unchanged on large scales, while on small scales, the spectrum is modified in such a way that power at small scales becomes progressively suppressed. We also show that the magnetic field generates turbulent motions in the initially turbulence-free plasma. On large scales, the slope of the resulting kinetic energy spectrum is consistent with that of white noise. Title: Spontaneous Formation of Magnetic Flux Concentrations in Stratified Turbulence Authors: Kemel, Koen; Brandenburg, Axel; Kleeorin, Nathan; Mitra, Dhrubaditya; Rogachevskii, Igor Bibcode: 2012SoPh..280..321K Altcode: 2012SoPh..tmp...48K; 2011arXiv1112.0279K The negative effective magnetic pressure instability discovered recently in direct numerical simulations (DNSs) may play a crucial role in the formation of sunspots and active regions in the Sun and stars. This instability is caused by a negative contribution of turbulence to the effective mean Lorentz force (the sum of turbulent and non-turbulent contributions) and results in the formation of large-scale inhomogeneous magnetic structures from an initially uniform magnetic field. Earlier investigations of this instability in DNSs of stably stratified, externally forced, isothermal hydromagnetic turbulence in the regime of large plasma β are now extended into the regime of larger scale separation ratios where the number of turbulent eddies in the computational domain is about 30. Strong spontaneous formation of large-scale magnetic structures is seen even without performing any spatial averaging. These structures encompass many turbulent eddies. The characteristic time of the instability is comparable to the turbulent diffusion time, L2t, where ηt is the turbulent diffusivity and L is the scale of the domain. DNSs are used to confirm that the effective magnetic pressure does indeed become negative for magnetic field strengths below the equipartition field. The dependence of the effective magnetic pressure on the field strength is characterized by fit parameters that seem to show convergence for larger values of the magnetic Reynolds number. Title: Ejections of Magnetic Structures Above a Spherical Wedge Driven by a Convective Dynamo with Differential Rotation Authors: Warnecke, Jörn; Käpylä, Petri J.; Mantere, Maarit J.; Brandenburg, Axel Bibcode: 2012SoPh..280..299W Altcode: 2012SoPh..tmp..214W; 2011arXiv1112.0505W We combine a convectively driven dynamo in a spherical shell with a nearly isothermal density-stratified cooling layer that mimics some aspects of a stellar corona to study the emergence and ejections of magnetic field structures. This approach is an extension of earlier models, where forced turbulence simulations were employed to generate magnetic fields. A spherical wedge is used which consists of a convection zone and an extended coronal region to ≈ 1.5 times the radius of the sphere. The wedge contains a quarter of the azimuthal extent of the sphere and 150 in latitude. The magnetic field is self-consistently generated by the turbulent motions due to convection beneath the surface. Magnetic fields are found to emerge at the surface and are ejected to the coronal part of the domain. These ejections occur at irregular intervals and are weaker than in earlier work. We tentatively associate these events with coronal mass ejections on the Sun, even though our model of the solar atmosphere is rather simplistic. Title: Mean-field transport in stratified and/or rotating turbulence (Corrigendum) Authors: Brandenburg, A.; Rädler, K. -H.; Kemel, K. Bibcode: 2012A&A...545C...1B Altcode: No abstract at ADS Title: Current Status of Turbulent Dynamo Theory. From Large-Scale to Small-Scale Dynamos Authors: Brandenburg, Axel; Sokoloff, Dmitry; Subramanian, Kandaswamy Bibcode: 2012SSRv..169..123B Altcode: 2012SSRv..tmp...57B; 2012arXiv1203.6195B Several recent advances in turbulent dynamo theory are reviewed. High resolution simulations of small-scale and large-scale dynamo action in periodic domains are compared with each other and contrasted with similar results at low magnetic Prandtl numbers. It is argued that all the different cases show similarities at intermediate length scales. On the other hand, in the presence of helicity of the turbulence, power develops on large scales, which is not present in non-helical small-scale turbulent dynamos. At small length scales, differences occur in connection with the dissipation cutoff scales associated with the respective value of the magnetic Prandtl number. These differences are found to be independent of whether or not there is large-scale dynamo action. However, large-scale dynamos in homogeneous systems are shown to suffer from resistive slow-down even at intermediate length scales. The results from simulations are connected to mean field theory and its applications. Recent work on magnetic helicity fluxes to alleviate large-scale dynamo quenching, shear dynamos, nonlocal effects and magnetic structures from strong density stratification are highlighted. Several insights which arise from analytic considerations of small-scale dynamos are discussed. Title: Magnetic twist: a source and property of space weather Authors: Warnecke, Jörn; Brandenburg, Axel; Mitra, Dhrubaditya AB(; ) Bibcode: 2012JSWSC...2A..11W Altcode: 2012arXiv1203.0959W Aim: We present evidence for finite magnetic helicity density in the heliosphere and numerical models thereof, and relate it to the magnetic field properties of the dynamo in the solar convection zone. Methods: We use simulations and solar wind data to compute magnetic helicity either directly from the simulations or indirectly using time series of the skew-symmetric components of the magnetic correlation tensor. Results: We find that the solar dynamo produces negative magnetic helicity at small scales and positive at large scales. However, in the heliosphere these properties are reversed and the magnetic helicity is now positive at small scales and negative at large scales. We explain this by the fact that a negative diffusive magnetic helicity flux corresponds to a positive gradient of magnetic helicity, which leads to a change of sign from negative to positive values at some radius in the northern hemisphere. Title: Cyclic Magnetic Activity due to Turbulent Convection in Spherical Wedge Geometry Authors: Käpylä, Petri J.; Mantere, Maarit J.; Brandenburg, Axel Bibcode: 2012ApJ...755L..22K Altcode: 2012arXiv1205.4719K We report on simulations of turbulent, rotating, stratified, magnetohydrodynamic convection in spherical wedge geometry. An initially small-scale, random, weak-amplitude magnetic field is amplified by several orders of magnitude in the course of the simulation to form oscillatory large-scale fields in the saturated state of the dynamo. The differential rotation is solar-like (fast equator), but neither coherent meridional poleward circulation nor near-surface shear layer develop in these runs. In addition to a poleward branch of magnetic activity beyond 50° latitude, we find for the first time a pronounced equatorward branch at around 20° latitude, reminiscent of the solar cycle. Title: Cycles and cycle modulations Authors: Brandenburg, Axel; Guerrero, Gustavo Bibcode: 2012IAUS..286...37B Altcode: 2011arXiv1111.3351B Some selected concepts of the solar activity cycle are reviewed. Cycle modulations through a stochastic α effect are being identified with limited scale separation ratios. Three-dimensional turbulence simulations with helicity and shear are compared at two different scale separation ratios. In both cases the level of fluctuations shows relatively little variation with the dynamo cycle. Prospects for a shallow origin of sunspots are discussed in terms of the negative effective magnetic pressure instability. Tilt angles of bipolar active regions are discussed as a consequence of shear rather than the Coriolis force. Title: Cosmic-Ray Current-driven Turbulence and Mean-field Dynamo Effect Authors: Rogachevskii, Igor; Kleeorin, Nathan; Brandenburg, Axel; Eichler, David Bibcode: 2012ApJ...753....6R Altcode: 2012arXiv1204.4246R We show that an α effect is driven by the cosmic-ray (CR) Bell instability exciting left-right asymmetric turbulence. Alfvén waves of a preferred polarization have maximally helical motion, because the transverse motion of each mode is parallel to its curl. We show how large-scale Alfvén modes, when rendered unstable by CR streaming, can create new net flux over any finite region, in the direction of the original large-scale field. We perform direct numerical simulations (DNSs) of a magnetohydrodynamic fluid with a forced CR current and use the test-field method to determine the α effect and the turbulent magnetic diffusivity. As follows from DNS, the dynamics of the instability has the following stages: (1) in the early stage, the small-scale Bell instability that results in the production of small-scale turbulence is excited; (2) in the intermediate stage, there is formation of larger-scale magnetic structures; (3) finally, quasi-stationary large-scale turbulence is formed at a growth rate that is comparable to that expected from the dynamo instability, but its amplitude over much longer timescales remains unclear. The results of DNS are in good agreement with the theoretical estimates. It is suggested that this dynamo is what gives weakly magnetized relativistic shocks such as those from gamma-ray bursts (GRBs) a macroscopic correlation length. It may also be important for large-scale magnetic field amplification associated with CR production and diffusive shock acceleration in supernova remnants (SNRs) and blast waves from GRBs. Magnetic field amplification by Bell turbulence in SNRs is found to be significant, but it is limited owing to the finite time available to the super-Alfvénicly expanding remnant. The effectiveness of the mechanisms is shown to be dependent on the shock velocity. Limits on magnetic field growth in longer-lived systems, such as the Galaxy and unconfined intergalactic CRs, are also discussed. Title: Lagrangian chaos in an ABC-forced nonlinear dynamo Authors: Rempel, Erico L.; C-L Chian, Abraham; Brandenburg, Axel Bibcode: 2012PhyS...86a8405R Altcode: 2012arXiv1201.4324R The Lagrangian properties of the velocity field in a magnetized fluid are studied using three-dimensional simulations of a helical magnetohydrodynamic dynamo. We compute the attracting and repelling Lagrangian coherent structures (LCS), which are dynamic lines and surfaces in the velocity field that delineate particle transport in flows with chaotic streamlines and act as transport barriers. Two dynamo regimes are explored, one with a robust coherent mean magnetic field and the other with intermittent bursts of magnetic energy. The LCS and the statistics of the finite-time Lyapunov exponents indicate that the stirring/mixing properties of the velocity field decay as a linear function of magnetic energy. The relevance of this study to the solar dynamo problem is also discussed. Title: Spontaneous chiral symmetry breaking in the Tayler instability Authors: Del Sordo, Fabio; Bonanno, Alfio; Brandenburg, Axel; Mitra, Dhrubaditya Bibcode: 2012IAUS..286...65D Altcode: 2011arXiv1111.1742D The chiral symmetry breaking properties of the Tayler instability are discussed. Effective amplitude equations are determined in one case. This model has three free parameters that are determined numerically. Comparison with chiral symmetry breaking in biochemistry is made. Title: Coronal ejections from convective spherical shell dynamos Authors: Warnecke, J.; Käpylä, P. J.; Mantere, M. J.; Brandenburg, A. Bibcode: 2012IAUS..286..154W Altcode: 2011arXiv1111.1763W We present a three-dimensional model of rotating convection combined with a simplified model of a corona in spherical coordinates. The motions in the convection zone generate a large-scale magnetic field which is sporadically ejected into the outer layers above. Our model corona is approximately isothermal, but it includes density stratification due to gravity. Title: Breakdown of chiral symmetry during saturation of the Tayler instability Authors: Bonanno, Alfio; Brandenburg, Axel; Del Sordo, Fabio; Mitra, Dhrubaditya Bibcode: 2012PhRvE..86a6313B Altcode: 2012arXiv1204.0081B We study spontaneous breakdown of chiral symmetry during the nonlinear evolution of the Tayler instability. We start with an initial steady state of zero helicity. Within linearized perturbation calculations, helical perturbations of this initial state have the same growth rate for either sign of helicity. Direct numerical simulations (DNS) of the fully nonlinear equations, however, show that an infinitesimal excess of one sign of helicity in the initial perturbation gives rise to a saturated helical state. We further show that this symmetry breaking can be described by weakly nonlinear finite-amplitude equations with undetermined coefficients which can be deduced solely from symmetry consideration. By fitting solutions of the amplitude equations to data from DNS, we further determine the coefficients of the amplitude equations. Title: Mean-field closure parameters for passive scalar turbulence Authors: Snellman, J. E.; Rheinhardt, M.; Käpylä, P. J.; Mantere, M. J.; Brandenburg, A. Bibcode: 2012PhyS...86a8406S Altcode: 2011arXiv1112.4777S Direct numerical simulations (DNSs) of isotropically forced homogeneous stationary turbulence with an imposed passive scalar concentration gradient are compared with an analytical closure model which provides evolution equations for the mean passive scalar flux and variance. Triple correlations of fluctuations appearing in these equations are described in terms of relaxation terms proportional to the quadratic correlations. Three methods are used to extract the relaxation timescales τi from DNSs. Firstly, we insert the closure ansatz into our equations, assume stationarity and solve for τi. Secondly, we use only the closure ansatz itself and obtain τi from the ratio of quadratic and triple correlations. Thirdly, we remove the imposed passive scalar gradient and fit an exponential law to the decaying solution. We vary the Reynolds (Re) and Péclet numbers (while fixing their ratio at unity) and the degree of scale separation and find for large Re a fair correspondence between the different methods. The ratio of the turbulent relaxation time of the passive scalar flux to the turnover time of the turbulent eddies is of the order of 3, which is in remarkable agreement with earlier work. Finally, we make an effort to extract the relaxation timescales relevant for the viscous and diffusive effects. We find two regimes that are valid for small and large Re, respectively, but the dependence of the parameters on scale separation suggests that they are not universal. Title: Detection of turbulent thermal diffusion of particles in numerical simulations Authors: Haugen, Nils Erland L.; Kleeorin, Nathan; Rogachevskii, Igor; Brandenburg, Axel Bibcode: 2012PhFl...24g5106H Altcode: 2011arXiv1101.4188H The phenomenon of turbulent thermal diffusion in temperature-stratified turbulence causing a non-diffusive turbulent flux (i.e., non-counter-gradient transport) of inertial and non-inertial particles in the direction of the turbulent heat flux is found using direct numerical simulations (DNS). In simulations with and without gravity, this phenomenon is found to cause a peak in the particle number density around the minimum of the mean fluid temperature for Stokes numbers less than 1, where the Stokes number is the ratio of particle Stokes time to turbulent Kolmogorov time at the viscous scale. Turbulent thermal diffusion causes the formation of inhomogeneities in the spatial distribution of inertial particles whose scale is large in comparison with the integral scale of the turbulence. The strength of this effect is maximum for Stokes numbers around unity, and decreases again for larger values. The dynamics of inertial particles is studied using Lagrangian modelling in forced temperature-stratified turbulence, whereas non-inertial particles and the fluid are described using DNS in an Eulerian framework. Title: Magnetic helicity fluxes and their effect on stellar dynamos Authors: Candelaresi, Simon; Brandenburg, Axel Bibcode: 2012IAUS..286...49C Altcode: 2011arXiv1111.2023C Magnetic helicity fluxes in turbulently driven α2 dynamos are studied to demonstrate their ability to alleviate catastrophic quenching. A one-dimensional mean-field formalism is used to achieve magnetic Reynolds numbers of the order of 105. We study both diffusive magnetic helicity fluxes through the mid-plane as well as those resulting from the recently proposed alternate dynamic quenching formalism. By adding shear we make a parameter scan for the critical values of the shear and forcing parameters for which dynamo action occurs. For this αΩ dynamo we find that the preferred mode is antisymmetric about the mid-plane. This is also verified in 3-D direct numerical simulations. Title: Special issue on current research in astrophysical magnetism Authors: Kosovichev, Alexander; Lundstedt, Henrik; Brandenburg, Axel Bibcode: 2012PhyS...86a0201K Altcode: Much of what Hannes Alfvén envisaged some 70 years ago has now penetrated virtually all branches of astrophysical research. Indeed, magnetic fields can display similar properties over a large range of scales. We have therefore been able to take advantage of the transparency of galaxies and the interstellar medium to obtain measurements inside them. On the other hand, the Sun is much closer, allowing us to obtain a detailed picture of the interaction of flows and magnetic fields at the surface, and more recently in the interior by helioseismology. Moreover, the solar timescales are generally much shorter, making studies of dynamical processes more direct.

This special issue on current research in astrophysical magnetism is based on work discussed during a one month Nordita program Dynamo, Dynamical Systems and Topology and comprises papers that fall into four different categories (A)-(D).

(A) Papers on small-scale magnetic fields and flows in astrophysics 1. E M de Gouveia Dal Pino, M R M Leão, R Santos-Lima, G Guerrero, G Kowal and A Lazarian Magnetic flux transport by turbulent reconnection in astrophysical flows 2. Philip R Goode, Valentyna Abramenko and Vasyl Yurchyshyn New solar telescope in Big Bear: evidence for super-diffusivity and small-scale solar dynamos? 3. I N Kitiashvili, A G Kosovichev, N N Mansour, S K Lele and A A Wray Vortex tubes of turbulent solar convection

The above collection of papers begins with a review of astrophysical reconnection and introduces the concept of dynamos necessary to explain the existence of contemporary magnetic fields both on galactic and solar scales (paper 1). This is complemented by observations with the new Big Bear Solar Observatory telescope, allowing us to see magnetic field amplification on small scales (paper 2). This in turn is complemented by realistic simulations of subsurface and surface flow patterns (paper 3).

(B) Papers on theoretical approaches to turbulent fluctuations 4. Nathan Kleeorin and Igor Rogachevskii Growth rate of small-scale dynamo at low magnetic Prandtl numbers 5. Erico L Rempel, Abraham C-L Chian and Axel Brandenburg Lagrangian chaos in an ABC-forced nonlinear dynamo 6. J E Snellman, M Rheinhardt, P J Käpylä, M J Mantere and A Brandenburg Mean-field closure parameters for passive scalar turbulence

Research in dynamo theory has been actively pursued for over half a century. It started by trying to understand the large-scale magnetic fields of the Sun and the Earth, and subsequently also in galaxies. Such large-scale fields can nowadays be understood in terms of mean-field dynamo theory that explains the possibility of large-scale field generation under anisotropic conditions lacking mirror symmetry. However, even when none of this is the case, dynamos can still work, and they are called small-scale dynamos that were referred to in paper 2. This was studied originally under the assumption that the flow is smooth compared with the magnetic field, but in the Sun the opposite is the case. This is because viscosity is much smaller than magnetic diffusivity, i.e., their ratio, which is the magnetic Prandtl number, is small. In that case the physics of small-scale dynamos changes, but dynamos still exist even then (paper 4). Tracing the flow lines in nonlinear small-scale dynamos is important for understanding their mixing properties (paper 5). Turbulent mixing is a generic concept that applies not only to magnetic field, but also to passive scalars which are often used as a prototype for studying this. Turbulence simulations have helped tremendously in quantifying the ability of turbulent flows to mix, but the more we know, the more complicated it becomes. It turns out that spatial and temporal coupling is an important consideration for allowing accurate comparison between numerical simulations and mean-field theory (paper 6).

(C) The large-scale solar cycle 7. V V Pipin and D D Sokoloff The fluctuating α-effect and Waldmeier relations in the nonlinear dynamo models1 8. Radostin D Simitev and Friedrich H Busse Solar cycle properties described by simple convection-driven dynamos

The mean-field concept has helped us constructing detailed models of the solar cycle and to make comparison with observed features of the solar 11-year cycle. One such feature is the Waldmeier relation between growth time and amplitude of the cycle, and there is another relation for the declining part of the cycle. These relations reflect nonlinear aspects of the model and therefore constitute an important test of the model (paper 7). While mean-field theory is a useful concept for modeling solar activity, it must eventually be tested against fully three-dimensional simulations. At present, such simulations are often quite idealized, because only the large scales of the turbulent convection of stars can be resolved. Nevertheless, numerical simulations begin to show many properties that are also seen in the Sun (paper 8).

(D) Flow and dynamo properties in spherical shells 9. Maxim Reshetnyak and Pavel Hejda Kinetic energy cascades in quasi-geostrophic convection in a spherical shell 10. Radostin D Simitev and Friedrich H Busse Bistable attractors in a model of convection-driven spherical dynamos

As the rotation speed is increased, the flow becomes more strongly constrained by the Coriolis force. In a spherical shell, such a flow is additionally constrained by gravity, or at least by the geometry of the domain. Such flows are called geostrophic. Only now are we beginning to learn about the subtle properties of the kinetic energy cascade in such flows (paper 9). Turbulent systems are highly nonlinear and it is in principle possible to find multiple solutions of the equations even for the same boundary and initial conditions. For turbulent systems, we can only ask about the statistical properties of the solutions, and the question of multiple solutions is then less obvious. However, in turbulent dynamos in convective shells, a nice example has been found where this is possible. A detailed account of this is given in paper 10.

Most of the participants of the Nordita program were able to stay for the full month of the program, allowing them to think about new ideas that will be reflected not only in papers on the short term, but also in new projects and collaborations on a larger scale in the years to come. We therefore thank Nordita for providing a stimulating atmosphere and acknowledge the generous support.

1This paper has been published as V V Pipin and D D Sokoloff 2011 Phys. Scr. 84 065903. Title: Negative effective magnetic pressure in turbulent convection Authors: Käpylä, P. J.; Brandenburg, A.; Kleeorin, N.; Mantere, M. J.; Rogachevskii, I. Bibcode: 2012MNRAS.422.2465K Altcode: 2011arXiv1104.4541K We investigate the effects of weakly and strongly stratified turbulent convection on the mean effective Lorentz force, and especially on the mean effective magnetic pressure. Earlier studies with isotropically forced non-stratified and stratified turbulence have shown that the contribution of the turbulence to the mean magnetic pressure is negative for mean horizontal magnetic fields that are smaller than the equipartition strength, so that the effective mean magnetic pressure that takes into account the turbulence effects can be negative. Compared with earlier cases of forced turbulence with an isothermal equation of state, we find that the turbulence effect is similar to or even stronger in the present case of turbulent convection. This is argued to be due to the anisotropy of turbulence in the vertical direction. Another important difference compared with earlier studies is the presence of an evolution equation for the specific entropy. Mean-field modelling with entropy evolution indicates that the negative effective magnetic pressure can still lead to a large-scale instability which forms local flux concentrations, even though the specific entropy evolution tends to have a stabilizing effect when applied to a stably stratified (e.g. isothermal) layer. It is argued that this large-scale instability could be important for the formation of solar large-scale magnetic structures such as active regions. Title: Transport of angular momentum and chemical species by anisotropic mixing in stellar radiative interiors Authors: Kitchatinov, L. L.; Brandenburg, A. Bibcode: 2012AN....333..230K Altcode: 2012arXiv1201.2484K Small levels of turbulence can be present in stellar radiative interiors due to, e.g., the instability of rotational shear. In this paper we estimate turbulent transport coefficients for stably stratified rotating stellar radiation zones. Stable stratification induces strong anisotropy with a very small ratio of radial-to-horizontal turbulence intensities. Angular momentum is transported mainly due to the correlation between azimuthal and radial turbulent motions induced by the Coriolis force. This non-diffusive transport known as the Λ-effect has outward direction in radius and is much more efficient compared to the effect of radial eddy viscosity. Chemical species are transported by small radial diffusion only. This result is confirmed using direct numerical simulations combined with the test-scalar method. As a consequence of the non-diffusive transport of angular momentum, the estimated characteristic time of rotational coupling (⪉100 Myr) between radiative core and convective envelope in young solar-type stars is much shorter compared to the time-scale of Lithium depletion (∼1 Gyr). Title: Kinetic helicity decay in linearly forced turbulence Authors: Brandenburg, A.; Petrosyan, A. Bibcode: 2012AN....333..195B Altcode: 2010arXiv1012.1464B The decay of kinetic helicity is studied in numerical models of forced turbulence using either an externally imposed forcing function as an inhomogeneous term in the equations or, alternatively, a term linear in the velocity giving rise to a linear instability. The externally imposed forcing function injects energy at the largest scales, giving rise to a turbulent inertial range with nearly constant energy flux while for linearly forced turbulence the spectral energy is maximum near the dissipation wavenumber. Kinetic helicity is injected once a statistically steady state is reached, but it is found to decay on a turbulent time scale regardless of the nature of the forcing and the value of the Reynolds number. Title: Commission 12: Solar Radiation and Structure Authors: Kosovichev, Alexander; Cauzzi, Gianna; Pillet, Valentin Martinez; Asplund, Martin; Brandenburg, Axel; Chou, Dean-Yi; Christensen-Dalsgaard, Jorgen; Gan, Weiqun; Kuznetsov, Vladimir D.; Rovira, Marta G.; Shchukina, Nataliya; Venkatakrishnan, P. Bibcode: 2012IAUTA..28...81K Altcode: 2012IAUTB..28...81K Commission 12 of the International Astronomical Union encompasses investigations of the internal structure and dynamics of the Sun, mostly accessible through the techniques of local and global helioseismology, the quiet solar atmosphere, solar radiation and its variability, and the nature of relatively stable magnetic structures like sunspots, faculae and the magnetic network. The Commission sees participation of over 350 scientists worldwide. Title: The Negative Effective Magnetic Pressure in Stratified Forced Turbulence Authors: Brandenburg, Axel; Kemel, Koen; Kleeorin, Nathan; Rogachevskii, Igor Bibcode: 2012ApJ...749..179B Altcode: 2010arXiv1005.5700B To understand the basic mechanism of the formation of magnetic flux concentrations, we determine by direct numerical simulations the turbulence contributions to the mean magnetic pressure in a strongly stratified isothermal layer with large plasma beta, where a weak uniform horizontal mean magnetic field is applied. The negative contribution of turbulence to the effective mean magnetic pressure is determined for strongly stratified forced turbulence over a range of values of magnetic Reynolds and Prandtl numbers. Small-scale dynamo action is shown to reduce the negative effect of turbulence on the effective mean magnetic pressure. However, the turbulence coefficients describing the negative effective magnetic pressure phenomenon are found to converge for magnetic Reynolds numbers between 60 and 600, which is the largest value considered here. In all these models, the turbulent intensity is arranged to be nearly independent of height, so the kinetic energy density decreases with height due to the decrease in density. In a second series of numerical experiments, the turbulent intensity increases with height such that the turbulent kinetic energy density is nearly independent of height. Turbulent magnetic diffusivity and turbulent pumping velocity are determined with the test-field method for both cases. The vertical profile of the turbulent magnetic diffusivity is found to agree with what is expected based on simple mixing length expressions. Turbulent pumping is shown to be down the gradient of turbulent magnetic diffusivity, but it is twice as large as expected. Corresponding numerical mean-field models are used to show that a large-scale instability can occur in both cases, provided the degree of scale separation is large enough and hence the turbulent magnetic diffusivity small enough. Title: Catastrophic Quenching in αΩ Dynamos Revisited Authors: Hubbard, Alexander; Brandenburg, Axel Bibcode: 2012ApJ...748...51H Altcode: 2011arXiv1107.0238H At large magnetic Reynolds numbers, magnetic helicity evolution plays an important role in astrophysical large-scale dynamos. The recognition of this fact led to the development of the dynamical α quenching formalism, which predicts catastrophically low mean fields in open systems. Here, we show that in oscillatory αΩ dynamos this formalism predicts an unphysical magnetic helicity transfer between scales. An alternative technique is proposed where this artifact is removed by using the evolution equation for the magnetic helicity of the total field in the shearing advective gauge. In the traditional dynamical α quenching formalism, this can be described by an additional magnetic helicity flux of small-scale fields that does not appear in homogeneous α2 dynamos. In αΩ dynamos, the alternative formalism is shown to lead to larger saturation fields than what has been obtained in some earlier models with the traditional formalism. We have compared the predictions of the two formalisms to results of direct numerical simulations, finding that the alternative formulation provides a better fit. This suggests that worries about catastrophic dynamo behavior in the limit of large magnetic Reynolds number are unfounded. Title: Dynamics of saturated energy condensation in two-dimensional turbulence Authors: Chan, Chi-kwan; Mitra, Dhrubaditya; Brandenburg, Axel Bibcode: 2012PhRvE..85c6315C Altcode: 2011arXiv1109.6937C In two-dimensional forced Navier-Stokes turbulence, energy cascades to the largest scales in the system to form a pair of coherent vortices known as the Bose condensate. We show, both numerically and analytically, that the energy condensation saturates and the system reaches a statistically stationary state. The time scale of saturation is inversely proportional to the viscosity and the saturation energy level is determined by both the viscosity and the force. We further show that, without sufficient resolution to resolve the small-scale enstrophy spectrum, numerical simulations can give a spurious result for the saturation energy level. We also find that the movement of the condensate is similar to the motion of an inertial particle with an effective drag force. Furthermore, we show that the profile of the saturated coherent vortices can be described by a Gaussian core with exponential wings. Title: Scaling and intermittency in incoherent α-shear dynamo Authors: Mitra, Dhrubaditya; Brandenburg, Axel Bibcode: 2012MNRAS.420.2170M Altcode: 2011arXiv1107.2419M We consider mean-field dynamo models with fluctuating α effect, both with and without large-scale shear. The α effect is chosen to be Gaussian white noise with zero mean and a given covariance. In the presence of shear, we show analytically that (in infinitely large domains) the mean-squared magnetic field shows exponential growth. The growth rate of the fastest growing mode is proportional to the shear rate. This result agrees with earlier numerical results of Yousef et al. and the recent analytical treatment by Heinemann, McWilliams & Schekochihin who use a method different from ours. In the absence of shear, an incoherent α2 dynamo may also be possible. We further show by explicit calculation of the growth rate of third- and fourth-order moments of the magnetic field that the probability density function of the mean magnetic field generated by this dynamo is non-Gaussian. Title: Mean-field transport in stratified and/or rotating turbulence Authors: Brandenburg, A.; Rädler, K. -H.; Kemel, K. Bibcode: 2012A&A...539A..35B Altcode: 2011arXiv1108.2264B Context. The large-scale magnetic fields of stars and galaxies are often described in the framework of mean-field dynamo theory. At moderate magnetic Reynolds numbers, the transport coefficients defining the mean electromotive force can be determined from simulations. This applies analogously also to passive scalar transport.
Aims: We investigate the mean electromotive force in the kinematic framework, that is, ignoring the back-reaction of the magnetic field on the fluid velocity, under the assumption of axisymmetric turbulence determined by the presence of either rotation, density stratification, or both. We use an analogous approach for the mean passive scalar flux. As an alternative to convection, we consider forced turbulence in an isothermal layer. When using standard ansatzes, the mean magnetic transport is then determined by nine, and the mean passive scalar transport by four coefficients. We give results for all these transport coefficients.
Methods: We use the test-field method and the test-scalar method, where transport coefficients are determined by solving sets of equations with properly chosen mean magnetic fields or mean scalars. These methods are adapted to mean fields which may depend on all three space coordinates.
Results: We find the anisotropy of turbulent diffusion to be moderate in spite of rapid rotation or strong density stratification. Contributions to the mean electromotive force determined by the symmetric part of the gradient tensor of the mean magnetic field, which were ignored in several earlier investigations, turn out to be important. In stratified rotating turbulence, the α effect is strongly anisotropic, suppressed along the rotation axis on large length scales, but strongly enhanced at intermediate length scales. Also the OO×meanJJ effect is enhanced at intermediate length scales. The turbulent passive scalar diffusivity is typically almost twice as large as the turbulent magnetic diffusivity. Both magnetic and passive scalar diffusion are slightly enhanced along the rotation axis, but decreased if there is gravity.
Conclusions: The test-field and test-scalar methods provide powerful tools for analyzing transport properties of axisymmetric turbulence. Future applications are proposed ranging from anisotropic turbulence due to the presence of a uniform magnetic field to inhomogeneous turbulence where the specific entropy is nonuniform, for example. Some of the contributions to the mean electromotive force which have been ignored in several earlier investigations, in particular those given by the symmetric part of the gradient tensor of the mean magnetic field, turn out to be of significant magnitude. Title: Vorticity production and survival in viscous and magnetized cosmologies Authors: Dosopoulou, F.; Del Sordo, F.; Tsagas, C. G.; Brandenburg, A. Bibcode: 2012PhRvD..85f3514D Altcode: 2011arXiv1112.6164D We study the role of viscosity and the effects of a magnetic field on a rotating, self-gravitating fluid, using Newtonian theory and adopting the ideal magnetohydrodynamic approximation. Our results confirm that viscosity can generate vorticity in inhomogeneous environments, while the magnetic tension can produce vorticity even in the absence of fluid pressure and density gradients. Linearizing our equations around an Einstein-de Sitter cosmology, we find that viscosity adds to the diluting effect of the universal expansion. Typically, however, the dissipative viscous effects are confined to relatively small scales. We also identify the characteristic length below which the viscous dissipation is strong and beyond which viscosity is essentially negligible. In contrast, magnetism seems to favor cosmic rotation. The magnetic presence is found to slow down the standard decay rate of linear vortices, thus leading to universes with more residual rotation than generally anticipated. Title: Plasma flow versus magnetic feature-tracking speeds in the Sun Authors: Guerrero, G.; Rheinhardt, M.; Brandenburg, A.; Dikpati, M. Bibcode: 2012MNRAS.420L...1G Altcode: 2011MNRAS.tmpL.375G; 2011arXiv1107.4801G We simulate the magnetic feature-tracking (MFT) speed using axisymmetric advective-diffusive transport models in both one and two dimensions. By depositing magnetic bipolar regions at different latitudes at the Sun’s surface and following their evolution for a prescribed meridional circulation and magnetic diffusivity profiles, we derive the MFT speed as a function of latitude. We find that in a one-dimensional surface-transport model the simulated MFT speed at the surface is always the same as the meridional flow speed used as input to the model, but is different in a two-dimensional transport model in the meridional (r, θ) plane. The difference depends on the value of the magnetic diffusivity and on the radial gradient of the latitudinal velocity. We have confirmed our results with two different codes in spherical and Cartesian coordinates. Title: Properties of the negative effective magnetic pressure instability Authors: Kemel, K.; Brandenburg, A.; Kleeorin, N.; Rogachevskii, I. Bibcode: 2012AN....333...95K Altcode: 2011arXiv1107.2752K As was demonstrated in earlier studies, turbulence can result in a negative contribution to the effective mean magnetic pressure, which, in turn, can cause a large-scale instability. In this study, hydromagnetic mean-field modelling is performed for an isothermally stratified layer in the presence of a horizontal magnetic field. The negative effective magnetic pressure instability (NEMPI) is comprehensively investigated. It is shown that, if the effect of turbulence on the mean magnetic tension force vanishes, which is consistent with results from direct numerical simulations of forced turbulence, the fastest growing eigenmodes of NEMPI are two-dimensional. The growth rate is found to depend on a parameter β_{star} characterizing the turbulent contribution of the effective mean magnetic pressure for moderately strong mean magnetic fields. A fit formula is proposed that gives the growth rate as a function of turbulent kinematic viscosity, turbulent magnetic diffusivity, the density scale height, and the parameter β_{star}. The strength of the imposed magnetic field does not explicitly enter provided the location of the vertical boundaries are chosen such that the maximum of the eigenmode of NEMPI fits into the domain. The formation of sunspots and solar active regions is discussed as possible applications of NEMPI. Title: Verification of Reynolds stress parameterizations from simulations Authors: Snellman, J. E.; Brandenburg, A.; Käpylä, P. J.; Mantere, M. J. Bibcode: 2012AN....333...78S Altcode: 2011arXiv1109.4857S We determine the timescales associated with turbulent decay }and isotropization in closure models using anisotropically forced and freely decaying turbulence simulations and study the applicability of these models. We compare the results from anisotropically forced three-dimensional numerical simulations with the predictions of the closure models and obtain the turbulent timescales mentioned above as functions of the Reynolds number. In a second set of simulations, turning the forcing off enables us to study the validity of the closures in freely decaying turbulence. Both types of experiments suggest that the timescale of turbulent decay converges to a constant value at higher Reynolds numbers. Furthermore, the relative importance of isotropization is found to be about 2.5 times larger at higher Reynolds numbers than in the more viscous regime. Title: Modeling spatio-temporal nonlocality in mean-field dynamos Authors: Rheinhardt, M.; Brandenburg, A. Bibcode: 2012AN....333...71R Altcode: 2011arXiv1110.2891R When scale separation in space and time is poor, the alpha effect and turbulent diffusivity have to be replaced by integral kernels. Earlier work in computing these kernels using the test-field method is now generalized to the case in which both spatial and temporal scale separations are poor. The approximate form of the kernel is such that it can be treated in a straightforward manner by solving a partial differential equation for the mean electromotive force. The resulting mean-field equations are solved for oscillatory alpha-shear dynamos as well as alpha^2 dynamos in which alpha is antisymmetric about the equator, making this dynamo also oscillatory. In both cases, the critical values of the dynamo number is lowered by the fact that the dynamo is oscillatory. Title: Theoretical comparison of plasma and magnetic feature tracking (MFT) flows: a perspective for assimilating meridional flow data in flux-transport models Authors: Guerrero, G.; Rheinhardt, M.; Brandenburg, A.; Dikpati, M. Bibcode: 2011AGUFMSH54A..03G Altcode: Doppler measurements of the poleward flow speed at the solar surface reveal a systematic difference from the speed inferred from magnetic feature-tracking (MFT). In order to understand the reason for this difference we simulate the MFT speed using advective-diffusive transport models in both one and two dimensions. By depositing magnetic bipolar regions at different latitudes at the Sun's surface and following their evolution for a prescribed meridional circulation and magnetic diffusivity profiles, we derive the MFT speed as a function of latitude. We find that in a one dimensional surface-transport model the simulated MFT speed at the surface is always the same as the meridional flow-speed used as input to the model, but is different in a two-dimensional transport model in the meridional (r,θ) plane. The difference depends on the value of the magnetic diffusivity and on the radial gradient of the latitudinal velocity. We have confirmed our results with two different codes in spherical and Cartesian coordinates. The possibility of assimilate time-varying meridional flow data in flux-transport dynamo models is also discussed. Title: Effects of stratification in spherical shell convection Authors: Käpylä, P. J.; Mantere, M. J.; Brandenburg, A. Bibcode: 2011AN....332..883K Altcode: 2011arXiv1109.4625K We report on simulations of mildly turbulent convection in spherical wedge geometry with varying density stratification. We vary the density contrast within the convection zone by a factor of 20 and study the influence of rotation on the solutions. We demonstrate that the size of convective cells decreases and the anisotropy of turbulence increases as the stratification is increased. Differential rotation is found to change from anti-solar (slow equator) to solar-like (fast equator) at roughly the same Coriolis number for all stratifications. The largest stratification runs, however, are sensitive to changes of the Reynolds number. Evidence for a near-surface shear layer is found in runs with strong stratification and large Reynolds numbers. Title: Pumping velocity in homogeneous helical turbulence with shear Authors: Rogachevskii, Igor; Kleeorin, Nathan; Käpylä, Petri J.; Brandenburg, Axel Bibcode: 2011PhRvE..84e6314R Altcode: 2011arXiv1105.5785R Using different analytical methods (the quasilinear approach, the path-integral technique, and the tau-relaxation approximation) we develop a comprehensive mean-field theory for a pumping effect of the mean magnetic field in homogeneous nonrotating helical turbulence with imposed large-scale shear. The effective pumping velocity is proportional to the product of α effect and large-scale vorticity associated with the shear, and causes a separation of the toroidal and poloidal components of the mean magnetic field along the direction of the mean vorticity. We also perform direct numerical simulations of sheared turbulence in different ranges of hydrodynamic and magnetic Reynolds numbers and use a kinematic test-field method to determine the effective pumping velocity. The results of the numerical simulations are in agreement with the theoretical predictions. Title: Nonlinear Small-scale Dynamos at Low Magnetic Prandtl Numbers Authors: Brandenburg, Axel Bibcode: 2011ApJ...741...92B Altcode: 2011arXiv1106.5777B Saturated small-scale dynamo solutions driven by isotropic non-helical turbulence are presented at low magnetic Prandtl numbers Pr M down to 0.01. For Pr M < 0.1, most of the energy is dissipated via Joule heat and, in agreement with earlier results for helical large-scale dynamos, kinetic energy dissipation is shown to diminish proportional to Pr1/2 M down to values of 0.1. In agreement with earlier work, there is, in addition to a short Golitsyn k -11/3 spectrum near the resistive scale, also some evidence for a short k -1 spectrum on larger scales. The rms magnetic field strength of the small-scale dynamo is found to depend only weakly on the value of Pr M and decreases by about a factor of two as Pr M is decreased from 1 to 0.01. The possibility of dynamo action at Pr M = 0.1 in the nonlinear regime is argued to be a consequence of a suppression of the bottleneck seen in the kinetic energy spectrum in the absence of a dynamo and, more generally, a suppression of kinetic energy near the dissipation wavenumber. Title: The fratricide of αΩ dynamos by their α2 siblings Authors: Hubbard, A.; Rheinhardt, M.; Brandenburg, A. Bibcode: 2011A&A...535A..48H Altcode: 2011arXiv1102.2617H Context. Helically forced magneto-hydrodynamic shearing-sheet turbulence can support different large-scale dynamo modes, although the αΩ mode is generally expected to dominate because it is the fastest growing one. In an αΩ dynamo, most of the field amplification is produced by the shear. As differential rotation is an ubiquitous source of shear in astrophysics, such dynamos are believed to be the source of most astrophysical large-scale magnetic fields.
Aims: We study the stability of oscillatory migratory αΩ type dynamos in turbulence simulations.
Methods: We use shearing-sheet simulations of hydromagnetic turbulence that is helically forced at a wavenumber that is about three times larger than the lowest wavenumber in the domain so that both αΩ and α2 dynamo action is possible.
Results: After initial dominance and saturation, the αΩ mode is found to be destroyed by an orthogonal α2 mode sustained by the helical turbulence alone. We show that there are at least two processes through which this transition can occur.
Conclusions: The fratricide of αΩ dynamos by its α2 sibling is discussed in the context of grand minima of stellar activity. However, the genesis of αΩ dynamos from an α2 dynamo has not yet been found. Title: Model of driven and decaying magnetic turbulence in a cylinder Authors: Kemel, Koen; Brandenburg, Axel; Ji, Hantao Bibcode: 2011PhRvE..84e6407K Altcode: 2011arXiv1106.1129K Using mean-field theory, we compute the evolution of the magnetic field in a cylinder with outer perfectly conducting boundaries and imposed axial magnetic and electric fields. The thus injected magnetic helicity in the system can be redistributed by magnetic helicity fluxes down the gradient of the local current helicity of the small-scale magnetic field. A weak reversal of the axial magnetic field is found to be a consequence of the magnetic helicity flux in the system. Such fluxes are known to alleviate so-called catastrophic quenching of the α effect in astrophysical applications. A stronger field reversal can be obtained if there is also a significant kinetic α effect. Application to the reversed field pinch in plasma confinement devices is discussed. Title: Detection of Negative Effective Magnetic Pressure Instability in Turbulence Simulations Authors: Brandenburg, Axel; Kemel, Koen; Kleeorin, Nathan; Mitra, Dhrubaditya; Rogachevskii, Igor Bibcode: 2011ApJ...740L..50B Altcode: 2011arXiv1109.1270B We present the first numerical demonstration of the negative effective magnetic pressure instability in direct numerical simulations of stably stratified, externally forced, isothermal hydromagnetic turbulence in the regime of large plasma beta. By the action of this instability, initially uniform horizontal magnetic field forms flux concentrations whose scale is large compared to the turbulent scale. We further show that the magnetic energy of these large-scale structures is only weakly dependent on the magnetic Reynolds number. Our results support earlier mean-field calculations and analytic work that identified this instability. Applications to the formation of active regions in the Sun are discussed. Title: Dynamo-driven plasmoid ejections above a spherical surface Authors: Warnecke, J.; Brandenburg, A.; Mitra, D. Bibcode: 2011A&A...534A..11W Altcode: 2011arXiv1104.0664W
Aims: We extend earlier models of turbulent dynamos with an upper, nearly force-free exterior to spherical geometry, and study how flux emerges from lower layers to the upper ones without being driven by magnetic buoyancy. We also study how this affects the possibility of plasmoid ejection.
Methods: A spherical wedge is used that includes northern and southern hemispheres up to mid-latitudes and a certain range in longitude of the Sun. In radius, we cover both the region that corresponds to the convection zone in the Sun and the immediate exterior up to twice the radius of the Sun. Turbulence is driven with a helical forcing function in the interior, where the sign changes at the equator between the two hemispheres.
Results: An oscillatory large-scale dynamo with equatorward migration is found to operate in the turbulence zone. Plasmoid ejections occur in regular intervals, similar to what is seen in earlier Cartesian models. These plasmoid ejections are tentatively associated with coronal mass ejections (CMEs). The magnetic helicity is found to change sign outside the turbulence zone, which is in agreement with recent findings for the solar wind.

Movie is available in electronic form at http://www.aanda.org Title: Theoretical comparison of plasma flow and magnetic feature tracking speeds in the Sun Authors: Guerrero, G.; Rheinhardt, M.; Brandenburg, A.; Dikpati, M. Bibcode: 2011sdmi.confE..94G Altcode: Doppler measurements of the poleward flow speed at the solar surface reveal a systematic difference from the speed inferred from magnetic feature-tracking (MFT). In order to understand the reason for this difference we simulate the magnetic feature tracking (MFT) speed using advective-diffusive transport models in both one and two dimensions. By depositing magnetic bipolar regions at different latitudes at the Sun's surface and following their evolution for a prescribed meridional circulation and magnetic diffusivity profiles, we derive the MFT speed as a function of latitude. We find that in a one dimensional surface-transport model the simulated MFT speed at the surface is always the same as the meridional flow-speed used as input to the model, but is different in a two-dimensional transport model in the meridional (r, theta) plane. The difference depends on the value of the magnetic diffusivity and on the radial gradient of the latitudinal velocity. We have confirmed our results with two different codes in spherical and Cartesian coordinates. Title: Active regions from near-surface dynamics Authors: Brandenburg, Axel; Kemel, Koen; Kleeorin, Nathan; Mitra, Dhrubaditya; Rogachevskii, Igor Bibcode: 2011sdmi.confE..38B Altcode: We present the first numerical demonstration of the negative effective magnetic pressure instability in direct numerical simulations of stably-stratified, externally-forced, isothermal hydromagnetic turbulence in the regime of large plasma beta. By the action of this instability, initially uniform horizontal magnetic field forms flux concentrations whose scale is large compared to the turbulent scale. We further show that the magnetic energy of these large-scale structures is only weakly dependent on the magnetic Reynolds number. Our results support earlier mean-field calculations and analytic work which identified this instability. Applications to the formation of active regions in the Sun are discussed. Title: Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows Authors: Rädler, Karl-Heinz; Brandenburg, Axel; Del Sordo, Fabio; Rheinhardt, Matthias Bibcode: 2011PhRvE..84d6321R Altcode: 2011arXiv1104.1613R Certain aspects of the mean-field theory of turbulent passive scalar transport and of mean-field electrodynamics are considered with particular emphasis on aspects of compressible fluids. It is demonstrated that the total mean-field diffusivity for passive scalar transport in a compressible flow may well be smaller than the molecular diffusivity. This is in full analogy to an old finding regarding the magnetic mean-field diffusivity in an electrically conducting turbulently moving compressible fluid. These phenomena occur if the irrotational part of the motion dominates the vortical part, the Péclet or magnetic Reynolds number is not too large, and, in addition, the variation of the flow pattern is slow. For both the passive scalar and the magnetic cases several further analytical results on mean-field diffusivities and related quantities found within the second-order correlation approximation are presented, as well as numerical results obtained by the test-field method, which applies independently of this approximation. Particular attention is paid to nonlocal and noninstantaneous connections between the turbulence-caused terms and the mean fields. Two examples of irrotational flows, in which interesting phenomena in the above sense occur, are investigated in detail. In particular, it is demonstrated that the decay of a mean scalar in a compressible fluid under the influence of these flows can be much slower than without any flow, and can be strongly influenced by the so-called memory effect, that is, the fact that the relevant mean-field coefficients depend on the decay rates themselves. Title: Alpha effect due to buoyancy instability of a magnetic layer Authors: Chatterjee, P.; Mitra, D.; Rheinhardt, M.; Brandenburg, A. Bibcode: 2011A&A...534A..46C Altcode: 2010arXiv1011.1218C Context. A strong toroidal field can exist in form of a magnetic layer in the overshoot region below the solar convection zone. This motivates a more detailed study of the magnetic buoyancy instability with rotation.
Aims: We calculate the α effect due to helical motions caused by an unstable magnetic layer in a rotating density-stratified system with angular velocity Ω making an angle θ with the vertical. We also study the dependence of the α effect on θ and the strength of the initial magnetic field.
Methods: We carry out three-dimensional hydromagnetic simulations in Cartesian geometry. A turbulent electromotive force (EMF) due to the correlations of the small scale velocity and magnetic field is generated. We use the test-field method to calculate the transport coefficients of the inhomogeneous turbulence produced by the layer.
Results: We show that the growth rate of the instability and the twist of the magnetic field vary monotonically with the ratio of thermal conductivity to magnetic diffusivity. The resulting α effect is non-uniform and increases with the strength of the initial magnetic field. It is thus an example of an "anti-quenched" α effect. The α effect is also nonlocal, i.e. scale dependent, requiring around 8-16 Fourier modes to reconstruct the actual mean EMF based on the actual mean field. Title: Shear-driven Instabilities in Hall-magnetohydrodynamic Plasmas Authors: Bejarano, Cecilia; Gómez, Daniel O.; Brandenburg, Axel Bibcode: 2011ApJ...737...62B Altcode: 2010arXiv1012.5284B The large-scale dynamics of plasmas is well described within the framework of magnetohydrodynamics (MHD). However, whenever the ion density of the plasma becomes sufficiently low, the Hall effect is likely to become important. The role of the Hall effect has been studied in several astrophysical plasma processes, such as magnetic reconnection, magnetic dynamo, MHD turbulence, or MHD instabilities. In particular, the development of small-scale instabilities is essential to understand the transport properties in a number of astrophysical plasmas. The magneto-rotational instability (MRI), which takes place in differentially rotating accretion disks embedded in relatively weak magnetic fields, is just one example. The influence of the large-scale velocity flows on small-scale instabilities is often approximated by a linear shear flow. In this paper, we quantitatively study the role of the Hall effect on plasmas embedded in large-scale shear flows. More precisely, we show that an instability develops when the Hall effect is present, which we therefore term as the Hall magneto-shear instability. As a particular case, we recover the so-called MRI and quantitatively assess the role of the Hall effect on its development and evolution. Title: The negative magnetic pressure effect in stratified turbulence Authors: Kemel, K.; Brandenburg, A.; Kleeorin, N.; Rogachevskii, I. Bibcode: 2011IAUS..273...83K Altcode: 2010arXiv1010.1659K While the rising flux tube paradigm is an elegant theory, its basic assumptions, thin flux tubes at the bottom of the convection zone with field strengths two orders of magnitude above equipartition, remain numerically unverified at best. As such, in recent years the idea of a formation of sunspots near the top of the convection zone has generated some interest. The presence of turbulence can strongly enhance diffusive transport mechanisms, leading to an effective transport coefficient formalism in the mean-field formulation. The question is what happens to these coefficients when the turbulence becomes anisotropic due to a strong large-scale mean magnetic field. It has been noted in the past that this anisotropy can also lead to highly non-diffusive behavior. In the present work we investigate the formation of large-scale magnetic structures as a result of a negative contribution of turbulence to the large-scale effective magnetic pressure in the presence of stratification. In direct numerical simulations of forced turbulence in a stratified box, we verify the existence of this effect. This phenomenon can cause formation of large-scale magnetic structures even from initially uniform large-scale magnetic field. Title: Recurrent flux emergence from dynamo-generated fields Authors: Warnecke, Jörn; Brandenburg, Axel Bibcode: 2011IAUS..271..407W Altcode: 2010arXiv1008.5278W we investigate the emergence of a large-scale magnetic field. This field is dynamo-generated by turbulence driven with a helical forcing function. Twisted arcade-like field structures are found to emerge in the exterior above the turbulence zone. Time series of the magnetic field structure show recurrent plasmoid ejections. Title: Vorticity from irrotationally forced flow Authors: Del Sordo, Fabio; Brandenburg, Axel Bibcode: 2011IAUS..271..375D Altcode: 2010arXiv1009.0147D; 2011IAUS..271..375S In the interstellar medium the turbulence is believed to be forced mostly through supernova explosions. In a first approximation these flows can be written as a gradient of a potential being thus devoid of vorticity. There are several mechanisms that could lead to vorticity generation, like viscosity and baroclinic terms, rotation, shear and magnetic fields, but it is not clear how effective they are, neither is it clear whether the vorticity is essential in determining the turbulent diffusion acting in the ISM. Here we present a study of the role of rotation, shear and baroclinicity in the generation of vorticity in the ISM. Title: Dynamo generated field emergence through recurrent plasmoid ejections Authors: Warnecke, Jörn; Brandenburg, Axel Bibcode: 2011IAUS..273..256W Altcode: 2010arXiv1010.0218W Magnetic buoyancy is believed to drive the transport of magnetic flux tubes from the convection zone to the surface of the Sun. The magnetic fields form twisted loop-like structures in the solar atmosphere. In this paper we use helical forcing to produce a large-scale dynamo-generated magnetic field, which rises even without magnetic buoyancy. A two layer system is used as computational domain where the upper part represents the solar atmosphere. Here, the evolution of the magnetic field is solved with the stress-and-relax method. Below this region a magnetic field is produced by a helical forcing function in the momentum equation, which leads to dynamo action. We find twisted magnetic fields emerging frequently to the outer layer, forming arch-like structures. In addition, recurrent plasmoid ejections can be found by looking at space-time diagrams of the magnetic field. Recent simulations in spherical coordinates show similar results. Title: Turbulence and magnetic spots at the surface of hot massive stars Authors: Cantiello, Matteo; Braithwaite, Jonathan; Brandenburg, Axel; Del Sordo, Fabio; Käpylä, Petri; Langer, Norbert Bibcode: 2011IAUS..273..200C Altcode: 2010arXiv1010.2498C Hot luminous stars show a variety of phenomena in their photospheres and in their winds which still lack clear physical explanations at this time. Among these phenomena are non-thermal line broadening, line profile variability (LPVs), discrete absorption components (DACs), wind clumping and stochastically excited pulsations. Cantiello et al. (2009) argued that a convection zone close to the surface of hot, massive stars, could be responsible for some of these phenomena. This convective zone is caused by a peak in the opacity due to iron recombination and for this reason is referred to as the ``iron convection zone'' (FeCZ). 3D MHD simulations are used to explore the possible effects of such subsurface convection on the surface properties of hot, massive stars. We argue that turbulence and localized magnetic spots at the surface are the likely consequence of subsurface convection in early type stars. Title: Influence of Magnetic Helicity in MHD Authors: Candelaresi, Simon; Del Sordo, Fabio; Brandenburg, Axel Bibcode: 2011IAUS..271..369C Altcode: 2010arXiv1008.5235C Observations have shown that the Sun's magnetic field has helical structures. The helicity content in magnetic field configurations is a crucial constraint on the dynamical evolution of the system. Since helicity is connected with the number of links we investigate configurations with interlocked magnetic flux rings and one with unlinked rings. It turns out that it is not the linking of the tubes which affects the magnetic field decay, but the content of magnetic helicity. Title: Spontaneous chiral symmetry breaking by hydromagnetic buoyancy Authors: Chatterjee, Piyali; Mitra, Dhrubaditya; Brandenburg, Axel; Rheinhardt, Matthias Bibcode: 2011PhRvE..84b5403C Altcode: 2010arXiv1011.1251C Evidence for the parity-breaking nature of the magnetic buoyancy instability in a stably stratified gas is reported. In the absence of rotation, no helicity is produced, but the nonhelical state is found to be unstable to small helical perturbations during the development of the instability. The parity-breaking nature of this magnetohydrodynamic instability appears to be the first of its kind and has properties similar to those in chiral symmetry breaking in biochemistry. Applications to the production of mean fields in galaxy clusters are discussed. Title: From convective to stellar dynamos Authors: Brandenburg, Axel; Käpylä, Petri J.; Korpi, Maarit J. Bibcode: 2011IAUS..271..279B Altcode: 2011arXiv1103.5475B Convectively driven dynamos with rotation generating magnetic fields on scales large compared with the scale of the turbulent eddies are being reviewed. It is argued that such fields can be understood as the result of an α effect. Simulations in Cartesian domains show that such large-scale magnetic fields saturate on a time scale compatible with the resistive one, suggesting that the magnitude of the α effect is here still constrained by approximate magnetic helicity conservation. It is argued that, in the absence of shear and/or any other known large-scale dynamo effects, these simulations prove the existence of turbulent α2-type dynamos. Finally, recent results are discussed in the context of solar and stellar dynamos. Title: 3D MHD simulations of subsurface convection in OB stars Authors: Cantiello, Matteo; Braithwaite, Jonathan; Brandenburg, Axel; Del Sordo, Fabio; Käpylä, Petri; Langer, Norbert Bibcode: 2011IAUS..272...32C Altcode: 2010arXiv1009.4462C During their main sequence evolution, massive stars can develop convective regions very close to their surface. These regions are caused by an opacity peak associated with iron ionization. Cantiello et al. (2009) found a possible connection between the presence of sub-photospheric convective motions and small scale stochastic velocities in the photosphere of early-type stars. This supports a physical mechanism where microturbulence is caused by waves that are triggered by subsurface convection zones. They further suggest that clumping in the inner parts of the winds of OB stars could be related to subsurface convection, and that the convective layers may also be responsible for stochastic excitation of non-radial pulsations. Furthermore, magnetic fields produced in the iron convection zone could appear at the surface of such massive stars. Therefore subsurface convection could be responsible for the occurrence of observable phenomena such as line profile variability and discrete absorption components. These phenomena have been observed for decades, but still evade a clear theoretical explanation. Here we present preliminary results from 3D MHD simulations of such subsurface convection. Title: Lagrangian Coherent Structures in Nonlinear Dynamos Authors: Rempel, E. L.; Chian, A. C. -L.; Brandenburg, A. Bibcode: 2011ApJ...735L...9R Altcode: 2010arXiv1011.6327R Turbulence and chaos play a fundamental role in stellar convective zones through the transport of particles, energy, and momentum, and in fast dynamos, through the stretching, twisting, and folding of magnetic flux tubes. A particularly revealing way to describe turbulent motions is through the analysis of Lagrangian coherent structures (LCSs), which are material lines or surfaces that act as transport barriers in the fluid. We report the detection of LCSs in helical MHD dynamo simulations with scale separation. In an Arnold-Beltrami-Childress flow, two dynamo regimes, a propagating coherent mean-field regime and an intermittent regime, are identified as the magnetic diffusivity is varied. The sharp contrast between the chaotic tangle of attracting and repelling LCSs in both regimes permits a unique analysis of the impact of the magnetic field on the velocity field. In a second example, LCSs reveal the link between the level of chaotic mixing of the velocity field and the saturation of a large-scale dynamo when the magnetic field exceeds the equipartition value. Title: Chandrasekhar-Kendall functions in astrophysical dynamos Authors: Brandenburg, Axel Bibcode: 2011Prama..77...67B Altcode: 2011arXiv1103.4976B Some of the contributions of Chandrasekhar to the field of magnetohydrodynamics are highlighted. Particular emphasis is placed on the Chandrasekhar-Kendall functions that allow a decomposition of a vector field into right- and left-handed contributions. Magnetic energy spectra of both contributions are shown for a new set of helically forced simulations at resolutions higher than what has been available so far. For a forcing function with positive helicity, these simulations show a forward cascade of the right-handed contributions to the magnetic field and nonlocal inverse transfer for the left-handed contributions. The speed of inverse transfer is shown to decrease with increasing value of the magnetic Reynolds number. Title: Decay of helical and nonhelical magnetic knots Authors: Candelaresi, Simon; Brandenburg, Axel Bibcode: 2011PhRvE..84a6406C Altcode: 2011arXiv1103.3518C We present calculations of the relaxation of magnetic field structures that have the shape of particular knots and links. A set of helical magnetic flux configurations is considered, which we call n-foil knots of which the trefoil knot is the most primitive member. We also consider two nonhelical knots; namely, the Borromean rings as well as a single interlocked flux rope that also serves as the logo of the Inter-University Centre for Astronomy and Astrophysics in Pune, India. The field decay characteristics of both configurations is investigated and compared with previous calculations of helical and nonhelical triple-ring configurations. Unlike earlier nonhelical configurations, the present ones cannot trivially be reduced via flux annihilation to a single ring. For the n-foil knots the decay is described by power laws that range form t-2/3 to t-1/3, which can be as slow as the t-1/3 behavior for helical triple-ring structures that were seen in earlier work. The two nonhelical configurations decay like t-1, which is somewhat slower than the previously obtained t-3/2 behavior in the decay of interlocked rings with zero magnetic helicity. We attribute the difference to the creation of local structures that contain magnetic helicity which inhibits the field decay due to the existence of a lower bound imposed by the realizability condition. We show that net magnetic helicity can be produced resistively as a result of a slight imbalance between mutually canceling helical pieces as they are being driven apart. We speculate that higher order topological invariants beyond magnetic helicity may also be responsible for slowing down the decay of the two more complicated nonhelical structures mentioned above. Title: Reynolds stress and heat flux in spherical shell convection Authors: Käpylä, P. J.; Mantere, M. J.; Guerrero, G.; Brandenburg, A.; Chatterjee, P. Bibcode: 2011A&A...531A.162K Altcode: 2010arXiv1010.1250K Context. Turbulent fluxes of angular momentum and enthalpy or heat due to rotationally affected convection play a key role in determining differential rotation of stars. Their dependence on latitude and depth has been determined in the past from convection simulations in Cartesian or spherical simulations. Here we perform a systematic comparison between the two geometries as a function of the rotation rate.
Aims: Here we want to extend the earlier studies by using spherical wedges to obtain turbulent angular momentum and heat transport as functions of the rotation rate from stratified convection. We compare results from spherical and Cartesian models in the same parameter regime in order to study whether restricted geometry introduces artefacts into the results. In particular, we want to clarify whether the sharp equatorial profile of the horizontal Reynolds stress found in earlier Cartesian models is also reproduced in spherical geometry.
Methods: We employ direct numerical simulations of turbulent convection in spherical and Cartesian geometries. In order to alleviate the computational cost in the spherical runs, and to reach as high spatial resolution as possible, we model only parts of the latitude and longitude. The rotational influence, measured by the Coriolis number or inverse Rossby number, is varied from zero to roughly seven, which is the regime that is likely to be realised in the solar convection zone. Cartesian simulations are performed in overlapping parameter regimes.
Results: For slow rotation we find that the radial and latitudinal turbulent angular momentum fluxes are directed inward and equatorward, respectively. In the rapid rotation regime the radial flux changes sign in accordance with earlier numerical results, but in contradiction with theory. The latitudinal flux remains mostly equatorward and develops a maximum close to the equator. In Cartesian simulations this peak can be explained by the strong "banana cells". Their effect in the spherical case does not appear to be as large. The latitudinal heat flux is mostly equatorward for slow rotation but changes sign for rapid rotation. Longitudinal heat flux is always in the retrograde direction. The rotation profiles vary from anti-solar (slow equator) for slow and intermediate rotation to solar-like (fast equator) for rapid rotation. The solar-like profiles are dominated by the Taylor-Proudman balance.

Movies and Appendix A are available in electronic form at http://www.aanda.org Title: How can vorticity be produced in irrotationally forced flows? Authors: Sordo, Fabio Del; Brandenburg, Axel Bibcode: 2011IAUS..274..373S Altcode: 2010arXiv1012.4772D A spherical hydrodynamical expansion flow can be described as the gradient of a potential. In that case no vorticity should be produced, but several additional mechanisms can drive its production. Here we analyze the effects of baroclinicity, rotation and shear in the case of a viscous fluid. Those flows resemble what happens in the interstellar medium. In fact in this astrophysical environment supernovae explosion are the dominant flows and, in a first approximation, they can be seen as spherical. One of the main difference is that in our numerical study we examine only weakly supersonic flows, while supernovae explosions are strongly supersonic. Title: Magnetic helicity fluxes in αΩ dynamos Authors: Candelaresi, Simon; Brandenburg, Axel Bibcode: 2011IAUS..274..464C Altcode: 2010arXiv1012.4354C In turbulent dynamos the production of large-scale magnetic fields is accompanied by a separation of magnetic helicity in scale. The large- and small-scale parts increase in magnitude. The small-scale part can eventually work against the dynamo and quench it, especially at high magnetic Reynolds numbers. A one-dimensional mean-field model of a dynamo is presented where diffusive magnetic helicity fluxes within the domain are important. It turns out that this effect helps to alleviate the quenching. Here we show that internal magnetic helicity fluxes, even within one hemisphere, can be important for alleviating catastrophic quenching. Title: Plasmoid ejections driven by dynamo action underneath a spherical surface Authors: Warnecke, Jörn; Brandenburg, Axel; Mitra, Dhrubaditya Bibcode: 2011IAUS..274..306W Altcode: 2010arXiv1011.4299W We present a unified three-dimensional model of the convection zone and upper atmosphere of the Sun in spherical geometry. In this model, magnetic fields, generated by a helically forced dynamo in the convection zone, emerge without the assistance of magnetic buoyancy. We use an isothermal equation of state with gravity and density stratification. Recurrent plasmoid ejections, which rise through the outer atmosphere, is observed. In addition, the current helicity of the small-scale field is transported outwards and form large structures like magnetic clouds. Title: Decay of trefoil and other magnetic knots Authors: Candelaresi, Simon; Del Sordo, Fabio; Brandenburg, Axel Bibcode: 2011IAUS..274..461C Altcode: 2010arXiv1011.0417C Two setups with interlocked magnetic flux tubes are used to study the evolution of magnetic energy and helicity on magnetohydrodynamical (MHD) systems like plasmas. In one setup the initial helicity is zero while in the other it is finite. To see if it is the actual linking or merely the helicity content that influences the dynamics of the system we also consider a setup with unlinked field lines as well as a field configuration in the shape of a trefoil knot. For helical systems the decay of magnetic energy is slowed down by the helicity which decays slowly. It turns out that it is the helicity content, rather than the actual linking, that is significant for the dynamics. Title: Simulations of astrophysical dynamos Authors: Brandenburg, Axel Bibcode: 2011IAUS..274..402B Altcode: 2010arXiv1012.5079B Numerical aspects of dynamos in periodic domains are discussed. Modifications of the solutions by numerically motivated alterations of the equations are being reviewed using the examples of magnetic hyperdiffusion and artificial diffusion when advancing the magnetic field in its Euler potential representation. The importance of using integral kernel formulations in mean-field dynamo theory is emphasized in cases where the dynamo growth rate becomes comparable with the inverse turnover time. Finally, the significance of microscopic magnetic Prandtl number in controlling the conversion from kinetic to magnetic energy is highlighted. Title: Scale Dependence of Magnetic Helicity in the Solar Wind Authors: Brandenburg, Axel; Subramanian, Kandaswamy; Balogh, André; Goldstein, Melvyn L. Bibcode: 2011ApJ...734....9B Altcode: 2011arXiv1101.1709B We determine the magnetic helicity, along with the magnetic energy, at high latitudes using data from the Ulysses mission. The data set spans the time period from 1993 to 1996. The basic assumption of the analysis is that the solar wind is homogeneous. Because the solar wind speed is high, we follow the approach first pioneered by Matthaeus et al. by which, under the assumption of spatial homogeneity, one can use Fourier transforms of the magnetic field time series to construct one-dimensional spectra of the magnetic energy and magnetic helicity under the assumption that the Taylor frozen-in-flow hypothesis is valid. That is a well-satisfied assumption for the data used in this study. The magnetic helicity derives from the skew-symmetric terms of the three-dimensional magnetic correlation tensor, while the symmetric terms of the tensor are used to determine the magnetic energy spectrum. Our results show a sign change of magnetic helicity at wavenumber k ≈ 2 AU-1 (or frequency ν ≈ 2 μHz) at distances below 2.8 AU and at k ≈ 30 AU-1 (or ν ≈ 25 μHz) at larger distances. At small scales the magnetic helicity is positive at northern heliographic latitudes and negative at southern latitudes. The positive magnetic helicity at small scales is argued to be the result of turbulent diffusion reversing the sign relative to what is seen at small scales at the solar surface. Furthermore, the magnetic helicity declines toward solar minimum in 1996. The magnetic helicity flux integrated separately over one hemisphere amounts to about 1045 Mx2 cycle-1 at large scales and to a three times lower value at smaller scales. Title: Turbulent magnetic pressure instability in stratified turbulence Authors: Kemel, K.; Brandenburg, A.; Kleeorin, N.; Rogachevskii, I. Bibcode: 2011IAUS..274..473K Altcode: 2010arXiv1012.4360K A reduction of total mean turbulent pressure due to the presence of magnetic fields was previously shown to be a measurable effect in direct numerical simulations. However, in the studied parameter regime the formation of large-scale structures, as anticipated from earlier mean-field simulations, was not found. An analysis of the relevant mean-field parameter dependency and the parameter domain of interest is conducted in order to clarify this apparent discrepancy. Title: Vorticity production through rotation, shear, and baroclinicity Authors: Del Sordo, F.; Brandenburg, A. Bibcode: 2011A&A...528A.145D Altcode: 2010arXiv1008.5281D Context. In the absence of rotation and shear, and under the assumption of constant temperature or specific entropy, purely potential forcing by localized expansion waves is known to produce irrotational flows that have no vorticity.
Aims: Here we study the production of vorticity under idealized conditions when there is rotation, shear, or baroclinicity, to address the problem of vorticity generation in the interstellar medium in a systematic fashion.
Methods: We use three-dimensional periodic box numerical simulations to investigate the various effects in isolation.
Results: We find that for slow rotation, vorticity production in an isothermal gas is small in the sense that the ratio of the root-mean-square values of vorticity and velocity is small compared with the wavenumber of the energy-carrying motions. For Coriolis numbers above a certain level, vorticity production saturates at a value where the aforementioned ratio becomes comparable with the wavenumber of the energy-carrying motions. Shear also raises the vorticity production, but no saturation is found. When the assumption of isothermality is dropped, there is significant vorticity production by the baroclinic term once the turbulence becomes supersonic. In galaxies, shear and rotation are estimated to be insufficient to produce significant amounts of vorticity, leaving therefore only the baroclinic term as the most favorable candidate. We also demonstrate vorticity production visually as a result of colliding shock fronts. Title: Astrophysical turbulence modeling Authors: Brandenburg, Axel; Nordlund, Åke Bibcode: 2011RPPh...74d6901B Altcode: 2009arXiv0912.1340B The role of turbulence in various astrophysical settings is reviewed. Among the differences to laboratory and atmospheric turbulence we highlight the ubiquitous presence of magnetic fields that are generally produced and maintained by dynamo action. The extreme temperature and density contrasts and stratifications are emphasized in connection with turbulence in the interstellar medium and in stars with outer convection zones, respectively. In many cases turbulence plays an essential role in facilitating enhanced transport of mass, momentum, energy and magnetic fields in terms of the corresponding coarse-grained mean fields. Those transport properties are usually strongly modified by anisotropies and often completely new effects emerge in such a description that have no correspondence in terms of the original (non-coarse-grained) fields. Title: Cross Helicity and Turbulent Magnetic Diffusivity in the Solar Convection Zone Authors: Rüdiger, G.; Kitchatinov, L. L.; Brandenburg, A. Bibcode: 2011SoPh..269....3R Altcode: 2010arXiv1004.4881R; 2010SoPh..tmp..241R In a density-stratified turbulent medium, the cross helicity «u'⋅B'» is considered as a result of the interaction of the velocity fluctuations and a large-scale magnetic field. By means of a quasilinear theory and by numerical simulations, we find the cross helicity and the mean vertical magnetic field to be anti-correlated. In the high-conductivity limit the ratio of the helicity and the mean magnetic field equals the ratio of the magnetic eddy diffusivity and the (known) density scale height. The result can be used to predict that the cross helicity at the solar surface will exceed the value of 1 gauss km s−1. Its sign is anti-correlated to that of the radial mean magnetic field. Alternatively, we can use our result to determine the value of the turbulent magnetic diffusivity from observations of the cross helicity. Title: Turbulence Tutorial and Q&A Joint Discussion of Turbulence11 and GGlusters11 Programs Authors: Brandenburg, Axel; Falkovich, Gregory; Kerr, Robert Bibcode: 2011gcca.progE..12B Altcode: No abstract at ADS Title: Alleviating α quenching by solar wind and meridional flows Authors: Mitra, D.; Moss, D.; Tavakol, R.; Brandenburg, A. Bibcode: 2011A&A...526A.138M Altcode: 2010arXiv1008.4226M
Aims: We study the ability of magnetic helicity expulsion to alleviate catastrophic α-quenching in mean field dynamos in two-dimensional spherical wedge domains.
Methods: Motivated by the physical state of the outer regions of the Sun, we consider α^2Ω mean field models with a dynamical α quenching. We include two mechanisms which have the potential to facilitate helicity expulsion, namely advection by a mean flow ("solar wind") and meridional circulation.
Results: We find that a wind alone can prevent catastrophic quenching, with the field saturating at finite amplitude. In certain parameter ranges, the presence of a large-scale meridional circulation can reinforce this alleviation. However, the saturated field strengths are typically below the equipartition field strength. We discuss possible mechanisms that might increase the saturated field. Title: Magnetic helicity fluxes in interface and flux transport dynamos Authors: Chatterjee, P.; Guerrero, G.; Brandenburg, A. Bibcode: 2011A&A...525A...5C Altcode: 2010arXiv1005.5335C Context. Dynamos in the Sun and other bodies tend to produce magnetic fields that possess magnetic helicity of opposite sign at large and small scales, respectively. The build-up of magnetic helicity at small scales provides an important saturation mechanism.
Aims: In order to understand the nature of the solar dynamo we need to understand the details of the saturation mechanism in spherical geometry. In particular, we aim to understand the effects of magnetic helicity fluxes from turbulence and meridional circulation.
Methods: We consider a model with only radial shear confined to a thin layer (tachocline) at the bottom of the convection zone. The kinetic α owing to helical turbulence is assumed to be localized in a region above the convection zone. The dynamical quenching formalism is used to describe the build-up of mean magnetic helicity in the model, which results in a magnetic α effect that feeds back on the kinetic α effect. In some cases we compare these results with those obtained from a model with a simple algebraic α quenching formula.
Results: In agreement with earlier findings, the magnetic α effect has the opposite sign compared with the kinetic α effect and leads to a catastrophic decrease of the saturation field strength proportional to the inverse magnetic Reynolds number. At high latitudes this quenching effect can lead to secondary dynamo waves that propagate poleward because of the opposite sign of α. These secondary dynamo waves are driven by small-scale magnetic helicity instead of the small-scale kinetic helicity. Magnetic helicity fluxes both from turbulent mixing and from meridional circulation alleviate catastrophic quenching. Interestingly, supercritical diffusive helicity fluxes also give rise to secondary dynamo waves and grand minima-like episodes. Title: Magnetic helicity transport in the advective gauge family Authors: Candelaresi, Simon; Hubbard, Alexander; Brandenburg, Axel; Mitra, Dhrubaditya Bibcode: 2011PhPl...18a2903C Altcode: 2010arXiv1010.6177C Magnetic helicity fluxes are investigated in a family of gauges in which the contribution from ideal magnetohydrodynamics takes the form of a purely advective flux. Numerical simulations of magnetohydrodynamic turbulence in this advective gauge family exhibit instabilities triggered by the build-up of unphysical irrotational contributions to the magnetic vector potential. As a remedy, the vector potential is evolved in a numerically well behaved gauge, from which the advective vector potential is obtained by a gauge transformation. In the kinematic regime, the magnetic helicity density evolves similarly to a passive scalar when resistivity is small and turbulent mixing is mild, i.e., when the fluid Reynolds number is not too large. In the dynamical regime, resistive contributions to the magnetic helicity flux in the advective gauge are found to be significant owing to the development of small length scales in the irrotational part of the magnetic vector potential. Title: A high-order public domain code for direct numerical simulations of turbulent combustion Authors: Babkovskaia, N.; Haugen, N. E. L.; Brandenburg, A. Bibcode: 2011JCoPh.230....1B Altcode: 2010arXiv1005.5301B A high-order scheme for direct numerical simulations of turbulent combustion is discussed. Its implementation in the massively parallel and publicly available PENCIL CODE is validated with the focus on hydrogen combustion. This is the first open source DNS code with detailed chemistry available. An attempt has been made to present, for the first time, the full set of evolution and auxiliary equations required for a complete description of single phase non-isothermal fluid dynamics with detailed chemical reactions. Ignition delay times (0D) and laminar flame velocities (1D) are calculated and compared with results from the commercially available Chemkin code. The scheme is verified to be fifth order in space. Upon doubling the resolution, a 32-fold increase in the accuracy of the flame front is demonstrated. Finally, also turbulent and spherical flame front velocities are calculated and the implementation of the non-reflecting so-called Navier-Stokes Characteristic Boundary Condition is validated in all three directions. Title: Dissipation in dynamos at low and high magnetic Prandtl numbers Authors: Brandenburg, A. Bibcode: 2011AN....332...51B Altcode: 2010arXiv1010.4805B Using simulations of helically driven turbulence, it is shown that the ratio of kinetic to magnetic energy dissipation scales with the magnetic Prandtl number in power law fashion with an exponent of approximately 0.6. Over six orders of magnitude in the magnetic Prandtl number the magnetic field is found to be sustained by large-scale dynamo action of alpha-squared type. This work extends a similar finding for small magnetic Prandtl numbers to the regime of large magnetic Prandtl numbers. At large magnetic Prandtl numbers, most of the energy is dissipated viscously, lowering thus the amount of magnetic energy dissipation, which means that simulations can be performed at magnetic Reynolds numbers that are large compared to the usual limits imposed by a given resolution. This is analogous to an earlier finding that at small magnetic Prandtl numbers, most of the energy is dissipated resistively, lowering the amount of kinetic energy dissipation, so simulations can then be performed at much larger fluid Reynolds numbers than otherwise. The decrease in magnetic energy dissipation at large magnetic Prandtl numbers is discussed in the context of underluminous accretion found in some strut{quasars}. Title: Turbulent front speed in the Fisher equation: Dependence on Damköhler number Authors: Brandenburg, Axel; Haugen, Nils Erland L.; Babkovskaia, Natalia Bibcode: 2011PhRvE..83a6304B Altcode: 2010arXiv1008.5145B Direct numerical simulations and mean-field theory are used to model reactive front propagation in a turbulent medium. In the mean-field approach, memory effects of turbulent diffusion are taken into account to estimate the front speed in cases in which the Damköhler number is large. This effect is found to saturate the front speed to values comparable with the speed of the turbulent motions. By comparing with direct numerical simulations, it is found that the effective correlation time is much shorter than for nonreacting flows. The nonlinearity of the reaction term is found to make the front speed slightly faster. Title: Magnetic Helicity Flux in the Presence of Shear Authors: Hubbard, Alexander; Brandenburg, Axel Bibcode: 2011ApJ...727...11H Altcode: 2010arXiv1006.3549H Magnetic helicity has risen to be a major player in dynamo theory, with the helicity of the small-scale field being linked to the dynamo saturation process for the large-scale field. It is a nearly conserved quantity, which allows its evolution equation to be written in terms of production and flux terms. The flux term can be decomposed in a variety of fashions. One particular contribution that has been expected to play a significant role in dynamos in the presence of mean shear was isolated by Vishniac & Cho. Magnetic helicity fluxes are explicitly gauge dependent however, and the correlations that have come to be called the Vishniac-Cho flux were determined in the Coulomb gauge, which turns out to be fraught with complications in shearing systems. While the fluxes of small-scale helicity are explicitly gauge dependent, their divergences can be gauge independent. We use this property to investigate magnetic helicity fluxes of the small-scale field through direct numerical simulations in a shearing-box system and find that in a numerically usable gauge the divergence of the small-scale helicity flux vanishes, while the divergence of the Vishniac-Cho flux remains finite. We attribute this seeming contradiction to the existence of horizontal fluxes of small-scale magnetic helicity with finite divergences. Title: Turbulent transport in hydromagnetic flows Authors: Brandenburg, A.; Chatterjee, P.; Del Sordo, F.; Hubbard, A.; Käpylä, P. J.; Rheinhardt, M. Bibcode: 2010PhST..142a4028B Altcode: 2010arXiv1004.5380B The predictive power of mean-field theory is emphasized by comparing theory with simulations under controlled conditions. The recently developed test-field method is used to extract turbulent transport coefficients both in the kinematic and the nonlinear or quasi-kinematic cases. A striking example of the quasi-kinematic method is provided by magnetic buoyancy-driven flows that produce an α effect and turbulent diffusion. Title: Shear-driven and diffusive helicity fluxes in αΩ dynamos Authors: Guerrero, G.; Chatterjee, P.; Brandenburg, A. Bibcode: 2010MNRAS.409.1619G Altcode: 2010MNRAS.tmp.1434G; 2010arXiv1005.4818G; 2010MNRAS.tmp.1451G We present non-linear mean-field αΩ dynamo simulations in spherical geometry with simplified profiles of kinetic α effect and shear. We take magnetic helicity evolution into account by solving a dynamical equation for the magnetic α effect. This gives a consistent description of the quenching mechanism in mean-field dynamo models. The main goal of this work is to explore the effects of this quenching mechanism in solar-like geometry, and in particular to investigate the role of magnetic helicity fluxes, specifically diffusive and Vishniac-Cho (VC) fluxes, at large magnetic Reynolds numbers (Rm). For models with negative radial shear or positive latitudinal shear, the magnetic α effect has predominantly negative (positive) sign in the Northern (Southern) hemisphere. In the absence of fluxes, we find that the magnetic energy follows an R-1m dependence, as found in previous works. This catastrophic quenching is alleviated in models with diffusive magnetic helicity fluxes resulting in magnetic fields comparable to the equipartition value even for Rm= 107. On the other hand, models with a shear-driven Vishniac-Cho flux show an increase in the amplitude of the magnetic field with respect to models without fluxes, but only for Rm < 104. This is partly a consequence of assuming a vacuum outside the Sun which cannot support a significant VC flux across the boundary. However, in contrast to the diffusive flux, the VC flux modifies the distribution of the magnetic field. In addition, if an ill-determined scaling factor in the expression for the VC flux is large enough, subcritical dynamo action is possible that is driven by the action of shear and the divergence of magnetic helicity flux. Title: Turbulent diffusion and galactic magnetism Authors: Brandenburg, Axel; Del Sordo, Fabio Bibcode: 2010HiA....15..432B Altcode: 2009arXiv0910.0072B Using the test-field method for nearly irrotational turbulence driven by spherical expansion waves it is shown that the turbulent magnetic diffusivity increases with magnetic Reynolds numbers. Its value levels off at several times the rms velocity of the turbulence multiplied by the typical radius of the expansion waves. This result is discussed in the context of the galactic mean-field dynamo. Title: Surface appearance of dynamo-generated large-scale fields Authors: Warnecke, J.; Brandenburg, A. Bibcode: 2010A&A...523A..19W Altcode: 2010arXiv1002.3620W
Aims: Twisted magnetic fields are frequently seen to emerge above the visible surface of the Sun. This emergence is usually associated with the rise of buoyant magnetic flux structures. Here we ask how magnetic fields from a turbulent large-scale dynamo appear above the surface if there is no magnetic buoyancy.
Methods: The computational domain is split into two parts. In the lower part, which we refer to as the turbulence zone, the flow is driven by an assumed helical forcing function leading to dynamo action. Above this region, which we refer to as the exterior, a nearly force-free magnetic field is computed at each time step using the stress-and-relax method.
Results: Twisted arcade-like field structures are found to emerge in the exterior above the turbulence zone. Strong current sheets tend to form above the neutral line, where the vertical field component vanishes. Time series of the magnetic field structure show recurrent plasmoid ejections. The degree to which the exterior field is force free is estimated as the ratio of the dot product of current density and magnetic field strength to their respective rms values. This ratio reaches values of up to 95% in the exterior. A weak outward flow is driven by the residual Lorentz force. Title: Magnetic helicity fluxes in an α2 dynamo embedded in a halo Authors: Hubbard, Alexander; Brandenburg, Axel Bibcode: 2010GApFD.104..577H Altcode: 2010arXiv1004.4591H We present the results of simulations of forced turbulence in a slab where the mean kinetic helicity has a maximum near the mid-plane, generating gradients of magnetic helicity of both large and small-scale fields. We also study systems that have poorly conducting buffer zones away from the midplane in order to assess the effects of boundaries. The dynamical α quenching phenomenology requires that the magnetic helicity in the small-scale fields approaches a nearly static, gauge independent state. To stress-test this steady state condition we choose a system with a uniform sign of kinetic helicity, so that the total magnetic helicity can reach a steady state value only through fluxes through the boundary, which are themselves suppressed by the velocity boundary conditions. Even with such a set up, the small-scale magnetic helicity is found to reach a steady state. In agreement with the earlier work, the magnetic helicity fluxes of small-scale fields are found to be turbulently diffusive. By comparing results with and without halos, we show that artificial constraints on magnetic helicity at the boundary do not have a significant impact on the evolution of the magnetic helicity, except that "softer" (halo) boundary conditions give a lower energy of the saturated mean magnetic field. Title: Can catastrophic quenching be alleviated by separating shear and α effect? Authors: Chatterjee, Piyali; Brandenburg, Axel; Guerrero, Gustavo Bibcode: 2010GApFD.104..591C Altcode: 2010arXiv1005.5708C The small-scale magnetic helicity produced as a by-product of the large-scale dynamo is believed to play a major role in dynamo saturation. In a mean-field model the generation of small-scale magnetic helicity can be modelled by using the dynamical quenching formalism. Catastrophic quenching refers to a decrease of the saturation field strength with increasing Reynolds number. It has been suggested that catastrophic quenching only affects the region of non-zero helical turbulence (i.e. where the kinematic α operates) and that it is possible to alleviate catastrophic quenching by separating the region of strong shear from the α layer. We perform a systematic study of a simple axisymmetric two-layer αΩ dynamo in a spherical shell for Reynolds numbers in the range 1 ≤ R m ≤ 105. In the framework of dynamical quenching we show that this may not be the case, suggesting that magnetic helicity fluxes would be necessary. Title: Pencil: Finite-difference Code for Compressible Hydrodynamic Flows Authors: Brandenburg, Axel; Dobler, Wolfgang Bibcode: 2010ascl.soft10060B Altcode: The Pencil code is a high-order finite-difference code for compressible hydrodynamic flows with magnetic fields. It is highly modular and can easily be adapted to different types of problems. The code runs efficiently under MPI on massively parallel shared- or distributed-memory computers, like e.g. large Beowulf clusters. The Pencil code is primarily designed to deal with weakly compressible turbulent flows. To achieve good parallelization, explicit (as opposed to compact) finite differences are used. Typical scientific targets include driven MHD turbulence in a periodic box, convection in a slab with non-periodic upper and lower boundaries, a convective star embedded in a fully nonperiodic box, accretion disc turbulence in the shearing sheet approximation, self-gravity, non-local radiation transfer, dust particle evolution with feedback on the gas, etc. A range of artificial viscosity and diffusion schemes can be invoked to deal with supersonic flows. For direct simulations regular viscosity and diffusion is being used. The code is written in well-commented Fortran90. Title: Test-field method for mean-field coefficients with MHD background Authors: Rheinhardt, M.; Brandenburg, A. Bibcode: 2010A&A...520A..28R Altcode: 2010arXiv1004.0689R
Aims: The test-field method for computing turbulent transport coefficients from simulations of hydromagnetic flows is extended to the regime with a magnetohydrodynamic (MHD) background.
Methods: A generalized set of test equations is derived using both the induction equation and a modified momentum equation. By employing an additional set of auxiliary equations, we obtain linear equations describing the response of the system to a set of prescribed test fields. Purely magnetic and MHD backgrounds are emulated by applying an electromotive force in the induction equation analogously to the ponderomotive force in the momentum equation. Both forces are chosen to have Roberts-flow like geometry.
Results: Examples with purely magnetic as well as MHD backgrounds are studied where the previously used quasi-kinematic test-field method breaks down. In cases with homogeneous mean fields it is shown that the generalized test-field method produces the same results as the imposed-field method, where the field-aligned component of the actual electromotive force from the simulation is used. Furthermore, results for the turbulent diffusivity are given, which are inaccessible to the imposed-field method. For MHD backgrounds, new mean-field effects are found that depend on the occurrence of cross-correlations between magnetic and velocity fluctuations. In particular, there is a contribution to the mean Lorentz force that is linear in the mean field and hence reverses sign upon a reversal of the mean field. For strong mean fields, α is found to be quenched proportional to the fourth power of the field strength, regardless of the type of background studied. Title: Oscillatory Migrating Magnetic Fields in Helical Turbulence in Spherical Domains Authors: Mitra, Dhrubaditya; Tavakol, Reza; Käpylä, Petri J.; Brandenburg, Axel Bibcode: 2010ApJ...719L...1M Altcode: 2009arXiv0901.2364M We present direct numerical simulations of the equations of compressible magnetohydrodynamics in a wedge-shaped spherical shell, without shear, but with random helical forcing which has negative (positive) helicity in the northern (southern) hemisphere. We find a large-scale magnetic field that is nearly uniform in the azimuthal direction and approximately antisymmetric about the equator. Furthermore, the large-scale field in each hemisphere oscillates on nearly dynamical timescales with reversals of polarity and equatorward migration. Corresponding mean-field models also show similar migratory oscillations with a frequency that is nearly independent of the magnetic Reynolds number. This mechanism may be relevant for understanding equatorward migration seen in the solar dynamo. Title: Angular Momentum Transport in Convectively Unstable Shear Flows Authors: Käpylä, Petri J.; Brandenburg, Axel; Korpi, Maarit J.; Snellman, Jan E.; Narayan, Ramesh Bibcode: 2010ApJ...719...67K Altcode: 2010arXiv1003.0900K Angular momentum transport due to hydrodynamic turbulent convection is studied using local three-dimensional numerical simulations employing the shearing box approximation. We determine the turbulent viscosity from non-rotating runs over a range of values of the shear parameter and use a simple analytical model in order to extract the non-diffusive contribution (Λ-effect) to the stress in runs where rotation is included. Our results suggest that the turbulent viscosity is on the order of the mixing length estimate and weakly affected by rotation. The Λ-effect is non-zero and a factor of 2-4 smaller than the turbulent viscosity in the slow rotation regime. We demonstrate that for Keplerian shear, the angular momentum transport can change sign and be outward when the rotation period is greater than the turnover time, i.e., when the Coriolis number is below unity. This result seems to be relatively independent of the value of the Rayleigh number. Title: Disc turbulence and viscosity Authors: Brandenburg, A. Bibcode: 2010tbha.book...61B Altcode: No abstract at ADS Title: Open and closed boundaries in large-scale convective dynamos Authors: Käpylä, P. J.; Korpi, M. J.; Brandenburg, A. Bibcode: 2010A&A...518A..22K Altcode: 2009arXiv0911.4120K Context. Earlier work has suggested that large-scale dynamos can reach and maintain equipartition field strengths on a dynamical time scale only if magnetic helicity of the fluctuating field can be shed from the domain through open boundaries.
Aims: Our aim is to test this scenario in convection-driven dynamos by comparing results for open and closed boundary conditions.
Methods: Three-dimensional numerical simulations of turbulent compressible convection with shear and rotation are used to study the effects of boundary conditions on the excitation and saturation of large-scale dynamos. Open (vertical-field) and closed (perfect- conductor) boundary conditions are used for the magnetic field. The shear flow is such that the contours of shear are vertical, crossing the outer surface, and are thus ideally suited for driving a shear-induced magnetic helicity flux.
Results: We find that for given shear and rotation rate, the growth rate of the magnetic field is larger if open boundary conditions are used. The growth rate first increases for small magnetic Reynolds number, Rm, but then levels off at an approximately constant value for intermediate values of Rm. For large enough Rm, a small-scale dynamo is excited and the growth rate of the field in this regime increases as Rm1/2. Regarding the nonlinear regime, the saturation level of the energy of the total magnetic field is independent of Rm when open boundaries are used. In the case of perfect-conductor boundaries, the saturation level first increases as a function of Rm, but then decreases proportional to Rm-1 for Rm ⪆ 30, indicative of catastrophic quenching. These results suggest that the shear-induced magnetic helicity flux is efficient in alleviating catastrophic quenching when open boundaries are used. The horizontally averaged mean field is still weakly decreasing as a function of Rm even for open boundaries. Title: Calibrating passive scalar transport in shear-flow turbulence Authors: Madarassy, Enikő J. M.; Brandenburg, Axel Bibcode: 2010PhRvE..82a6304M Altcode: 2009arXiv0906.3314M The turbulent diffusivity tensor is determined for linear shear-flow turbulence using numerical simulations. For moderately strong shear, the diagonal components are found to increase quadratically with Peclet and Reynolds numbers below about 10 and then become constant. The diffusivity tensor is found to have components proportional to the symmetric and antisymmetric parts of the velocity gradient matrix, as well as products of these. All components decrease with the wave number of the mean field in a Lorentzian fashion. The components of the diffusivity tensor are found not to depend significantly on the presence of helicity in the turbulence. The signs of the leading terms in the expression for the diffusion tensor are found to be in good agreement with estimates based on a simple closure assumption. Title: Numerical simulations of the decay of primordial magnetic turbulence Authors: Kahniashvili, Tina; Brandenburg, Axel; Tevzadze, Alexander G.; Ratra, Bharat Bibcode: 2010PhRvD..81l3002K Altcode: 2010arXiv1004.3084K We perform direct numerical simulations of forced and freely decaying 3D magnetohydrodynamic turbulence in order to model magnetic field evolution during cosmological phase transitions in the early Universe. Our approach assumes the existence of a magnetic field generated either by a process during inflation or shortly thereafter, or by bubble collisions during a phase transition. We show that the final configuration of the magnetic field depends on the initial conditions, while the velocity field is nearly independent of initial conditions. Title: The α effect in rotating convection with sinusoidal shear Authors: Käpylä, P. J.; Korpi, M. J.; Brandenburg, A. Bibcode: 2010MNRAS.402.1458K Altcode: 2009arXiv0908.2423K; 2009MNRAS.tmp.1866K Using three-dimensional convection simulations, it is shown that a sinusoidal variation of horizontal shear leads to a kinematic α effect with a similar sinusoidal variation. The effect exists even for weak stratification and arises owing to the inhomogeneity of turbulence and the presence of impenetrable vertical boundaries. This system produces large-scale magnetic fields that also show a sinusoidal variation in the cross-stream direction. It is argued that earlier investigations overlooked these phenomena partly because of the use of horizontal averaging and also because measurements of α using an imposed field combined with long time averages give erroneous results. It is demonstrated that in such cases the actual horizontally averaged mean field becomes non-uniform. The turbulent magnetic diffusion term resulting from such non-uniform fields can then no longer be neglected and begins to balance the α effect. Title: Magnetic-field decay of three interlocked flux rings with zero linking number Authors: Del Sordo, Fabio; Candelaresi, Simon; Brandenburg, Axel Bibcode: 2010PhRvE..81c6401D Altcode: 2009arXiv0910.3948D The resistive decay of chains of three interlocked magnetic flux rings is considered. Depending on the relative orientation of the magnetic field in the three rings, the late-time decay can be either fast or slow. Thus, the qualitative degree of tangledness is less important than the actual value of the linking number or, equivalently, the net magnetic helicity. Our results do not suggest that invariants of higher order than that of the magnetic helicity need to be considered to characterize the decay of the field. Title: Homochirality and the Need for Energy Authors: Plasson, Raphaël; Brandenburg, Axel Bibcode: 2010OLEB...40...93P Altcode: 2009OLEB..tmp...26P; 2009arXiv0908.0658P The mechanisms for explaining how a stable asymmetric chemical system can be formed from a symmetric chemical system, in the absence of any asymmetric influence other than statistical fluctuations, have been developed during the last decades, focusing on the non-linear kinetic aspects. Besides the absolute necessity of self-amplification processes, the importance of energetic aspects is often underestimated. Going down to the most fundamental aspects, the distinction between a single object—that can be intrinsically asymmetric—and a collection of objects—whose racemic state is the more stable one—must be emphasized. A system of strongly interacting objects can be described as one single object retaining its individuality and a single asymmetry; weakly or non-interacting objects keep their own individuality, and are prone to racemize towards the equilibrium state. In the presence of energy fluxes, systems can be maintained in an asymmetric non-equilibrium steady-state. Such dynamical systems can retain their asymmetry for times longer than their racemization time. Title: Oscillatory migratory large-scale fields in mean-field and direct simulations Authors: Mitra, Dhrubaditya; Tavakol, Reza; Brandenburg, Axel; Käpylä, Petri J. Bibcode: 2010IAUS..264..197M Altcode: We summarise recent results form direct numerical simulations of both non-rotating helically forced and rotating convection driven MHD equations in spherical wedge-shape domains. In the former, using perfect-conductor boundary conditions along the latitudinal boundaries we observe oscillations, polarity reversals and equatorward migration of the large-scale magnetic fields. In the latter we obtain angular velocity with cylindrical contours and large-scale magnetic field which shows oscillations, polarity reversals but poleward migration. The occurrence of these behviours in direct numerical simulations is clearly of interest. However the present models as they stand are not directly applicable to the solar dynamo problem. Nevertheless, they provide general insights into the operation of turbulent dynamos. Title: Mean electromotive force proportional to mean flow in MHD turbulence Authors: Rädler, K. -H.; Brandenburg, A. Bibcode: 2010AN....331...14R Altcode: 2009arXiv0910.0071R In mean-field magnetohydrodynamics the mean electromotive force due to velocity and magnetic-field fluctuations plays a crucial role. In general it consists of two parts, one independent of and another one proportional to the mean magnetic field. The first part may be nonzero only in the presence of mhd turbulence, maintained, e.g., by small-scale dynamo action. It corresponds to a battery, which lets a mean magnetic field grow from zero to a finite value. The second part, which covers, e.g., the \alpha effect, is important for large-scale dynamos. Only a few examples of the aforementioned first part of the mean electromotive force have been discussed so far. It is shown that a mean electromotive force proportional to the mean fluid velocity, but independent of the mean magnetic field, may occur in an originally homogeneous isotropic mhd turbulence if there are nonzero correlations of velocity and electric current fluctuations or, what is equivalent, of vorticity and magnetic field fluctuations. This goes beyond the Yoshizawa effect, which consists in the occurrence of mean electromotive forces proportional to the mean vorticity or to the angular velocity defining the Coriolis force in a rotating frame and depends on the cross-helicity defined by the velocity and magnetic field fluctuations. Contributions to the mean electromotive force due to inhomogeneity of the turbulence are also considered. Possible consequences of the above findings for the generation of magnetic fields in cosmic bodies are discussed. Title: Magnetic field evolution in simulations with Euler potentials Authors: Brandenburg, Axel Bibcode: 2010MNRAS.401..347B Altcode: 2009arXiv0907.1906B; 2009MNRAS.tmp.1492B Using two- and three-dimensional hydromagnetic simulations for a range of different flows, including laminar and turbulent ones, it is shown that solutions expressing the field in terms of Euler potentials (EP) are in general incorrect if the EP are evolved with an artificial diffusion term. In three dimensions, standard methods using the magnetic vector potential are found to permit dynamo action when the EP give decaying solutions. With an imposed field, the EP method yields excessive power at small scales. This effect is more exaggerated in the dynamic case, suggesting an unrealistically reduced feedback from the Lorentz force. The EP approach agrees with standard methods only at early times when magnetic diffusivity did not have time to act. It is demonstrated that the usage of EP with even a small artificial magnetic diffusivity does not converge to a proper solution of hydromagnetic turbulence. The source of this disagreement is not connected with magnetic helicity or the three-dimensionality of the magnetic field, but is simply due to the fact that the non-linear representation of the magnetic field in terms of EP that depend on the same coordinates is incompatible with the linear diffusion operator in the induction equation. Title: Equatorial magnetic helicity flux in simulations with different gauges Authors: Mitra, D.; Candelaresi, S.; Chatterjee, P.; Tavakol, R.; Brandenburg, A. Bibcode: 2010AN....331..130M Altcode: 2009arXiv0911.0969M We use direct numerical simulations of forced MHD turbulence with a forcing function that produces two different signs of kinetic helicity in the upper and lower parts of the domain. We show that the mean flux of magnetic helicity from the small-scale field between the two parts of the domain can be described by a Fickian diffusion law with a diffusion coefficient that is approximately independent of the magnetic Reynolds number and about one third of the estimated turbulent magnetic diffusivity. The data suggest that the turbulent diffusive magnetic helicity flux can only be expected to alleviate catastrophic quenching at Reynolds numbers of more than several thousands. We further calculate the magnetic helicity density and its flux in the domain for three different gauges. We consider the Weyl gauge, in which the electrostatic potential vanishes, the pseudo-Lorenz gauge, where the speed of light is replaced by the sound speed, and the `resistive gauge' in which the Laplacian of the magnetic vector potential acts as a resistive term. We find that, in the statistically steady state, the time-averaged magnetic helicity density and the magnetic helicity flux are the same in all three gauges. Title: Convective dynamos in spherical wedge geometry Authors: Käpylä, P. J.; Korpi, M. J.; Brandenburg, A.; Mitra, D.; Tavakol, R. Bibcode: 2010AN....331...73K Altcode: 2009arXiv0909.1330K Self-consistent convective dynamo simulations in wedge-shaped spherical shells are presented. Differential rotation is generated by the interaction of convection with rotation. Equatorward acceleration and dynamo action are obtained only for sufficiently rapid rotation. The angular velocity tends to be constant along cylinders. Oscillatory large-scale fields are found to migrate in the poleward direction. Comparison with earlier simulations in full spherical shells and Cartesian domains is made. Title: Surface appearance of dynamo-generated large-scale fields Authors: Brandenburg, Axel Bibcode: 2010cosp...38.2826B Altcode: 2010cosp.meet.2826B Twisted magnetic fields are frequently seen to emerge above the visible surface of the Sun. This emergence is usually associated with the rise of buoyant magnetic flux structures. Here we address the question about magnetic field structures that are generated by a turbulent large-scale dynamo just beneath the surface. The computational domain is split into two parts. In the lower part, which we refer to as the turbulence zone, the flow is driven by an adopted helical forcing function leading to dynamo action. Above this region, which we refer to as the exterior, a nearly force-free magnetic field is computed at each time step using the stress-and-relax method. A twisted arcade-like field structure is found to emerge in the exterior above the turbulence zone. Strong current sheets tend to be formed above the neutral line, where the vertical field component vanishes. The degree to which the exterior field is force-free is estimated as the ratio of the dot product of current density and field strength to their respective rms values. This ratio reaches values of up to 95driven by the residual Lorentz force. Title: Large-scale magnetic flux concentrations from turbulent stresses Authors: Brandenburg, A.; Kleeorin, N.; Rogachevskii, I. Bibcode: 2010AN....331....5B Altcode: 2009arXiv0910.1835B % In this study we provide the first numerical demonstration of the effects of turbulence on the mean Lorentz force and the resulting formation of large-scale magnetic structures. Using three-dimensional direct numerical simulations (DNS) of forced turbulence we show that an imposed mean magnetic field leads to a decrease of the turbulent hydromagnetic pressure and tension. This phenomenon is quantified by determining the relevant functions that relate the sum of the turbulent Reynolds and Maxwell stresses with the Maxwell stress of the mean magnetic field. Using such a parameterization, we show by means of two-dimensional and three-dimensional mean-field numerical modelling that an isentropic density stratified layer becomes unstable in the presence of a uniform imposed magnetic field. This large-scale instability results in the formation of loop-like magnetic structures which are concentrated at the top of the stratified layer. In three dimensions these structures resemble the appearance of bipolar magnetic regions in the Sun. The results of DNS and mean-field numerical modelling are in good agreement with theoretical predictions. We discuss our model in the context of a distributed solar dynamo where active regions and sunspots might be rather shallow phenomena.}

\begin{document Title: From Fibril to Diffuse Fields During Dynamo Saturation Authors: Brandenburg, A. Bibcode: 2009ASPC..416..433B Altcode: 2009arXiv0904.2842B The degree of intermittency of the magnetic field of a large-scale dynamo is considered. Based on simulations it is argued that there is a tendency for the field to become more diffuse and non-intermittent as the dynamo saturates. The simulations are idealized in that the turbulence is strongly helical and shear is strong, so the tendency for the field to become more diffuse is somewhat exaggerated. Earlier results concerning the effects of magnetic buoyancy are discussed. It is emphasized that the resulting magnetic buoyancy is weak compared with the stronger effects of simultaneous downward pumping. These findings are used to support the notion that the solar dynamo might operate in a distributed fashion where the near-surface shear layer could play an important role. Title: The critical role of magnetic helicity in astrophysical large-scale dynamos Authors: Brandenburg, Axel Bibcode: 2009PPCF...51l4043B Altcode: 2009arXiv0909.4377B The role of magnetic helicity in astrophysical large-scale dynamos is reviewed and compared with cases where there is no energy supply and an initial magnetic field can only decay. In both cases magnetic energy tends to get redistributed to larger scales. Depending on the efficiency of magnetic helicity fluxes the decay of a helical field can speed up. Likewise, the saturation of a helical dynamo can speed up through magnetic helicity fluxes. The astrophysical importance of these processes is reviewed in the context of the solar dynamo and an estimated upper limit for the magnetic helicity flux of 1046 Mx2/cycle is given. Title: Memory Effects in Turbulent Transport Authors: Hubbard, Alexander; Brandenburg, Axel Bibcode: 2009ApJ...706..712H Altcode: 2008arXiv0811.2561H In the mean-field theory of magnetic fields, turbulent transport, i.e., the turbulent electromotive force is described by a combination of the α effect and turbulent magnetic diffusion, which are usually assumed to be proportional, respectively, to the mean field and its spatial derivatives. For a passive scalar, there is just turbulent diffusion, where the mean flux of concentration depends on the gradient of the mean concentration. However, these proportionalities are approximations that are valid only if the mean field or the mean concentration vary slowly in time. Examples are presented where turbulent transport possesses memory, i.e., where it depends crucially on the past history of the mean field. Such effects are captured by replacing turbulent transport coefficients with time integral kernels, resulting in transport coefficients that depend effectively on the frequency or the growth rate of the mean field itself. In this paper, we perform numerical experiments to find the characteristic timescale (or memory length) of this effect as well as simple analytical models of the integral kernels in the case of passive scalar concentrations and kinematic dynamos. The integral kernels can then be used to find self-consistent growth or decay rates of the mean fields. In mean-field dynamos, the growth rates and cycle periods based on steady state values of α effect, and turbulent diffusivity can be quite different from the actual values. Title: The role of the Yoshizawa effect in the Archontis dynamo Authors: Sur, Sharanya; Brandenburg, Axel Bibcode: 2009MNRAS.399..273S Altcode: 2009MNRAS.tmp.1087S; 2009arXiv0902.2394S The generation of mean magnetic fields is studied for a simple non-helical flow where a net cross-helicity of either sign can emerge. This flow, which is also known as the Archontis flow, is a generalization of the Arnold-Beltrami-Childress flow, but with the cosine terms omitted. The presence of cross-helicity leads to a mean-field dynamo effect that is known as the Yoshizawa effect. Direct numerical simulations of such flows demonstrate the presence of magnetic fields on scales larger than the scale of the flow. Contrary to earlier expectations, the Yoshizawa effect is found to be proportional to the mean magnetic field and can therefore lead to its exponential instead of just linear amplification for magnetic Reynolds numbers that exceed a certain critical value. Unlike α effect dynamos, it is found that the Yoshizawa effect is not notably constrained by the presence of a conservation law. It is argued that this is due to the presence of a forcing term in the momentum equation, which leads to a non-zero correlation with the magnetic field. Finally, the application to energy convergence in solar wind turbulence is discussed. Title: The α effect with imposed and dynamo-generated magnetic fields Authors: Hubbard, A.; Del Sordo, F.; Käpylä, P. J.; Brandenburg, A. Bibcode: 2009MNRAS.398.1891H Altcode: 2009MNRAS.tmp.1219H; 2009arXiv0904.2773H Estimates for the non-linear α effect in helical turbulence with an applied magnetic field are presented using two different approaches: the imposed-field method where the electromotive force owing to the applied field is used, and the test-field method where separate evolution equations are solved for a set of different test fields. Both approaches agree for stronger fields, but there are apparent discrepancies for weaker fields that can be explained by the influence of dynamo-generated magnetic fields on the scale of the domain that are referred to as meso-scale magnetic fields. Examples are discussed where these meso-scale fields can lead to both drastically overestimated and underestimated values of α compared with the kinematic case. It is demonstrated that the kinematic value can be recovered by resetting the fluctuating magnetic field to zero in regular time intervals. It is concluded that this is the preferred technique both for the imposed-field and the test-field methods. Title: Small-scale magnetic helicity losses from a mean-field dynamo Authors: Brandenburg, Axel; Candelaresi, Simon; Chatterjee, Piyali Bibcode: 2009MNRAS.398.1414B Altcode: 2009MNRAS.tmp..979B; 2009arXiv0905.0242B Using mean-field models with a dynamical quenching formalism, we show that in finite domains magnetic helicity fluxes associated with small-scale magnetic fields are able to alleviate catastrophic quenching. We consider fluxes that result from advection by a mean flow, the turbulent mixing down the gradient of mean small-scale magnetic helicity density or the explicit removal which may be associated with the effects of coronal mass ejections in the Sun. In the absence of shear, all the small-scale magnetic helicity fluxes are found to be equally strong for both large- and small-scale fields. In the presence of shear, there is also an additional magnetic helicity flux associated with the mean field, but this flux does not alleviate catastrophic quenching. Outside the dynamo-active region, there are neither sources nor sinks of magnetic helicity, so in a steady state this flux must be constant. It is shown that unphysical behaviour emerges if the small-scale magnetic helicity flux is forced to vanish within the computational domain. Title: Shear-driven magnetic buoyancy oscillations Authors: Vermersch, V.; Brandenburg, A. Bibcode: 2009AN....330..797V Altcode: 2009arXiv0909.0324V The effects of uniform horizontal shear on a stably stratified layer of gas is studied. The system is initially destabilized by a magnetically buoyant flux tube pointing in the cross-stream direction. The shear amplifies the initial field to Lundquist numbers of about 200-400, but then its value drops to about 100-300, depending on the value of the sub-adiabatic gradient. The larger values correspond to cases where the stratification is strongly stable and nearly isothermal. At the end of the runs the magnetic field is nearly axisymmetric, i.e. uniform in the streamwise direction. In view of Cowling's theorem the sustainment of the field remains a puzzle and may be due to subtle numerical effects that have not yet been identified in detail. In the final state the strength of the magnetic field decreases with height in such a way that the field is expected to be unstable. Low amplitude oscillations are seen in the vertical velocity even at late times, suggesting that they might be persistent. Title: Turbulent Dynamos with Shear and Fractional Helicity Authors: Käpylä, Petri J.; Brandenburg, Axel Bibcode: 2009ApJ...699.1059K Altcode: 2008arXiv0810.2298K Dynamo action owing to helically forced turbulence and large-scale shear is studied using direct numerical simulations. The resulting magnetic field displays propagating wave-like behavior. This behavior can be modeled in terms of an αΩ dynamo. In most cases super-equipartition fields are generated. By varying the fraction of helicity of the turbulence the regeneration of poloidal fields via the helicity effect (corresponding to the α-effect) is regulated. The saturation level of the magnetic field in the numerical models is consistent with a linear dependence on the ratio of the fractional helicities of the small and large-scale fields, as predicted by a simple nonlinear mean-field model. As the magnetic Reynolds number (Re M ) based on the wavenumber of the energy-carrying eddies is increased from 1 to 180, the cycle frequency of the large-scale field is found to decrease by a factor of about 6 in cases where the turbulence is fully helical. This is interpreted in terms of the turbulent magnetic diffusivity, which is found to be only weakly dependent on the Re M . Title: Large-scale Dynamos in Rigidly Rotating Turbulent Convection Authors: Käpylä, Petri J.; Korpi, Maarit J.; Brandenburg, Axel Bibcode: 2009ApJ...697.1153K Altcode: 2008arXiv0812.3958K The existence of large-scale dynamos in rigidly rotating turbulent convection without shear is studied using three-dimensional numerical simulations of penetrative rotating compressible convection. We demonstrate that rotating convection in a Cartesian domain can drive a large-scale dynamo even in the absence of shear. The large-scale field contains a significant fraction of the total field in the saturated state. The simulation results are compared with one-dimensional mean-field dynamo models where turbulent transport coefficients, as determined using the test field method, are used. The reason for the absence of large-scale dynamo action in earlier studies is shown to be due to the rotation being too slow: whereas the α-effect can change sign, its magnitude stays approximately constant as a function of rotation, and the turbulent diffusivity decreases monotonically with increasing rotation. Only when rotation is rapid enough a large-scale dynamo can be excited. The one-dimensional mean-field model with dynamo coefficients from the test-field results predicts reasonably well the dynamo excitation in the direct simulations. This result further validates the test field procedure and reinforces the interpretation that the observed dynamo is driven by a turbulent α-effect. This result demonstrates the existence of an α-effect and an α2-dynamo with natural forcing. Title: Large-scale Dynamos at Low Magnetic Prandtl Numbers Authors: Brandenburg, Axel Bibcode: 2009ApJ...697.1206B Altcode: 2008arXiv0808.0961B Using direct simulations of hydromagnetic turbulence driven by random polarized waves it is shown that dynamo action is possible over a wide range of magnetic Prandtl numbers from 10-3 to 1. Triply periodic boundary conditions are being used. In the final saturated state the resulting magnetic field has a large-scale component of Beltrami type. For the kinematic phase, growth rates have been determined for magnetic Prandtl numbers between 0.01 and 1, but only the case with the smallest magnetic Prandtl number shows large-scale magnetic fields. It is less organized than in the nonlinear stage. For small magnetic Prandtl numbers the growth rates are comparable to those calculated from an alpha squared mean-field dynamo. In the linear regime the magnetic helicity spectrum has a short inertial range compatible with a -5/3 power law, while in the nonlinear regime it is the current helicity whose spectrum may be compatible with such a law. In the saturated case, the spectral magnetic energy in the inertial range is in slight excess over the spectral kinetic energy, although for small magnetic Prandtl numbers the magnetic energy spectrum reaches its resistive cut off wavenumber more quickly. The viscous energy dissipation declines with the square root of the magnetic Prandtl number, which implies that most of the energy is dissipated via Joule heat. Title: Alpha effect and turbulent diffusion from convection Authors: Käpylä, P. J.; Korpi, M. J.; Brandenburg, A. Bibcode: 2009A&A...500..633K Altcode: 2008arXiv0812.1792K Aims: We study turbulent transport coefficients that describe the evolution of large-scale magnetic fields in turbulent convection.
Methods: We use the test field method, together with three-dimensional numerical simulations of turbulent convection with shear and rotation, to compute turbulent transport coefficients describing the evolution of large-scale magnetic fields in mean-field theory in the kinematic regime. We employ one-dimensional mean-field models with the derived turbulent transport coefficients to examine whether they give results that are compatible with direct simulations.
Results: The results for the α-effect as a function of rotation rate are consistent with earlier numerical studies, i.e. increasing magnitude as rotation increases and approximately cos θ latitude profile for moderate rotation. Turbulent diffusivity, η_t, is proportional to the square of the turbulent vertical velocity in all cases. Whereas ηt decreases approximately inversely proportional to the wavenumber of the field, the α-effect and turbulent pumping show a more complex behaviour with partial or full sign changes and the magnitude staying roughly constant. In the presence of shear and no rotation, a weak α-effect is induced which does not seem to show any consistent trend as a function of shear rate. Provided that the shear is large enough, this small α-effect is able to excite a dynamo in the mean-field model. The coefficient responsible for driving the shear-current effect shows several sign changes as a function of depth but is also able to contribute to dynamo action in the mean-field model. The growth rates in these cases are, however, well below those in direct simulations, suggesting that an incoherent α-shear dynamo may also act in the simulations. If both rotation and shear are present, the α-effect is more pronounced. At the same time, the combination of the shear-current and Ω×{ J}-effects is also stronger than in the case of shear alone, but subdominant to the α-shear dynamo. The results of direct simulations are consistent with mean-field models where all of these effects are taken into account without the need to invoke incoherent effects. Title: Emergence of Protometabolisms and the Self-Organization of Non-equilibrium Reaction Networks Authors: Plasson, Raphael; Bersini, Hugues; Brandenburg, Axel Bibcode: 2009OLEB...39..263P Altcode: The debate between Metabolism first and Replication first theories is shaping the discussion about how life originated (Pross, 2004), emphasizing either the necessity of a structured reaction network to maintain information, or the necessity of information to shape the reaction network. In order to solve this apparent paradox, a general approach comes down to understanding how protometabolisms can lead to the emergence of the first template replicators (Shapiro, 2006; de Duve, 2007), from which open-ended evolutive systems can develop (Ruiz-Mirazo et al., 2008). On the one hand, replication systems must maintain their informational integrity, characterized by a specific topology of the reaction network, implying the necessity of a continuous consumption and use of energy. On the other hand, the presence of a source of free energy should have lead to the self-organization of reaction networks (Plasson and Bersini, submitted), that is to the emergence and maintenance of protometabolisms. Such reservoirs of energy (originating from several external energy sources, like sun light, reduced material from Earth crust, meteorites entering the atmosphere, etc.) generate both linear fluxes of reaction and reaction loops, as attractors of the network (Plasson et al. submitted). This implies the spontaneous generation of network catalysis and autocatalysis, which introduces positive and negative feedbacks inside the system. In such dynamical reaction networks, bifurcation mechanisms leads to the extinction of some pathways, favoring the persistence of other. The topology of the reaction network is subjected to a spontaneous evolution, driven by free energy transfers. Rather than the increase of complexity, this process can be better described as a change in the nature of the complexity, from horizontal complexity (i.e. a large number of simple molecules reacting non-selectively with each other) to vertical complexity (i.e. a large number of complex molecules, built on a limited number of building blocks, engaged in autocatalytic cycles). Such self-organization phenomenoncanbelinked toanevolution of the logical depthas described by Bennett (1986). A model of dynamic polymerization of amino acids will be described as a simple example of such self-organization of reaction network by bifurcation mechanisms (Plasson et al. 2007). In this scope, the gap separating prebiotic systems from the first reproductive systems can be described as evolutive protometabolisms. The bifurcations, driven by the fighting mechanisms between the network sub-elements, are sources of topological changes inside the reaction networks, from randomness to structures organized around some central compounds. This may have constituted the first replicators, not as template replicators of similar molecules, bu as network replicators of similar reaction cycles, competing with each others. Title: Turbulent diffusion with rotation or magnetic fields Authors: Brandenburg, Axel; Svedin, Andreas; Vasil, Geoffrey M. Bibcode: 2009MNRAS.395.1599B Altcode: 2009MNRAS.tmp..519B; 2009arXiv0901.2112B The turbulent diffusion tensor describing the evolution of the mean concentration of a passive scalar is investigated for non-helically forced turbulence in the presence of rotation or a magnetic field. With rotation, the Coriolis force causes a sideways deflection of the flux of mean concentration. Within the magnetohydrodynamics approximation there is no analogous effect from the magnetic field because the effects on the flow do not depend on the sign of the field. Both rotation and magnetic fields tend to suppress turbulent transport, but this suppression is weaker in the direction along the magnetic field. Turbulent transport along the rotation axis is not strongly affected by rotation, except on shorter length-scales, i.e. when the scale of the variation of the mean field becomes comparable with the scale of the energy-carrying eddies. These results are discussed in the context of anisotropic convective energy transport in the Sun. Title: Turbulent Dynamos in Spherical Shell Segments of Varying Geometrical Extent Authors: Mitra, Dhrubaditya; Tavakol, Reza; Brandenburg, Axel; Moss, David Bibcode: 2009ApJ...697..923M Altcode: 2008arXiv0812.3106M We use three-dimensional direct numerical simulations of the helically forced magnetohydrodynamic equations in spherical shell segments in order to study the effects of changes in the geometrical shape and size of the domain on the growth and saturation of large-scale magnetic fields. We inject kinetic energy along with kinetic helicity in spherical domains via helical forcing using Chandrasekhar-Kendall functions. We take perfect conductor boundary conditions for the magnetic field to ensure that no magnetic helicity escapes the domain boundaries. We find dynamo action giving rise to magnetic fields at scales larger than the characteristic scale of the forcing. The magnetic energy exceeds the kinetic energy over dissipative timescales, similar to that seen earlier in Cartesian simulations in periodic boxes. As we increase the size of the domain in the azimuthal direction, we find that the nonlinearly saturated magnetic field organizes itself in long-lived cellular structures with aspect ratios close to unity. These structures tile the domain along the azimuthal direction, thus resulting in very small longitudinally averaged magnetic fields for large domain sizes. The scales of these structures are determined by the smallest scales of the domain, which in our simulations is usually the radial scale. We also find that increasing the meridional extent of the domains produces little qualitative change, except a marginal increase in the large-scale field. We obtain qualitatively similar results in Cartesian domains with similar aspect ratios. Title: Advances in Theory and Simulations of Large-Scale Dynamos Authors: Brandenburg, Axel Bibcode: 2009SSRv..144...87B Altcode: 2009arXiv0901.0329B Recent analytical and computational advances in the theory of large-scale dynamos are reviewed. The importance of the magnetic helicity constraint is apparent even without invoking mean-field theory. The tau approximation yields expressions that show how the magnetic helicity gets incorporated into mean-field theory. The test-field method allows an accurate numerical determination of turbulent transport coefficients in linear and nonlinear regimes. Finally, some critical views on the solar dynamo are being offered and targets for future research are highlighted. Title: Paradigm shifts in solar dynamo modeling Authors: Brandenburg, Axel Bibcode: 2009IAUS..259..159B Altcode: 2009arXiv0901.3789B Selected topics in solar dynamo theory are being highlighted. The possible relevance of the near-surface shear layer is discussed. The role of turbulent downward pumping is mentioned in connection with earlier concerns that a dynamo-generated magnetic field would be rapidly lost from the convection zone by magnetic buoyancy. It is argued that shear-mediated small-scale magnetic helicity fluxes are responsible for the success of some of the recent large-scale dynamo simulations. These fluxes help in disposing of excess small-scale magnetic helicity. This small-scale magnetic helicity, in turn, is generated in response to the production of an overall tilt in each Parker loop. Some preliminary calculations of this helicity flux are presented for a system with uniform shear. In the Sun the effects of magnetic helicity fluxes may be seen in coronal mass ejections shedding large amounts of magnetic helicity. Title: Alpha effect and diffusivity in helical turbulence with shear Authors: Mitra, D.; Käpylä, P. J.; Tavakol, R.; Brandenburg, A. Bibcode: 2009A&A...495....1M Altcode: 2008arXiv0806.1608M Aims: We study the dependence of turbulent transport coefficients, such as the components of the α tensor (αij) and the turbulent magnetic diffusivity tensor (ηij), on shear and magnetic Reynolds number in the presence of helical forcing.
Methods: We use three-dimensional direct numerical simulations with periodic boundary conditions and measure the turbulent transport coefficients using the kinematic test field method. In all cases the magnetic Prandtl number is taken as unity.
Results: We find that with increasing shear the diagonal components of αij quench, whereas those of ηij increase. The antisymmetric parts of both tensors increase with increasing shear. We also propose a simple expression for the turbulent pumping velocity (or γ effect). This pumping velocity is proportional to the kinetic helicity of the turbulence and the vorticity of the mean flow. For negative helicity, i.e. for a positive trace of αij, it points in the direction of the mean vorticity, i.e. perpendicular to the plane of the shear flow. Our simulations support this expression for low shear and magnetic Reynolds number. The transport coefficients depend on the wavenumber of the mean flow in a Lorentzian fashion, just as for non-shearing turbulence. Title: Mean-field effects in the Galloway-Proctor flow Authors: Rädler, Karl-Heinz; Brandenburg, Axel Bibcode: 2009MNRAS.393..113R Altcode: 2008arXiv0809.0851R In the framework of mean-field electrodynamics the coefficients defining the mean electromotive force in Galloway-Proctor flows are determined. These flows show a two-dimensional pattern and are helical. The pattern wobbles in its plane. Apart from one exception a circularly polarized Galloway-Proctor flow, i.e. a circular motion of the flow pattern is assumed. This corresponds to one of the cases considered recently by Courvoisier, Hughes & Tobias. An analytic theory of the α effect and related effects in this flow is developed within the second-order correlation approximation and a corresponding fourth-order approximation. In the validity range of these approximations there is an α effect but no γ effect, or pumping effect. Numerical results obtained with the test-field method, which are independent of these approximations, confirm the results for α and show that γ is in general non-zero. Both α and γ show a complex dependency on the magnetic Reynolds number and other parameters that define the flow, that is, amplitude and frequency of the circular motion. Some results for the magnetic diffusivity ηt and a related quantity are given, too. Finally, a result for α in the case of a randomly varying linearly polarized Galloway-Proctor flow, without the aforementioned circular motion, is presented. The flows investigated show quite interesting effects. There is, however, no straightforward way to relate these flows to turbulence and to use them for studying properties of the α effect and associated effects under realistic conditions. Title: Turbulent stresses as a function of shear rate in a local disk model Authors: Liljeström, A. J.; Korpi, M. J.; Käpylä, P. J.; Brandenburg, A.; Lyra, W. Bibcode: 2009AN....330...92L Altcode: 2008arXiv0811.2341L We present local numerical models of accretion disk turbulence driven by the magnetorotational instability with varying shear rate. The resulting turbulent stresses are compared with predictions of a closure model in which triple correlations are modelled in terms of quadratic correlations. This local model uses five nondimensional parameters to describe the properties of the flow. We attempt to determine these closure parameters for our simulations and find that the model does produce qualitatively correct behaviour. In addition, we present results concerning the shear rate dependency of the magnetic to kinetic energy ratio. We find both the turbulent stress ratio and the total stress to be strongly dependent on the shear rate. Title: Numerical study of large-scale vorticity generation in shear-flow turbulence Authors: Käpylä, Petri J.; Mitra, Dhrubaditya; Brandenburg, Axel Bibcode: 2009PhRvE..79a6302K Altcode: 2008arXiv0810.0833K Simulations of stochastically forced shear-flow turbulence in a shearing-periodic domain are used to study the spontaneous generation of large-scale flow patterns in the direction perpendicular to the plane of the shear. Based on an analysis of the resulting large-scale velocity correlations it is argued that the mechanism behind this phenomenon could be the mean-vorticity dynamo effect pioneered by Elperin, Kleeorin, and Rogachevskii [Phys. Rev. E 68, 016311 (2003)]. This effect is based on the anisotropy of the eddy viscosity tensor. One of its components may be able to replenish cross-stream mean flows by acting upon the streamwise component of the mean flow. Shear, in turn, closes the loop by acting upon the cross-stream mean flow to produce stronger streamwise mean flows. The diagonal component of the eddy viscosity is found to be of the order of the rms turbulent velocity divided by the wave number of the energy-carrying eddies. Title: Solar Dynamo and Magnetic Self-Organization Authors: Kosovichev, A. G.; Arlt, R.; Bonanno, A.; Brandenburg, A.; Brun, A. S.; Busse, F.; Dikpati, M.; Hill, F.; Gilman, P. A.; Nordlund, A.; Ruediger, G.; Stein, R. F.; Sekii, T.; Stenflo, J. O.; Ulrich, R. K.; Zhao, J. Bibcode: 2009astro2010S.160K Altcode: No abstract at ADS Title: Advances in Theory and Simulations of Large-Scale Dynamos Authors: Brandenburg, Axel Bibcode: 2009odsm.book...87B Altcode: Recent analytical and computational advances in the theory of large-scale dynamos are reviewed. The importance of the magnetic helicity constraint is apparent even without invoking mean-field theory. The tau approximation yields expressions that show how the magnetic helicity gets incorporated into mean-field theory. The test-field method allows an accurate numerical determination of turbulent transport coefficients in linear and nonlinear regimes. Finally, some critical views on the solar dynamo are being offered and targets for future research are highlighted. Title: A growing dynamo from a saturated Roberts flow dynamo Authors: Tilgner, Andreas; Brandenburg, Axel Bibcode: 2008MNRAS.391.1477T Altcode: 2008arXiv0808.2141T Using direct simulations, weakly non-linear theory and non-linear mean-field theory, it is shown that the quenched velocity field of a saturated non-linear dynamo can itself act as a kinematic dynamo. The flow is driven by a forcing function that would produce a Roberts flow in the absence of a magnetic field. This result confirms an analogous finding by Cattaneo & Tobias for the more complicated case of turbulent convection, suggesting that this may be a common property of non-linear dynamos; see also the talk given online at the Kavli Institute for Theoretical Physics (http://online.kitp.ucsb.edu/online/dynamo_c08/cattaneo). It is argued that this property can be used to test non-linear mean-field dynamo theories. Title: Large-scale dynamos in turbulent convection with shear Authors: Käpylä, P. J.; Korpi, M. J.; Brandenburg, A. Bibcode: 2008A&A...491..353K Altcode: 2008arXiv0806.0375K Aims: To study the existence of large-scale convective dynamos under the influence of shear and rotation.
Methods: Three-dimensional numerical simulations of penetrative compressible convection with uniform horizontal shear are used to study dynamo action and the generation of large-scale magnetic fields. We consider cases where the magnetic Reynolds number is either marginal or moderately supercritical with respect to small-scale dynamo action in the absence of shear and rotation. Our magnetic Reynolds number is based on the wavenumber of the depth of the convectively unstable layer. The effects of magnetic helicity fluxes are studied by comparing results for the magnetic field with open and closed boundaries.
Results: Without shear no large-scale dynamos are found even if the ingredients necessary for the α-effect (rotation and stratification) are present in the system. When uniform horizontal shear is added, a large-scale magnetic field develops, provided the boundaries are open. In this case the mean magnetic field contains a significant fraction of the total field. For those runs where the magnetic Reynolds number is between 60 and 250, an additional small-scale dynamo is expected to be excited, but the field distribution is found to be similar to cases with smaller magnetic Reynolds number where the small-scale dynamo is not excited. In the case of closed (perfectly conducting) boundaries, magnetic helicity fluxes are suppressed and no large-scale fields are found. Similarly, poor large-scale field development is seen when vertical shear is used in combination with periodic boundary conditions in the horizontal directions. If, however, open (normal-field) boundary conditions are used in the x-direction, a large-scale field develops. These results support the notion that shear not only helps to generate the field, but it also plays a crucial role in driving magnetic helicity fluxes out of the system along the isocontours of shear, thereby allowing efficient dynamo action. Title: Magnetic Quenching of α and Diffusivity Tensors in Helical Turbulence Authors: Brandenburg, Axel; Rädler, Karl-Heinz; Rheinhardt, Matthias; Subramanian, Kandaswamy Bibcode: 2008ApJ...687L..49B Altcode: 2008arXiv0805.1287B The effect of a dynamo-generated mean magnetic field of Beltrami type on the mean electromotive force is studied. In the absence of the mean magnetic field the turbulence is assumed to be homogeneous and isotropic, but it becomes inhomogeneous and anisotropic with this field. Using the test-field method the dependence of the α and turbulent diffusivity tensors on the magnetic Reynolds number ReM is determined for magnetic fields that have reached approximate equipartition with the velocity field. The tensor components are characterized by a pseudoscalar α and a scalar turbulent magnetic diffusivity ηt. Increasing ReM from 2 to 600 reduces ηt by a factor ≈5, suggesting that the quenching of ηt is, in contrast to the two-dimensional case, only weakly dependent on ReM. Over the same range of ReM, however, α is reduced by a factor ≈14, which can be explained by a corresponding increase of a magnetic contribution to the α-effect with opposite sign. Within this framework, the corresponding kinetic contribution to the α-effect turns out to be independent of ReM for 2 <= ReM <= 600. The level of fluctuations of α and ηt is only 10% and 20% of the respective kinematic reference values. Title: Nonlinear aspects of astrobiological research Authors: Brandenburg, Axel Bibcode: 2008arXiv0809.0261B Altcode: Several aspects of mathematical astrobiology are discussed. It is argued that around the time of the origin of life the handedness of biomolecules must have established itself through an instability. Possible pathways of producing a certain handedness include mechanisms involving either autocatalysis or, alternatively, epimerization as governing effects. Concepts for establishing hereditary information are discussed in terms of the theory of hypercycles. Instabilities toward parasites and possible remedies by invoking spatial extent are reviewed. Finally, some effects of early life are discussed that contributed to modifying and regulating atmosphere and climate of the Earth, and that could have contributed to the highly oxidized state of its crust. Title: The dual role of shear in large-scale dynamos Authors: Brandenburg, A. Bibcode: 2008AN....329..725B Altcode: 2008arXiv0808.0959B The role of shear in alleviating catastrophic quenching by shedding small-scale magnetic helicity through fluxes along contours of constant shear is discussed. The level of quenching of the dynamo effect depends on the quenched value of the turbulent magnetic diffusivity. Earlier estimates that might have suffered from the force-free degeneracy of Beltrami fields are now confirmed for shear flows where this degeneracy is lifted. For a dynamo that is saturated near equipartition field strength those estimates result in a 5-fold decrease of the magnetic diffusivity as the magnetic Reynolds number based on the wavenumber of the energy-carrying eddies is increased from 2 to 600. Finally, the role of shear in driving turbulence and large-scale fields by the magneto-rotational instability is emphasized. New simulations are presented and the 3\pi/4 phase shift between poloidal and toroidal fields is confirmed. It is suggested that this phase shift might be a useful diagnostic tool in identifying mean-field dynamo action in simulations and to distinguish this from other scenarios invoking magnetic buoyancy as a means to explain migration away from the midplane. Title: Lambda effect from forced turbulence simulations Authors: Käpylä, P. J.; Brandenburg, A. Bibcode: 2008A&A...488....9K Altcode: 2008arXiv0806.3751K Aims: We determine the components of the Λ-effect tensor that quantifies the contributions to the turbulent momentum transport even for uniform rotation.
Methods: Three-dimensional numerical simulations are used to study turbulent transport in triply periodic cubes under the influence of rotation and anisotropic forcing. Comparison is made with analytical results obtained via the so-called minimal tau-approximation.
Results: In the case where the turbulence intensity in the vertical direction dominates, the vertical stress is always negative. This situation is expected to occur in stellar convection zones. The horizontal component of the stress is weaker and exhibits a maximum at latitude 30° - regardless of how rapid the rotation is. The minimal tau-approximation captures many of the qualitative features of the numerical results, provided the relaxation time tau is close to the turnover time, i.e. the Strouhal number is of order unity.

Tables [see full textsee full textsee full text]-[see full textsee full textsee full text] are only available in electronic form at http.//www.aanda.org Title: Turbulent protostellar discs Authors: Brandenburg, A. Bibcode: 2008PhST..130a4016B Altcode: 2008arXiv0808.0960B Aspects of turbulence in protostellar accretion discs are being reviewed. The emergence of dead zones due to poor ionization and alternatives to the magneto-rotational instability are discussed. The coupling between dust and gas in protostellar accretion discs is explained and the turbulent drag is compared with laminar drag in the Stokes and Epstein regimes. Finally, the significance of magnetic-field generation in turbulent discs is emphasized in connection with driving outflows and with star disc coupling. Title: A solar mean field dynamo benchmark Authors: Jouve, L.; Brun, A. S.; Arlt, R.; Brandenburg, A.; Dikpati, M.; Bonanno, A.; Käpylä, P. J.; Moss, D.; Rempel, M.; Gilman, P.; Korpi, M. J.; Kosovichev, A. G. Bibcode: 2008A&A...483..949J Altcode: Context: The solar magnetic activity and cycle are linked to an internal dynamo. Numerical simulations are an efficient and accurate tool to investigate such intricate dynamical processes.
Aims: We present the results of an international numerical benchmark study based on two-dimensional axisymmetric mean field solar dynamo models in spherical geometry. The purpose of this work is to provide reference cases that can be analyzed in detail and that can help in further development and validation of numerical codes that solve such kinematic problems.
Methods: The results of eight numerical codes solving the induction equation in the framework of mean field theory are compared for three increasingly computationally intensive models of the solar dynamo: an αΩ dynamo with constant magnetic diffusivity, an αΩ dynamo with magnetic diffusivity sharply varying with depth and an example of a flux-transport Babcock-Leighton dynamo which includes a non-local source term and one large single cell of meridional circulation per hemisphere. All cases include a realistic profile of differential rotation and thus a sharp tachocline.
Results: The most important finding of this study is that all codes agree quantitatively to within less than a percent for the αΩ dynamo cases and within a few percent for the flux-transport case. Both the critical dynamo numbers for the onset of dynamo action and the corresponding cycle periods are reasonably well recovered by all codes. Detailed comparisons of butterfly diagrams and specific cuts of both toroidal and poloidal fields at given latitude and radius confirm the good quantitative agreement.
Conclusions: We believe that such a benchmark study will be a very useful tool since it provides detailed standard cases for comparison and reference. Title: Scale dependence of alpha effect and turbulent diffusivity Authors: Brandenburg, A.; Rädler, K. -H.; Schrinner, M. Bibcode: 2008A&A...482..739B Altcode: 2008arXiv0801.1320B Aims: We determine the alpha effect and turbulent magnetic diffusivity for mean magnetic fields with profiles of different length scales from simulations of isotropic turbulence. We then relate these results to nonlocal formulations in which alpha and the turbulent magnetic diffusivity correspond to integral kernels.
Methods: We solve evolution equations for magnetic fields that give the response to imposed test fields. These test fields correspond to mean fields with various wavenumbers. Both an imposed fully helical steady flow consisting of a pattern of screw-like motions (Roberts flow) and time-dependent, statistically steady isotropic turbulence are considered. In the latter case the evolution equations are solved simultaneously with the momentum and continuity equations. The corresponding results for the electromotive force are used to calculate alpha and magnetic diffusivity tensors.
Results: For both, the Roberts flow under the second-order correlation approximation and the isotropic turbulence alpha and turbulent magnetic diffusivity are greatest on large scales and these values diminish toward smaller scales. In both cases, the alpha effect and turbulent diffusion kernels are approximated by exponentials, corresponding to Lorentzian profiles in Fourier space. For isotropic turbulence, the turbulent diffusion kernel is half as wide as the alpha effect kernel. For the Roberts flow beyond the second-order correlation approximation, the turbulent diffusion kernel becomes negative on large scales. Title: Boundary layer on the surface of a neutron star Authors: Babkovskaia, N.; Brandenburg, A.; Poutanen, J. Bibcode: 2008MNRAS.386.1038B Altcode: 2008arXiv0802.1663B; 2008MNRAS.tmp..447B In an attempt to model the accretion on to a neutron star in low-mass X-ray binaries, we present 2D hydrodynamical models of the gas flow in close vicinity of the stellar surface. First, we consider a gas pressure-dominated case, assuming that the star is non-rotating. For the stellar mass we take Mstar = 1.4 × 10-2Msolar and for the gas temperature T = 5 × 106 K. Our results are qualitatively different in the case of a realistic neutron star mass and a realistic gas temperature of T ~= 108 K, when the radiation pressure dominates. We show that to get the stationary solution in a latter case, the star most probably has to rotate with the considerable velocity. Title: Core Mass Function: The Role of Gravity Authors: Dib, Sami; Brandenburg, Axel; Kim, Jongsoo; Gopinathan, Maheswar; André, Philippe Bibcode: 2008ApJ...678L.105D Altcode: 2008arXiv0801.2257D We analyze the mass distribution of cores formed in an isothermal, magnetized, turbulent, and self-gravitating nearly critical molecular cloud model. Cores are identified at two density threshold levels. Our main results are that the presence of self-gravity modifies the slopes of the core mass function (CMF) at the high-mass end. At low thresholds, the slope is shallower than the one predicted by pure turbulent fragmentation. The shallowness of the slope is due to the effects of core coalescence and gas accretion. Most importantly, the slope of the CMF at the high-mass end steepens when cores are selected at higher density thresholds, or alternatively, if the CMF is fitted with a lognormal function, the width of the lognormal distribution decreases with increasing threshold. This is due to the fact that gravity plays a more important role in denser structures selected at higher density threshold and leads to the conclusion that the role of gravity is essential in generating a CMF that bears more resemblance to the IMF when cores are selected with an increasing density threshold in the observations. Title: Modeling a Maunder minimum Authors: Brandenburg, A.; Spiegel, E. A. Bibcode: 2008AN....329..351B Altcode: 2008arXiv0801.2156B We introduce on/off intermittency into a mean field dynamo model by imposing stochastic fluctuations in either the alpha effect or through the inclusion of a fluctuating electromotive force. Sufficiently strong small scale fluctuations with time scales of the order of 0.3-3 years can produce long term variations in the system on time scales of the order of hundreds of years. However, global suppression of magnetic activity in both hemispheres at once was not observed. The variation of the magnetic field does not resemble that of the sunspot number, but is more reminiscent of the 10Be record. The interpretation of our results focuses attention on the connection between the level of magnetic activity and the sunspot number, an issue that must be elucidated if long term solar effects are to be well understood. Title: Magnetic Diffusivity Tensor and Dynamo Effects in Rotating and Shearing Turbulence Authors: Brandenburg, A.; Rädler, K. -H.; Rheinhardt, M.; Käpylä, P. J. Bibcode: 2008ApJ...676..740B Altcode: 2007arXiv0710.4059B The turbulent magnetic diffusivity tensor is determined in the presence of rotation or shear. The question is addressed whether dynamo action from the shear-current effect can explain large-scale magnetic field generation found in simulations with shear. For this purpose a set of evolution equations for the response to imposed test fields is solved with turbulent and mean motions calculated from the momentum and continuity equations. The corresponding results for the electromotive force are used to calculate turbulent transport coefficients. The diagonal components of the turbulent magnetic diffusivity tensor are found to be very close together, but their values increase slightly with increasing shear and decrease with increasing rotation rate. In the presence of shear, the sign of the two off-diagonal components of the turbulent magnetic diffusion tensor is the same and opposite to the sign of the shear. This implies that dynamo action from the shear-current effect is impossible, except perhaps for high magnetic Reynolds numbers. However, even though there is no alpha effect on the average, the components of the α tensor display Gaussian fluctuations around zero. These fluctuations are strong enough to drive an incoherent alpha-shear dynamo. The incoherent shear-current effect, on the other hand, is found to be subdominant. Title: Kinematic α-effect in isotropic turbulence simulations Authors: Sur, Sharanya; Brandenburg, Axel; Subramanian, Kandaswamy Bibcode: 2008MNRAS.385L..15S Altcode: 2008MNRAS.tmpL...7S; 2007arXiv0711.3789S Using numerical simulations at moderate magnetic Reynolds numbers up to 220, it is shown that in the kinematic regime, isotropic helical turbulence leads to an α-effect and a turbulent diffusivity whose values are independent of the magnetic Reynolds number, Rm, provided Rm exceeds unity. These turbulent coefficients are also consistent with expectations from the first-order smoothing approximation. For small values of Rm, α and turbulent diffusivity are proportional to Rm. Over finite time-intervals, meaningful values of α and turbulent diffusivity can be obtained even when there is small-scale dynamo action that produces strong magnetic fluctuations. This suggests that the fields generated by the small-scale dynamo do not make a correlated contribution to the mean electromotive force. Title: α -effect dynamos with zero kinetic helicity Authors: Rädler, Karl-Heinz; Brandenburg, Axel Bibcode: 2008PhRvE..77b6405R Altcode: 2008arXiv0801.0602R A simple explicit example of a Roberts-type dynamo is given in which the α effect of mean-field electrodynamics exists in spite of pointwise vanishing kinetic helicity of the fluid flow. In this way, it is shown that α -effect dynamos do not necessarily require nonzero kinetic helicity. A mean-field theory of Roberts-type dynamos is established within the framework of the second-order correlation approximation. In addition, numerical solutions of the original dynamo equations are given that are independent of any approximation of that kind. Both theory and numerical results demonstrate the possibility of dynamo action in the absence of kinetic helicity. Title: The helicity constraint in spherical shell dynamos Authors: Brandenburg, A.; Käpylä, P. J.; Mitra, D.; Moss, D.; Tavakol, R. Bibcode: 2007AN....328.1118B Altcode: 2007arXiv0711.3616B The motivation for considering distributed large scale dynamos in the solar context is reviewed in connection with the magnetic helicity constraint. Preliminary accounts of 3-dimensional direct numerical simulations (in spherical shell segments) and simulations of 2-dimensional mean field models (in spherical shells) are presented. Interesting similarities as well as some differences are noted. Title: Turbulent viscosity and Λ-effect from numerical turbulence models Authors: Käpylä, P. J.; Brandenburg, A. Bibcode: 2007AN....328.1006K Altcode: 2007arXiv0710.5632K Homogeneous anisotropic turbulence simulations are used to determine off-diagonal components of the Reynolds stress tensor and its parameterization in terms of turbulent viscosity and Λ-effect. The turbulence is forced in an anisotropic fashion by enhancing the strength of the forcing in the vertical direction. The Coriolis force is included with a rotation axis inclined relative to the vertical direction. The system studied here is significantly simpler than that of turbulent stratified convection which has often been used to study Reynolds stresses. Certain puzzling features of the results for convection, such as sign changes or highly concentrated latitude distributions, are not present in the simpler system considered here. Title: Homochirality in an Early Peptide World Authors: Brandenburg, Axel; Lehto, Harry J.; Lehto, Kirsi M. Bibcode: 2007AsBio...7..725B Altcode: 2006q.bio....10051B A recently proposed model of non-autocatalytic reactions in dipeptide formation that leads to spontaneous symmetry breaking and homochirality was examined. The model is governed by activation, polymerization, epimerization, and depolymerization of amino acids. Symmetry breaking was determined to result primarily from the different rates of reactions that involve homodimers and heterodimers, i.e., stereoselective reactions, and the fact that epimerization can only occur on the N-terminal residue and not on the C-terminal residue. This corresponds to an auto-inductive cyclic process that works only in one direction. It is argued that epimerization mimics autocatalytic behavior as well as mutual antagonism, both of which are known to be crucial for the production of full homochirality. Title: Magnetic helicity effects in astrophysical and laboratory dynamos Authors: Brandenburg, A.; Käpylä, P. J. Bibcode: 2007NJPh....9..305B Altcode: 2007arXiv0705.3507B Magnetic helicity effects are discussed in laboratory and astro-physical settings. Firstly, dynamo action in Taylor Green flows is discussed for different boundary conditions. However, because of the lack of scale separation with respect to the container, no large-scale field is being produced and there is no resistively slow saturation phase as otherwise expected. Secondly, the build-up of a large-scale field is demonstrated in a simulation where a localized magnetic eddy produces field on a larger scale if the eddy possesses a swirl. Such a set-up might be realizable experimentally through coils. Finally, new emerging issues regarding the connection between magnetic helicity and the solar dynamo are discussed. It is demonstrated that dynamos with a nonlocal (Babcock Leighton type) α effect can also be catastrophically quenched, unless there are magnetic helicity fluxes. Title: Why coronal mass ejections are necessary for the dynamo Authors: Brandenburg, Axel Bibcode: 2007HiA....14..291B Altcode: 2007astro.ph..1056B Large scale dynamo-generated fields are a combination of interlocked poloidal and toroidal fields. Such fields possess magnetic helicity that needs to be regenerated and destroyed during each cycle. A number of numerical experiments now suggests that stars may do this by shedding magnetic helicity. In addition to plain bulk motions, a favorite mechanism involves magnetic helicity flux along lines of constant rotation. We also know that the sun does shed the required amount of magnetic helicity mostly in the form of coronal mass ejections. Solar-like stars without cycles do not face such strong constraints imposed by magnetic helicity evolution and may not display coronal activity to that same extent. I discuss the evidence leading to this line of argument. In particular, I discuss simulations showing the generation of strong mean toroidal fields provided the outer boundary condition is left open so as to allow magnetic helicity to escape. Control experiments with closed boundaries do not produce strong mean fields. Title: Simulations of the anisotropic kinetic and magnetic alpha effects Authors: Brandenburg, A.; Subramanian, K. Bibcode: 2007AN....328..507B Altcode: 2007arXiv0705.3508B Using simulations of isotropically forced helical turbulence the contributions to kinetic and magnetic alpha effects are computed. It is shown that for the parameter regimes considered in an earlier publication (Brandenburg & Subramanian 2005), the expressions for isotropic and anisotropic alpha effects give quantitatively similar results. Both kinetic and magnetic alpha effects are proportional to a relaxation time whose value, in units of the turnover time, is shown to be approximately unity and independent of the magnetic Reynolds number. Title: Near-surface shear layer dynamics Authors: Brandenburg, Axel Bibcode: 2007IAUS..239..457B Altcode: 2007astro.ph..1057B The outer surface layers of the sun show a clear deceleration at low latitudes. This is generally thought to be the result of a strong dominance of vertical turbulent motions associated with strong downdrafts. This strong negative radial shear should not only contribute to amplifying the toroidal field locally and to expelling magnetic helicity, but it may also be responsible for producing a strong prograde pattern speed in the supergranulation layer. Using simulations of rotating stratified convection in cartesian boxes located at low latitudes around the equator it is shown that in the surface layers patterns move in the prograde direction on top of a retrograde mean background flow. These patterns may also be associated with magnetic tracers and even sunspot proper motions that are known to be prograde relative to the much slower surface plasma. Title: Kinetic and magnetic α-effects in non-linear dynamo theory Authors: Sur, Sharanya; Subramanian, Kandaswamy; Brandenburg, Axel Bibcode: 2007MNRAS.376.1238S Altcode: 2007MNRAS.tmp..151S; 2007astro.ph..1001S The backreaction of the Lorentz force on the α-effect is studied in the limit of small magnetic and fluid Reynolds numbers, using the first-order smoothing approximation (FOSA) to solve both the induction and momentum equations. Both steady and time-dependent forcings are considered. In the low Reynolds number limit, the velocity and magnetic fields can be expressed explicitly in terms of the forcing function. The non-linear α-effect is then shown to be expressible in several equivalent forms in agreement with formalisms that are used in various closure schemes. On one hand, one can express α completely in terms of the helical properties of the velocity field as in traditional FOSA, or, alternatively, as the sum of two terms, a so-called kinetic α-effect and an oppositely signed term proportional to the helical part of the small-scale magnetic field. These results hold for both steady and time-dependent forcing at arbitrary strength of the mean field. In addition, the τ-approximation is considered in the limit of small fluid and magnetic Reynolds numbers. In this limit, the τ closure term is absent and the viscous and resistive terms must be fully included. The underlying equations are then identical to those used under FOSA, but they reveal interesting differences between the steady and time-dependent forcing. For steady forcing, the correlation between the forcing function and the small-scale magnetic field turns out to contribute in a crucial manner to determine the net α-effect. However for delta-correlated time-dependent forcing, this force-field correlation vanishes, enabling one to write α exactly as the sum of kinetic and magnetic α-effects, similar to what one obtains also in the large Reynolds number regime in the τ-approximation closure hypothesis. In the limit of strong imposed fields, B0, we find α ~ B-20 for delta-correlated forcing, in contrast to the well-known α ~ B-30 behaviour for the case of a steady forcing. The analysis presented here is also shown to be in agreement with numerical simulations of steady as well as random helical flows. Title: Probing turbulence in OMC1 at the star forming scale: observations and simulations Authors: Gustafsson, Maiken; Brandenburg, Axel; Lemaire, Jean-Louis; Field, David Bibcode: 2007IAUS..237..183G Altcode: 2006IAUS..237E..32G A key to understanding the mechanism of star formation is to characterise in detail the dynamics of the turbulent, highly perturbed and magnetized plasma from which stars are forming. This can be achieved by statistical analysis of the turbulent velocity structure and should involve both observations and simulated data. To this purpose we use high spatial resolution IR K-band observations of velocities of vibrationally excited H2 in the Orion Molecular Cloud (OMC1). Data cover scales of 70 AU to 30000 AU [1]. OMC1 is the archetypal massive star forming region and is highly active. This is exemplified by the presence of protostars and fast outflows. We compare the observational results with numerical simulations of supersonic hydrodynamic turbulence. We present the structure functions and the scaling of the structure functions with their order. The structure functions for OMC1 show clear deviations from power laws, that is, deviations from fractal scaling, around 1000-2000 AU and around 300 AU. The scaling of the higher order structure functions with order deviates from the standard scaling for supersonic turbulence [1,2]. The unusual scaling is explained as a selection effect of preferentially observing the shocked part of the gas. The scaling can be reproduced using line-of-sight integrated velocity data from subsets of simulations that select regions of strong flow convergence associated with shock structure. The simulations, which do not include self-gravity or magnetic fields, are unable to reproduce the deviations from power laws of the structure functions. These deviations could be ascribed to the presence of low mass protostars and associated structures such as outflows and circumstellar disks [4]. [1] Gustafsson et al. 2006a, A&A, 445,601, [2] She & Leveque 1994, PRL, 72, 336, [3] Boldyrev 2002, ApJ, 569, 841, [4] Gustafsson et al 2006b, A&A in press, astro-ph/0512214 Title: Thermal Instability in Shearing and Periodic Turbulence Authors: Brandenburg, Axel; Korpi, Maarit J.; Mee, Antony J. Bibcode: 2007ApJ...654..945B Altcode: 2006astro.ph..4244B The thermal instability with a piecewise power law cooling function is investigated using one- and three-dimensional simulations with periodic and shearing-periodic boundary conditions in the presence of constant thermal diffusion and kinematic viscosity coefficients. Consistent with earlier findings, the flow behavior depends on the average density, <ρ>. When <ρ> is in the range (1-5)×10-24 g cm-3, the system is unstable and segregates into cool and warm phases with temperatures of roughly 100 and 104 K, respectively. However, in all cases the resulting average pressure

is independent of <ρ> and just a little above the minimum value. For a constant heating rate of 0.015 ergs g-1 s-1, the mean pressure is around 24×10-14 dyn (corresponding to p/kB~1750 K cm-3). Cool patches tend to coalesce into bigger ones. In all cases investigated, there is no sustained turbulence, which is in agreement with earlier results. Simulations in which turbulence is driven by a body force show that when rms velocities of between 10 and 30 km s-1 are obtained, the resulting dissipation rates are comparable to the thermal energy input rate. The resulting mean pressures are then about 30×10-14 dyn, corresponding to p/kB~2170 K cm-3. This is comparable to the value expected for the Galaxy. Differential rotation tends to make the flow two-dimensional, that is, uniform in the streamwise direction, but this does not lead to instability. Title: Dynamos in accretion discs Authors: Brandenburg, A.; von Rekowski, B. Bibcode: 2007MmSAI..78..374B Altcode: 2007astro.ph..2493B It is argued that accretion discs in young stellar objects may have hot coronae that are heated by magnetic reconnection. This is a consequence of the magneto-rotational instability driving turbulence in the disc. Magnetic reconnection away from the midplane leads to heating of the corona which, in turn, contributes to driving disc winds. Title: Disk Winds, Jets, and Outflows: Theoretical and Computational Foundations Authors: Pudritz, R. E.; Ouyed, R.; Fendt, Ch.; Brandenburg, A. Bibcode: 2007prpl.conf..277P Altcode: 2006astro.ph..3592P We review advances in the theoretical and computational studies of disk winds, jets, and outflows, including the connection between accretion and jets, the launch of jets from magnetized disks, the coupled evolution of jets and disks, the interaction of magnetized young stellar objects with their surrounding disks and the relevance to outflows, and finally, the link between jet formation and gravitational collapse. We also address the predictions the theory makes about jet kinematics, collimation, and rotation that have recently been confirmed by high-spatial- and high-spectral-resolution observations. Disk winds have a universal character that may account for jets and outflows during the formation of massive stars as well as brown dwarfs. Title: The Solar Interior-Radial Structure, Rotation, Solar Activity Cycle Authors: Brandenburg, A. Bibcode: 2007hste.book...28B Altcode: 2007astro.ph..3711B Some basic properties of the solar convection zone are considered and the use of helioseismology as an observational tool to determine its depth and internal angular velocity is discussed. Aspects of solar magnetism are described and explained in the framework of dynamo theory. The main focus is on mean field theories for the Sun's magnetic field and its differential rotation. Title: Location of the Solar Dynamo and Near-Surface Shear Authors: Brandenburg, A. Bibcode: 2006ASPC..354..121B Altcode: 2005astro.ph.12637B The location of the solar dynamo is discussed in the context of new insights into the theory of nonlinear turbulent dynamos. It is argued that, from a dynamo-theoretic point of view, the bottom of the convection zone is not a likely location for the solar dynamo, but that it may be distributed over the convection zone. The near surface shear layer produces not only east-west field alignment, but it also helps the dynamo to dispose of its excess small scale magnetic helicity. Title: Simulating field-aligned diffusion of a cosmic ray gas Authors: Snodin, Andrew P.; Brandenburg, Axel; Mee, Antony J.; Shukurov, Anvar Bibcode: 2006MNRAS.373..643S Altcode: 2006MNRAS.tmp.1221S; 2005astro.ph..7176S The macroscopic behaviour of cosmic rays in turbulent magnetic fields is discussed. An implementation of anisotropic diffusion of cosmic rays with respect to the magnetic field in a non-conservative, high-order, finite-difference magnetohydrodynamic code is discussed. It is shown that the standard implementation fails near singular X-points of the magnetic field, which are common if the field is random. A modification to the diffusion model for cosmic rays is described and the resulting telegraph equation (implemented by solving a dynamic equation for the diffusive flux of cosmic rays) is used; it is argued that this modification may better describe the physics of cosmic ray diffusion. The present model reproduces several processes important for the propagation and local confinement of cosmic rays, including spreading perpendicular to the local large-scale magnetic field, controlled by the random-to-total magnetic field ratio, and the balance between cosmic ray pressure and magnetic tension. Cosmic ray diffusion is discussed in the context of a random magnetic field produced by turbulent dynamo action. It is argued that energy equipartition between cosmic rays and other constituents of the interstellar medium does not necessarily imply that cosmic rays play a significant role in the balance of forces. Title: Magnetic Helicity Density and Its Flux in Weakly Inhomogeneous Turbulence Authors: Subramanian, Kandaswamy; Brandenburg, Axel Bibcode: 2006ApJ...648L..71S Altcode: 2005astro.ph..9392S A gauge-invariant and hence physically meaningful definition of magnetic helicity density for random fields is proposed, using the Gauss linking formula, as the density of correlated field line linkages. This definition is applied to the random small-scale field in weakly inhomogeneous turbulence, whose correlation length is small compared with the scale on which the turbulence varies. For inhomogeneous systems, with or without boundaries, our technique then allows one to study the local magnetic helicity density evolution in a gauge-independent fashion, which was not possible earlier. This evolution equation is governed by local sources (owing to the mean field) and by the divergence of a magnetic helicity flux density. The role of magnetic helicity fluxes in alleviating catastrophic quenching of mean field dynamos is discussed. Title: The nature of turbulence in OMC1 at the scale of star formation: observations and simulations Authors: Gustafsson, M.; Brandenburg, A.; Lemaire, J. L.; Field, D. Bibcode: 2006A&A...454..815G Altcode: 2005astro.ph.12214G Aims.To study turbulence in the Orion Molecular Cloud (OMC1) by comparing observed and simulated characteristics of the gas motions. Methods: Using a dataset of vibrationally excited H2 emission in OMC1 containing radial velocity and brightness which covers scales from 70 AU to 30 000 AU, we present the structure functions and the scaling of the structure functions with their order. These are compared with the predictions of two-dimensional projections of simulations of supersonic hydrodynamic turbulence. Results: The structure functions of OMC1 are not well represented by power laws, but show clear deviations below 2000 AU. However, using the technique of extended self-similarity, power laws are recovered at scales down to 160 AU. The scaling of the higher order structure functions with order deviates from the standard scaling for supersonic turbulence. This is explained as a selection effect of preferentially observing the shocked part of the gas and the scaling can be reproduced using line-of-sight integrated velocity data from subsets of supersonic turbulence simulations. These subsets select regions of strong flow convergence and high density associated with shock structure. Deviations of the structure functions in OMC1 from power laws cannot however be reproduced in simulations and remains an outstanding issue. Title: Why coronal mass ejections are necessary for the dynamo Authors: Brandenburg, A. Bibcode: 2006IAUJD...8E..62B Altcode: Large scale dynamo-generated fields are a combination of interlocked poloidal and toroidal fields. Such fields possess magnetic helicity that needs to be regenerated and destroyed during each cycle. A sequence of numerical experiments now suggests that stars may do this by shedding magnetic helicity. In addition to plain bulk motions, a favorite mechanism involves magnetic helicity flux along lines of constant rotation. We also know that the sun does shed the required amount of magnetic helicity mostly in the form of coronal mass ejections. Solar-like stars without cycles do not face such strong constraints imposed by magnetic helicity evolution and may not display coronal activity to that same extent. In my talk I will discuss the evidence leading to this line of argument. In particular, I will discuss simulations showing the generation of strong mean toroidal fields provided the outer boundary condition is left open so as to allow magnetic helicity to escape. Control experiments with closed boundaries do not produce strong mean fields. Title: Hydrodynamic and hydromagnetic energy spectra from large eddy simulations Authors: Haugen, Nils Erland L.; Brandenburg, Axel Bibcode: 2006PhFl...18g5106H Altcode: 2004astro.ph.12666H Direct and large eddy simulations of hydrodynamic and hydromagnetic turbulence have been performed in an attempt to isolate artifacts from real and possibly asymptotic features in the energy spectra. It is shown that in a hydrodynamic turbulence simulation with a Smagorinsky subgrid scale model using 5123 mesh points, two important features of the 40963 simulation on the Earth simulator [Y. Kaneda et al., Phys. Fluids 15, L21 (2003)] are reproduced: a k-0.1 correction to the inertial range with a k-5/3 Kolmogorov slope and the form of the bottleneck just before the dissipative subrange. Furthermore, it is shown that, while a Smagorinsky-type model for the induction equation causes an artificial and unacceptable reduction in the dynamo efficiency, hyper-resistivity yields good agreement with direct simulations. In the large-scale part of the inertial range, an excess of the spectral magnetic energy over the spectral kinetic energy is confirmed. However, a trend toward spectral equipartition at smaller scales in the inertial range can be identified. With magnetic fields, no explicit bottleneck effect is seen. Title: Turbulence from localized random expansion waves Authors: Mee, Antony J.; Brandenburg, Axel Bibcode: 2006MNRAS.370..415M Altcode: 2006MNRAS.tmp..668M; 2006astro.ph..2057M In an attempt to determine the outer scale of turbulence driven by localized sources, such as supernova explosions in the interstellar medium, we consider a forcing function given by the gradient of Gaussian profiles localized at random positions. Different coherence times of the forcing function are considered. In order to isolate the effects specific to the nature of the forcing function, we consider the case of a polytropic equation of state and restrict ourselves to forcing amplitudes such that the flow remains subsonic. When the coherence time is short, the outer scale agrees with the half-width of the Gaussian. Longer coherence times can cause extra power at large scales, but this would not yield power-law behaviour at scales larger than that of the expansion waves. At scales smaller than the scale of the expansion waves the spectrum is close to power law with a spectral exponent of -2. The resulting flow is virtually free of vorticity. Viscous driving of vorticity turns out to be weak and self-amplification through the non-linear term is found to be insignificant. No evidence for small-scale dynamo action is found in cases where the magnetic induction equation is solved simultaneously with the other equations. Title: Magnetic helicity in primordial and dynamo scenarios of galaxies Authors: Brandenburg, A. Bibcode: 2006AN....327..461B Altcode: 2006astro.ph..1496B Some common properties of helical magnetic fields in decaying and driven turbulence are discussed. These include mainly the inverse cascade that produces fields on progressively larger scales. Magnetic helicity also restricts the evolution of the large-scale field: the field decays less rapidly than a non-helical field, but it also saturates more slowly, i.e. on a resistive time scale if there are no magnetic helicity fluxes. The former effect is utilized in primordial field scenarios, while the latter is important for successfully explaining astrophysical dynamos that saturate faster than resistively. Dynamo action is argued to be important not only in the galactic dynamo, but also in accretion discs in active galactic nuclei and around protostars, both of which contribute to producing a strong enough seed magnetic field. Although primordial magnetic fields may be too weak to compete with these astrophysical mechanisms, such fields could perhaps still be important in producing polarization effects in the cosmic background radiation. Title: Nonaxisymmetric stability in the shearing sheet approximation Authors: Brandenburg, A.; Dintrans, B. Bibcode: 2006A&A...450..437B Altcode: 2001astro.ph.11313B Aims.To quantify the transient growth of nonaxisymmetric perturbations in unstratified magnetized and stratified non-magnetized rotating linear shear flows in the shearing sheet approximation of accretion disc flows.
Methods: .The Rayleigh quotient in modal approaches for the linearized equations (with time-dependent wavenumber) and the amplitudes from direct shearing sheet simulations using a finite difference code are compared.
Results: .Both approaches agree in their predicted growth behavior. The magneto-rotational instability for axisymmetric and non-axisymmetric perturbations is shown to have the same dependence of the (instantaneous) growth rate on the wavenumber along the magnetic field, but in the nonaxisymmetric case the growth is only transient. However, a meaningful dependence of the Rayleigh quotient on the radial wavenumber is obtained. While in the magnetized case the total amplification factor can be several orders of magnitude, it is only of order ten or less in the nonmagnetic case. Stratification is shown to have a stabilizing effect. In the present case of shearing-periodic boundaries the (local) strato-rotational instability seems to be absent.
Title: Radiative transfer in decomposed domains Authors: Heinemann, T.; Dobler, W.; Nordlund, Å.; Brandenburg, A. Bibcode: 2006A&A...448..731H Altcode: 2005astro.ph..3510H Aims. An efficient algorithm for calculating radiative transfer on massively parallel computers using domain decomposition is presented. Methods. The integral formulation of the transfer equation is used to divide the problem into a local but compute-intensive part for calculating the intensity and optical depth integrals, and a nonlocal part for communicating the intensity between adjacent processors. Results. The waiting time of idle processors during the nonlocal communication part does not have a severe impact on the scaling. The wall clock time thus scales nearly linearly with the inverse number of processors. Title: Galactic dynamo and helicity losses through fountain flow Authors: Shukurov, A.; Sokoloff, D.; Subramanian, K.; Brandenburg, A. Bibcode: 2006A&A...448L..33S Altcode: 2005astro.ph.12592S Aims. Nonlinear behaviour of galactic dynamos is studied, allowing for magnetic helicity removal by the galactic fountain flow.Methods. A suitable advection speed is estimated, and a one-dimensional mean-field dynamo model with dynamic α-effect is explored. Results. It is shown that the galactic fountain flow is efficient in removing magnetic helicity from galactic discs. This alleviates the constraint on the galactic mean-field dynamo resulting from magnetic helicity conservation and thereby allows the mean magnetic field to saturate at a strength comparable to equipartition with the turbulent kinetic energy. Title: Magnetic Field Generation in Fully Convective Rotating Spheres Authors: Dobler, Wolfgang; Stix, Michael; Brandenburg, Axel Bibcode: 2006ApJ...638..336D Altcode: 2004astro.ph.10645D Magnetohydrodynamic simulations of fully convective, rotating spheres with volume heating near the center and cooling at the surface are presented. The dynamo-generated magnetic field saturates at equipartition field strength near the surface. In the interior, the field is dominated by small-scale structures, but outside the sphere, by the global scale. Azimuthal averages of the field reveal a large-scale field of smaller amplitude also inside the star. The internal angular velocity shows some tendency to be constant along cylinders and is ``antisolar'' (fastest at the poles and slowest at the equator). Title: Stellar dynamo driven wind braking versus disc coupling Authors: von Rekowski, B.; Brandenburg, A. Bibcode: 2006AN....327...53V Altcode: 2005astro.ph..4053V Star-disc coupling is considered in numerical models where the stellar field is not an imposed perfect dipole, but instead a more irregular self-adjusting dynamo-generated field. Using axisymmetric simulations of the hydromagnetic mean-field equations, it is shown that the resulting stellar field configuration is more complex, but significantly better suited for driving a stellar wind. In agreement with recent findings by a number of people, star-disc coupling is less efficient in braking the star than previously thought. Moreover, stellar wind braking becomes equally important. In contrast to a perfect stellar dipole field, dynamo-generated stellar fields favor field-aligned accretion with considerably higher velocity at low latitudes, where the field is weaker and originating in the disc. Accretion is no longer nearly periodic (as it is in the case of a stellar dipole), but it is more irregular and episodic. Title: The angular momentum transport by the strato-rotational instability in simulated Taylor-Couette flows Authors: Brandenburg, A.; Ruediger, G. Bibcode: 2005astro.ph.12409B Altcode: Aims: To investigate the stability and angular momentum transport by the strato-rotational instability in the nonlinear regime. Methods: The hydrodynamic compressible equations are solved in a cartesian box in which the outer cylinder is embedded. Gravity along the rotation axis leads to density stratification. No-slip boundary conditions are used in the radial direction, while free-slip conditions are used on the two ends of the cylinders. Results: The strato-rotational instability is confirmed and the Reynolds stress is shown to transport angular momentum away from the axis. However, the growth rate decreases with increasing Reynolds number. This, as well as the presence of boundaries renders this instability less relevant for astrophysical applications. Title: Distributed versus tachocline dynamos Authors: Brandenburg, Axel Bibcode: 2005astro.ph.12638B Altcode: Arguments are presented in favor of the idea that the solar dynamo may operate not just at the bottom of the convection zone, i.e. in the tachocline, but it may operate in a more distributed fashion in the entire convection zone. The near-surface shear layer is likely to play an important role in this scenario. Title: Connection between active longitudes and magnetic helicity Authors: Brandenburg, A.; Käpylä, P. J. Bibcode: 2005astro.ph.12639B Altcode: A two-dimensional mean field dynamo model is solved where magnetic helicity conservation is fully included. The model has a negative radial velocity gradient giving rise to equatorward migration of magnetic activity patterns. In addition the model develops longitudinal variability with activity patches travelling in longitude. These patches may be associated with active longitudes. Title: Dissociation in a Polymerization Model of Homochirality Authors: Brandenburg, A.; Andersen, A. C.; Nilsson, M. Bibcode: 2005OLEB...35..507B Altcode: 2005q.bio.....2008B A fully self-contained model of homochirality is presented that contains the effects of both polymerization and dissociation. The dissociation fragments are assumed to replenish the substrate from which new monomers can grow and undergo new polymerization. The mean length of isotactic polymers is found to grow slowly with the normalized total number of corresponding building blocks. Alternatively, if one assumes that the dissociation fragments themselves can polymerize further, then this corresponds to a strong source of short polymers, and an unrealistically short average length of only 3. By contrast, without dissociation, isotactic polymers becomes infinitely long. Title: Turbulence and its parameterization in accretion discs Authors: Brandenburg, A. Bibcode: 2005AN....326..787B Altcode: 2005astro.ph.10015B Accretion disc turbulence is investigated in the framework of the shearing box approximation. The turbulence is either driven by the magneto-rotational instability or, in the non-magnetic case, by an explicit and artificial forcing term in the momentum equation. Unlike the magnetic case, where most of the dissipation occurs in the disc corona, in the forced hydrodynamic case most of the dissipation occurs near the midplane. In the hydrodynamic case evidence is presented for the stochastic excitation of epicycles. When the vertical and radial epicyclic frequencies are different (modeling the properties around rotating black holes), the beat frequency between these two frequencies appear to show up as a peak in the temporal power spectrum in some cases. Finally, the full turbulent resistivity tensor is determined and it is found that, if the turbulence is driven by a forcing term, the signs of its off-diagonal components are such that this effect would not be capable of dynamo action by the shear-current effect. Title: Effect of the radiative background flux in convection Authors: Brandenburg, A.; Chan, K. L.; Nordlund, Å.; Stein, R. F. Bibcode: 2005AN....326..681B Altcode: 2005astro.ph..8404B Numerical simulations of turbulent stratified convection are used to study models with approximately the same convective flux, but different radiative fluxes. As the radiative flux is decreased, for constant convective flux: the entropy jump at the top of the convection zone becomes steeper, the temperature fluctuations increase and the velocity fluctuations decrease in magnitude, and the distance that low entropy fluid from the surface can penetrate increases. Velocity and temperature fluctuations follow mixing length scaling laws. Title: Unidirectional polymerization leading to homochirality in the RNA world Authors: Nilsson, M.; Brandenburg, A.; Andersen, A. C.; Höfner, S. Bibcode: 2005IJAsB...4..233N Altcode: 2005q.bio.....5041N The differences between unidirectional and bidirectional polymerization are considered. The unidirectional case is discussed in the framework of the RNA world. Similar to earlier models of this type, where polymerization was assumed to proceed in a bidirectional fashion (presumed to be relevant to peptide nucleic acids), left- and right-handed monomers are produced via an autocatalysis from an achiral substrate. The details of the bifurcation from a racemic solution to a homochiral state of either handedness is shown to be remarkably independent of whether the polymerization is unidirectional or bidirectional. Slightly larger differences are seen when dissociation is allowed and the dissociation fragments are recycled into the achiral substrate. Title: Astrophysical magnetic fields and nonlinear dynamo theory Authors: Brandenburg, Axel; Subramanian, Kandaswamy Bibcode: 2005PhR...417....1B Altcode: 2004astro.ph..5052B The current understanding of astrophysical magnetic fields is reviewed, focusing on their generation and maintenance by turbulence. In the astrophysical context this generation is usually explained by a self-excited dynamo, which involves flows that can amplify a weak ‘seed’ magnetic field exponentially fast. Particular emphasis is placed on the nonlinear saturation of the dynamo. Analytic and numerical results are discussed both for small scale dynamos, which are completely isotropic, and for large scale dynamos, where some form of parity breaking is crucial. Central to the discussion of large scale dynamos is the so-called alpha effect which explains the generation of a mean field if the turbulence lacks mirror symmetry, i.e. if the flow has kinetic helicity. Large scale dynamos produce small scale helical fields as a waste product that quench the large scale dynamo and hence the alpha effect. With this in mind, the microscopic theory of the alpha effect is revisited in full detail and recent results for the loss of helical magnetic fields are reviewed. Title: Minimal tau approximation and simulations of the alpha effect Authors: Brandenburg, A.; Subramanian, K. Bibcode: 2005A&A...439..835B Altcode: 2005astro.ph..4222B The validity of a closure called the minimal tau approximation (MTA), is tested in the context of dynamo theory, wherein triple correlations are assumed to provide relaxation of the turbulent electromotive force. Under MTA, the alpha effect in mean field dynamo theory becomes proportional to a relaxation time scale multiplied by the difference between kinetic and current helicities. It is shown that the value of the relaxation time is positive and, in units of the turnover time at the forcing wavenumber, it is of the order of unity. It is quenched by the magnetic field - roughly independently of the magnetic Reynolds number. However, this independence becomes uncertain at large magnetic Reynolds number. Kinetic and current helicities are shown to be dominated by large scale properties of the flow. Title: Spectrum and amplitudes of internal gravity waves excited by penetrative convection in solar-type stars Authors: Dintrans, B.; Brandenburg, A.; Nordlund, Å.; Stein, R. F. Bibcode: 2005A&A...438..365D Altcode: 2005astro.ph..2138D The excitation of internal gravity waves by penetrative convective plumes is investigated using 2-D direct simulations of compressible convection. The wave generation is quantitatively studied from the linear response of the radiative zone to the plumes penetration, using projections onto the g-modes solutions of the associated linear eigenvalue problem for the perturbations. This allows an accurate determination of both the spectrum and amplitudes of the stochastically excited modes. Using time-frequency diagrams of the mode amplitudes, we then show that the lifetime of a mode is around twice its period and that during times of significant excitation up to 40% of the total kinetic energy may be contained into g-modes. Title: Scaling laws in decaying helical hydromagnetic turbulence Authors: Christensson, M.; Hindmarsh, M.; Brandenburg, A. Bibcode: 2005AN....326..393C Altcode: 2002astro.ph..9119C We study the evolution of growth and decay laws for the magnetic field coherence length ξ, energy E_M and magnetic helicity H in freely decaying 3D MHD turbulence. We show that with certain assumptions, self-similarity of the magnetic power spectrum alone implies that ξ σm t1/2. This in turn implies that magnetic helicity decays as Hσm t-2s, where s=(ξ_diff/ξH)2, in terms of ξ_diff, the diffusion length scale, and ξ_H, a length scale defined from the helicity power spectrum. The relative magnetic helicity remains constant, implying that the magnetic energy decays as E_M σm t-1/2-2s. The parameter s is inversely proportional to the magnetic Reynolds number Re_M, which is constant in the self-similar regime. Title: Strong mean field dynamos require supercritical helicity fluxes Authors: Brandenburg, A.; Subramanian, K. Bibcode: 2005AN....326..400B Altcode: 2005astro.ph..5457B Several one and two dimensional mean field models are analyzed where the effects of current helicity fluxes and boundaries are included within the framework of the dynamical quenching model. In contrast to the case with periodic boundary conditions, the final saturation energy of the mean field decreases inversely proportional to the magnetic Reynolds number. If a nondimensional scaling factor in the current helicity flux exceeds a certain critical value, the dynamo can operate even without kinetic helicity, i.e. it is based only on shear and current helicity fluxes, as first suggested by Vishniac & Cho (2001, ApJ 550, 752). Only above this threshold is the current helicity flux also able to alleviate catastrophic quenching. The fact that certain turbulence simulations have now shown apparently non-resistively limited mean field saturation amplitudes may be suggestive of the current helicity flux having exceeded this critical value. Even below this critical value the field still reaches appreciable strength at the end of the kinematic phase, which is in qualitative agreement with dynamos in periodic domains. However, for large magnetic Reynolds numbers the field undergoes subsequent variations on a resistive time scale when, for long periods, the field can be extremely weak. Title: Homochiral Growth Through Enantiomeric Cross-Inhibition Authors: Brandenburg, A.; Andersen, A. C.; Höfner, S.; Nilsson, M. Bibcode: 2005OLEB...35..225B Altcode: 2004q.bio.....1036B The stability and conservation properties of a recently proposed polymerization model are studied. The achiral (racemic) solution is linearly unstable once the relevant control parameter (here the fidelity of the catalyst) exceeds a critical value. The growth rate is calculated for different fidelity parameters and cross-inhibition rates. A chirality parameter is defined and shown to be conserved by the nonlinear terms of the model. Finally, a truncated version of the model is used to derive a set of two ordinary differential equations and it is argued that these equations are more realistic than those used in earlier models of that form. Title: Nonhelical turbulent dynamos: shocks and shear Authors: Brandenburg, A.; Haugen, N.; Mee, A. Bibcode: 2005mpge.conf..139B Altcode: 2005astro.ph..1006B Small scale turbulent dynamo action in compressible transonic turbulence is discussed. It is shown that the critical value of the magnetic Reynolds number displays a bimodal behavior and changes from a typical value of 35 for small Mach numbers to about 80 for larger Mach numbers. The transition between the two regimes is relatively sharp. The direct simulations are then compared with simulations where shocks are captured using a shock viscosity that becomes large at locations where there are shocks. In the presence of shear it is shown that large scale dynamo action is possible. Title: Signatures of axinos and gravitinos at colliders Authors: Brandenburg, A.; Covi, L.; Hamaguchi, K.; Roszkowski, L.; Steffen, F. D. Bibcode: 2005PhLB..617...99B Altcode: 2005hep.ph....1287B The axino and the gravitino are well-motivated candidates for the lightest supersymmetric particle (LSP) and also for cold dark matter in the Universe. Assuming that a charged slepton is the next-to-lightest supersymmetric particle (NLSP), we show how the NLSP decays can be used to probe the axino LSP scenario in hadronic axion models as well as the gravitino LSP scenario at the Large Hadron Collider and the International Linear Collider. We show how one can identify experimentally the scenario realized in nature. In the case of the axino LSP, the NLSP decays will allow one to estimate the value of the axino mass and the Peccei Quinn scale. Title: The Onset of a Small-Scale Turbulent Dynamo at Low Magnetic Prandtl Numbers Authors: Schekochihin, A. A.; Haugen, N. E. L.; Brandenburg, A.; Cowley, S. C.; Maron, J. L.; McWilliams, J. C. Bibcode: 2005ApJ...625L.115S Altcode: 2004astro.ph.12594S We study numerically the dependence of the critical magnetic Reynolds number Rmc for the turbulent small-scale dynamo on the hydrodynamic Reynolds number Re. The turbulence is statistically homogeneous, isotropic, and mirror-symmetric. We are interested in the regime of low magnetic Prandtl number Pm=Rm/Re<1, which is relevant for stellar convective zones, protostellar disks, and laboratory liquid-metal experiments. The two asymptotic possibilities are Rmc-->const as Re-->∞ (a small-scale dynamo exists at low Pm) or Rmc/Re=Pmc-->const as Re-->∞ (no small-scale dynamo exists at low Pm). Results obtained in two independent sets of simulations of MHD turbulence using grid and spectral codes are brought together and found to be in quantitative agreement. We find that at currently accessible resolutions, Rmc grows with Re with no sign of approaching a constant limit. We reach the maximum values of Rmc~500 for Re~3000. By comparing simulations with Laplacian viscosity, fourth-, sixth-, and eighth-order hyperviscosity, and Smagorinsky large-eddy viscosity, we find that Rmc is not sensitive to the particular form of the viscous cutoff. This work represents a significant extension of the studies previously published by Schekochihin et al. (2004a) and Haugen et al. (2004a) and the first detailed scan of the numerically accessible part of the stability curve Rmc(Re). Title: The Case for a Distributed Solar Dynamo Shaped by Near-Surface Shear Authors: Brandenburg, Axel Bibcode: 2005ApJ...625..539B Altcode: 2005astro.ph..2275B Arguments for and against the widely accepted picture of a solar dynamo being seated in the tachocline are reviewed, and alternative ideas concerning dynamos operating in the bulk of the convection zone, or perhaps even in the near-surface shear layer, are discussed. Based on the angular velocities of magnetic tracers, it is argued that the observations are compatible with a distributed dynamo that may be strongly shaped by the near-surface shear layer. Direct simulations of dynamo action in a slab with turbulence and shear are presented to discuss filling factor and tilt angles of bipolar regions in such a model. Title: Investigation of Top Quark Spin Correlations at Hadron Colliders Authors: Bernreuther, W.; Brandenburg, A.; Si, Z. G.; Uwer, P. Bibcode: 2005iche.conf.1166B Altcode: 2004hep.ph...10197B; 2004iche.conf.1166B We report on our results about hadronic tbar {t} production at NLO QCD including t ,bar {t} spin effects, especially on tbar {t} spin correlations. Title: The problem of small and large scale fields in the solar dynamo Authors: Brandenburg, A.; Haugen, N. E. L.; Käpylä, P. J.; Sandin, C. Bibcode: 2005AN....326..174B Altcode: 2004astro.ph.12364B Three closely related stumbling blocks of solar mean field dynamo theory are discussed: how dominant are the small scale fields, how is the alpha effect quenched, and whether magnetic and current helicity fluxes alleviate the quenching? It is shown that even at the largest currently available resolution there is no clear evidence of power law scaling of the magnetic and kinetic energy spectra in turbulence. However, using subgrid scale modeling, some indications of asymptotic equipartition can be found. The frequently used first order smoothing approach to calculate the alpha effect and other transport coefficients is contrasted with the superior minimal tau approximation. The possibility of catastrophic alpha quenching is discussed as a result of magnetic helicity conservation. Magnetic and current helicity fluxes are shown to alleviate catastrophic quenching in the presence of shear. Evidence for strong large scale dynamo action, even in the absence of helicity in the forcing, is presented. Title: Spatial dynamics of homochiralization Authors: Multamäki, Tuomas; Brandenburg, Axel Bibcode: 2005IJAsB...4...75M Altcode: 2005q.bio.....5040M The emergence and spread of chirality on the early Earth is considered by studying a set of reaction-diffusion equations based on a polymerization model. It is found that effective mixing of the early oceans is necessary to reach the present homochiral state. The possibility of introducing mass extinctions and modifying the emergence rate of life are discussed. Title: Ejection of Bi-Helical Fields from the Sun Authors: Brandenburg, Axel; Blackman, Eric G. Bibcode: 2005HiA....13..101B Altcode: Over the past decade the measurement of magnetic and current helicity at the solar surface has attracted significant interest. There is now general consensus that the two helicities are negative in the north and positive in the south. On the other hand the tilt of bipolar regions in the clockwise direction in the north corresponds to a positive writhe helicity. In the south the tilt is counterclockwise corresponding to negative writhe helicity. These signs of writhe helicity which are thus apposite to the twist helicity measured as current helicity are also suggested by N-shaped sigmoids in the north and S-shaped sigmoids in the south. We interpret these as bi-helical magnetic field structures which have in the north negative magnetic helicity at smaller scales and positive magnetic helicity at the largest scales and oppositely in the south. This is also what is expected and required from dynamo theory in order that the dynamo cycle is able to reverse the entire field in a time as short as 11 years. The generation and evolution of bi-helical fields is studied using hydromagnetic turbulence simulations both for the convection zone and the solar wind. Title: Editorial Authors: Anderson, Anja C.; Brandenburg, Axel Bibcode: 2005IJAsB...4....1A Altcode: No abstract at ADS Title: Thermal Production of Axinos in the Early Universe Authors: Brandenburg, A.; Steffen, F. D. Bibcode: 2005sem..conf..271B Altcode: 2004hep.ph....7324B We compute the thermal axino production rate in supersymmetric QCD to leading order in the gauge coupling. Using hard thermal loop resummation and the Braaten-Yuan prescription, we obtain a finite result in a gauge-invariant way, which takes into account Debye screening in the hot quark-gluon-squark-gluino plasma. The relic axino density from thermal reactions in the early Universe is evaluated assuming the axino is the lightest supersymmetric particle and stable due to R-parity conservation. From the comparison with the WMAP results, we find that axinos could provide the dominant part of cold dark matter, for example, for an axino mass of 100 keV and a reheating temperature of 106 GeV. Title: Importance of Magnetic Helicity in Dynamos Authors: Brandenburg, Axel Bibcode: 2005LNP...664..219B Altcode: 2004astro.ph.12366B Magnetic helicity is nearly conserved and its evolution equation provides a dynamical feedback on the alpha effect that is distinct from the conventional algebraic alpha quenching. The seriousness of this dynamical alpha quenching is particularly evident in the case of closed or periodic boxes. The explicit connection with catastrophic alpha quenching is reviewed and the alleviating effects of magnetic and current helicity fluxes are discussed. Title: Delayed correlation between turbulent energy injection and dissipation Authors: Pearson, Bruce R.; Yousef, Tarek A.; Haugen, Nils Erland L.; Brandenburg, Axel; Krogstad, Per-Åge Bibcode: 2004PhRvE..70e6301P Altcode: 2004physics...4114P The dimensionless kinetic energy dissipation rate Cɛ is estimated from numerical simulations of statistically stationary isotropic box turbulence that is slightly compressible. The Taylor microscale Reynolds number (Reλ) range is 20≲Reλ≲220 and the statistical stationarity is achieved with a random phase forcing method. The strong Reλ dependence of Cɛ abates when Reλ≈100 after which Cɛ slowly approaches ≈0.5 , a value slightly different from previously reported simulations but in good agreement with experimental results. If Cɛ is estimated at a specific time step from the time series of the quantities involved it is necessary to account for the time lag between energy injection and energy dissipation. Also, the resulting value can differ from the ensemble averaged value by up to ±30% . This may explain the spread in results from previously published estimates of Cɛ . Title: Catastrophic alpha quenching alleviated by helicity flux and shear Authors: Brandenburg, A.; Sandin, C. Bibcode: 2004A&A...427...13B Altcode: 2004astro.ph..1267B A new simulation set-up is proposed for studying mean field dynamo action. The model combines the computational advantages of local Cartesian geometry with the ability to include a shear profile that resembles the sun's differential rotation at low latitudes. It is shown that in a two-dimensional mean field model this geometry produces cyclic solutions with dynamo waves traveling away from the equator - as expected for a positive alpha effect in the northern hemisphere. In three dimensions with turbulence driven by a helical forcing function, an alpha effect is self-consistently generated in the presence of a finite imposed toroidal magnetic field. The results suggest that, due to a finite flux of current helicity out of the domain, alpha quenching appears to be non-catastrophic - at least for intermediate values of the magnetic Reynolds number. For larger values of the magnetic Reynolds number, however, there is evidence for a reversal of the trend and that α may decrease with increasing magnetic Reynolds number. Control experiments with closed boundaries confirm that in the absence of a current helicity flux, but with shear as before, alpha quenching is always catastrophic and alpha decreases inversely proportional to the magnetic Reynolds number. For solar parameters, our results suggest a current helicity flux of about 0.001 Gtwopers. This corresponds to a magnetic helicity flux, integrated over the northern hemisphere and over the 11 year solar cycle, of about 1046 Mx2. Title: Nonlinear Current Helicity Fluxes in Turbulent Dynamos and Alpha Quenching Authors: Subramanian, Kandaswamy; Brandenburg, Axel Bibcode: 2004PhRvL..93t5001S Altcode: 2004astro.ph..8020S Large scale dynamos produce small scale current helicity as a waste product that quenches the large scale dynamo process (alpha effect). This quenching can be catastrophic (i.e., intensify with magnetic Reynolds number) unless one has fluxes of small scale magnetic (or current) helicity out of the system. We derive the form of helicity fluxes in turbulent dynamos, taking also into account the nonlinear effects of Lorentz forces due to fluctuating fields. We confirm the form of an earlier derived magnetic helicity flux term, and also show that it is not renormalized by the small scale magnetic field, just like turbulent diffusion. Additional nonlinear fluxes are identified, which are driven by the anisotropic and antisymmetric parts of the magnetic correlations. These could provide further ways for turbulent dynamos to transport out small scale magnetic helicity, so as to avoid catastrophic quenching. Title: Shearing and embedding box simulations of the magnetorotational instability Authors: Brandenburg, Axel; Dintrans, Boris; Haugen, Nils Erland L. Bibcode: 2004AIPC..733..122B Altcode: 2004astro.ph.12363B Two different computational approaches to the magnetorotational instability (MRI) are pursued: the shearing box approach which is suited for local simulations and the embedding box approach whereby a Taylor Couette flow is embedded in a box so that numerical problems with the coordinate singularity are avoided. New shearing box simulations are presented and differences between regular and hyperviscosity are discussed. Preliminary simulations of spherical nonlinear Taylor Couette flow in an embedding box are presented and the effects of an axial field on the background flow are studied. Title: Suppression of small scale dynamo action by an imposed magnetic field Authors: Haugen, Nils Erland L.; Brandenburg, Axel Bibcode: 2004PhRvE..70c6408H Altcode: 2004astro.ph..2281H Nonhelical hydromagnetic turbulence with an externally imposed magnetic field is investigated using direct numerical simulations. It is shown that the imposed magnetic field lowers the spectral magnetic energy in the inertial range. This is explained by a suppression of the small scale dynamo. At large scales, however, the spectral magnetic energy increases with increasing imposed field strength for moderately strong fields, and decreases only slightly for even stronger fields. The presence of Alfvén waves is explicitly confirmed by monitoring the evolution of magnetic field and velocity at one point. The frequency ω agrees with vAk1 , where vA is the Alfvén speed and k1 is the smallest wave number in the box. Title: Mach number dependence of the onset of dynamo action Authors: Haugen, Nils Erland L.; Brandenburg, Axel; Mee, Antony J. Bibcode: 2004MNRAS.353..947H Altcode: 2004astro.ph..5453H The effect of compressibility on the onset of non-helical turbulent dynamo action is investigated using both direct simulations as well as simulations with shock-capturing viscosities, keeping, however, the regular magnetic diffusivity. It is found that the critical magnetic Reynolds number increases from about 35 in the subsonic regime to about 70 in the supersonic regime. Although the shock structures are sharper in the high-resolution direct simulations compared with the low-resolution shock-capturing simulations, the magnetic field looks roughly similar in both cases and does not show any shock structures. Similarly, the onset of dynamo action is not significantly affected by the shock-capturing viscosity. Title: Inertial range scaling in numerical turbulence with hyperviscosity Authors: Haugen, Nils Erland L.; Brandenburg, Axel Bibcode: 2004PhRvE..70b6405H Altcode: 2004astro.ph..2301H Numerical turbulence with hyperviscosity is studied and compared with direct simulations using ordinary viscosity and data from wind tunnel experiments. It is shown that the inertial range scaling is similar in all three cases. Furthermore, the bottleneck effect is approximately equally broad (about one order of magnitude) in these cases and only its height is increased in the hyperviscous case—presumably as a consequence of the steeper decent of the spectrum in the hyperviscous subrange. The mean normalized dissipation rate is found to be in agreement with both wind tunnel experiments and direct simulations. The structure function exponents agree with the She-Leveque model. Decaying turbulence with hyperviscosity still gives the usual t-1.25 decay law for the kinetic energy, and also the bottleneck effect is still present and about equally strong. Title: Self-Regulating Supernova Heating in Interstellar Medium Simulations Authors: Sarson, Graeme R.; Shukurov, Anvar; Nordlund, Åke; Gudiksen, Boris; Brandenburg, Axel Bibcode: 2004Ap&SS.292..267S Altcode: 2003astro.ph..7013S Numerical simulations of the multi-phase interstellar medium have been carried out, using a 3D, nonlinear, magnetohydrodynamic, shearing-box model, with random motions driven by supernova explosions. These calculations incorporate the effects of magnetic fields and rotation in 3D; these play important dynamical roles in the galaxy, but are neglected in many other simulations. The supernovae driving the motions are not arbitrarily imposed, but occur where gas accumulates into cold, dense clouds; their implementation uses a physically motivated model for the evolution of such clouds. The process is self-regulating, and produces mean supernova rates as part of the solution. Simulations with differing mean density show a power law relation between the supernova rate and density, with exponent 1.7; this value is within the range suggested from observations (taking star formation rate as a proxy for supernova rate). The global structure of the supernova driven medium is strongly affected by the presence of magnetic fields; e.g. for one solution the filling factor of hot gas is found to vary from 0.19 (with no field) to 0.12 (with initial mid-plane field B 0= 6 μG). Title: Outflows from Dynamo-Active Protostellar Accretion Discs Authors: von Rekowski, Brigitta; Brandenburg, Axel; Dobler, Wolfgang; Shukurov, Anvar Bibcode: 2004Ap&SS.292..493V Altcode: 2003astro.ph..6603V An axisymmetric model of a cool, dynamo-active accretion disc is applied to protostellar discs. Thermally and magnetically driven outflows develop that are not collimated within 0.1 AU. In the presence of a central magnetic field from the protostar, accretion onto the protostar is highly episodic, which is in agreement with earlier work. Title: High-Resolution Simulations of Nonhelical MHD Turbulence Authors: Haugen, N. E. L.; Brandenburg, A.; Dobler, W. Bibcode: 2004Ap&SS.292...53H Altcode: 2003astro.ph..6453H According to the kinematic theory of nonhelical dynamo action, the magnetic energy spectrum increases with wavenumber and peaks at the resistive cutoff wavenumber. It has previously been argued that even in the dynamical case, the magnetic energy peaks at the resistive scale. Using high resolution simulations (up to 10243 meshpoints) with no large-scale imposed field, we show that the magnetic energy peaks at a wavenumber that is independent of the magnetic Reynolds number and about five times larger than the forcing wavenumber. Throughout the inertial range, the spectral magnetic energy exceeds the kinetic energy by a factor of two to three. Both spectra are approximately parallel. The total energy spectrum seems to be close to k -3/2, but there is a strong bottleneck effect and we suggest that the asymptotic spectrum is instead k -5/3. This is supported by the value of the second-order structure function exponent that is found to be ζ2=0.70, suggesting a k -1.70 spectrum. The third-order structure function scaling exponent is very close to unity,—in agreement with Goldreich Sridhar theory. Title: Identification of gravity waves in hydrodynamical simulations Authors: Dintrans, B.; Brandenburg, A. Bibcode: 2004A&A...421..775D Altcode: 2003astro.ph.11094D The excitation of internal gravity waves by an entropy bubble oscillating in an isothermal atmosphere is investigated using direct two-dimensional numerical simulations. The oscillation field is measured by a projection of the simulated velocity field onto the anelastic solutions of the linear eigenvalue problem for the perturbations. This facilitates a quantitative study of both the spectrum and the amplitudes of excited g-modes.

Appendices are only available in electronic form at http://www.edpsciences.org Title: Structured, Dynamo Driven Stellar and Disc Winds Authors: von Rekowski, B.; Brandenburg, A. Bibcode: 2004ASPC..313..476V Altcode: 2004apnw.conf..476V; 2003astro.ph.10398V Considerable progress has been made in understanding the hydrodynamics, but only to a certain extent the magnetohydrodynamics, of shaping bipolar outflows forming protoplanetary nebulae (PPNs) and planetary nebulae (PNs). In particular, Blackman et al. (2001a, 2001b) point out two problems related to the formation of PNs and PPNs, regarding the formation of multipolar structures and the origin of the nebulae. They propose a solution by giving a semi-quantitative physical model which should be investigated by numerical simulations. Title: How long can left and right handed life forms coexist? Authors: Brandenburg, Axel; Multamäki, Tuomas Bibcode: 2004IJAsB...3..209B Altcode: 2004q.bio.....7008B Reaction-diffusion equations based on a polymerization model are solved to simulate the spreading of hypothetic left and right-handed life forms on the Earth's surface. The equations exhibit front-like behavior as is familiar from the theory of the spreading of epidemics. It is shown that the relevant time scale for achieving global homochirality is not, however, the time scale of front propagation, but the much longer global diffusion time. The process can be sped up by turbulence and large scale flows. It is speculated that, if the deep layers of the early ocean were sufficiently quiescent, there may have been the possibility of competing early life forms with opposite handedness. Title: Simulations of nonhelical hydromagnetic turbulence Authors: Haugen, Nils Erland; Brandenburg, Axel; Dobler, Wolfgang Bibcode: 2004PhRvE..70a6308H Altcode: 2003astro.ph..7059H Nonhelical hydromagnetic forced turbulence is investigated using large scale simulations on up to 256 processors and 10243 mesh points. The magnetic Prandtl number is varied between 1/8 and 30, although in most cases it is unity. When the magnetic Reynolds number is based on the inverse forcing wave number, the critical value for dynamo action is shown to be around 35 for magnetic Prandtl number of unity. For small magnetic Prandtl numbers we find the critical magnetic Reynolds number to increase with decreasing magnetic Prandtl number. The Kazantsev k3/2 spectrum for magnetic energy is confirmed for the kinematic regime, i.e., when nonlinear effects are still unimportant and when the magnetic Prandtl number is unity. In the nonlinear regime, the energy budget converges for large Reynolds numbers (around 1000) such that for our parameters about 70% is in kinetic energy and about 30% is in magnetic energy. The energy dissipation rates are converged to 30% viscous dissipation and 70% resistive dissipation. Second-order structure functions of the Elsasser variables give evidence for a k-5/3 spectrum. Nevertheless, the three-dimensional spectrum is close to k-3/2 , but we argue that this is due to the bottleneck effect. The bottleneck effect is shown to be equally strong both for magnetic and nonmagnetic turbulence, but it is far weaker in one-dimensional spectra that are normally studied in laboratory turbulence. Structure function exponents for other orders are well described by the She-Leveque formula, but the velocity field is significantly less intermittent and the magnetic field is more intermittent than the Elsasser variables. Title: Outflows and accretion in a star-disc system with stellar magnetosphere and disc dynamo Authors: von Rekowski, B.; Brandenburg, A. Bibcode: 2004A&A...420...17V Altcode: 2003astro.ph..7201V The interaction between a protostellar magnetosphere and a surrounding dynamo-active accretion disc is investigated using an axisymmetric mean-field model. In all models investigated, the dynamo-generated magnetic field in the disc arranges itself such that in the corona, the field threading the disc is anti-aligned with the central dipole so that no X-point forms. When the magnetospheric field is strong enough (stellar surface field strength around 2 kG or larger), accretion happens in a recurrent fashion with periods of around 15 to 30 days, which is somewhat longer than the stellar rotation period of around 10 days. In the case of a stellar surface field strength of at least a few 100 G, the star is being spun up by the magnetic torque exerted on the star. The stellar accretion rates are always reduced by the presence of a magnetosphere which tends to divert a much larger fraction of the disc material into the wind. Both, a pressure-driven stellar wind and a disc wind form. In all our models with disc dynamo, the disc wind is structured and driven by magneto-centrifugal as well as pressure forces. Title: New Algorithms for Magnetohydrodynamics and Gravity that Emphasize Resolution and Speed. Authors: Maron, J.; Dennis, T.; Howes, G.; Brandenburg, A.; Chandran, B.; Blackman, E. Bibcode: 2004DDA....35.0407M Altcode: 2004BAAS...36..854M The Gradient Particle Magnetohydrodynamics (GPM) algorithm combines the strengths of an adaptive grid code (AMR) and a smoothed particle code (SPH) by instilling grid-quality gradients into a Lagrangian particle code. It is of particular utility for disk/jet systems.

The hypergradient code uses high-precision tuned finite differences to achieve spectral-quality resolution with 5 times the speed of a spectral code. The finite differencing is not based on a high-order polynomial fit. The polynomial scheme has supurb accuracy for low-wavenumber gradients but fails at high wavenumbers. We instead use a scheme tuned to enhance high-wavenumber accuracy at the expense of low wavenumbers, although the loss of low-wavenumber accuracy is negligibly slight. A tuned gradient is capable of capturing all wavenumbers up to 80 percent of the Nyquist limit with an error of no worse than 1 percent. The fact that gradients are based on finite differences enables diverse geometries to be considered and eliminates the parallel communications bottleneck.

The gravity algorithm is based on the Barnes-Hut tree. It evades the latencies associated with memory accesses, divides, and square roots by grouping bundles of particles together into a simultaneous treewalk and using a polynomial series to approximate the divides and square roots. The algorithm runs 10 times faster than the standard tree codes with no loss of accuracy and it works for individual timesteps. Title: Magnetic helicity evolution in a periodic domain with imposed field Authors: Brandenburg, Axel; Matthaeus, William H. Bibcode: 2004PhRvE..69e6407B Altcode: 2003astro.ph..5373B In helical hydromagnetic turbulence with an imposed magnetic field (which is constant in space and time) the magnetic helicity of the field within a periodic domain is no longer an invariant of the ideal equations. Alternatively, there is a generalized magnetic helicity that is an invariant of the ideal equations. It is shown that this quantity is not gauge invariant and that it can therefore not be used in practice. Instead, the evolution equation of the magnetic helicity of the field describing the deviation from the imposed field is shown to be a useful tool. It is demonstrated that this tool can determine steady state quenching of the alpha-effect. A simple three-scale model is derived to describe the evolution of the magnetic helicity and to predict its sign as a function of the imposed field strength. The results of the model agree favorably with simulations. Title: Self-similar scaling in decaying numerical turbulence Authors: Yousef, Tarek A.; Haugen, Nils Erland L.; Brandenburg, Axel Bibcode: 2004PhRvE..69e6303Y Altcode: 2003astro.ph.12505Y Decaying turbulence is studied numerically using as initial condition a random flow whose shell-integrated energy spectrum increases with wave number k like kq . Alternatively, initial conditions are generated from a driven turbulence simulation by simply stopping the driving. It is known that the dependence of the decaying energy spectrum on wave number, time, and viscosity can be collapsed onto a unique scaling function that depends only on two parameters. This is confirmed using three-dimensional simulations and the dependence of the scaling function on its two arguments is determined. Title: Simulations of dust-trapping vortices in protoplanetary discs Authors: Johansen, A.; Andersen, A. C.; Brandenburg, A. Bibcode: 2004A&A...417..361J Altcode: 2003astro.ph.10059J Local three-dimensional shearing box simulations of the compressible coupled dust-gas equations are used in the fluid approximation to study the evolution of different initial vortex configurations in a protoplanetary disc and their dust-trapping capabilities. The initial conditions for the gas are derived from an analytic solution to the compressible Euler equation and the continuity equation. The solution is valid if there is a vacuum outside the vortex. In the simulations the vortex is either embedded in a hot corona, or it is extended in a cylindrical fashion in the vertical direction. Both configurations are found to survive for at least one orbit and lead to accumulation of dust inside the vortex. This confirms earlier findings that dust accumulates in anticyclonic vortices, indicating that this is a viable mechanism for planetesimal formation. Title: Non-Fickian diffusion and tau approximation from numerical turbulence Authors: Brandenburg, Axel; Käpylä, Petri J.; Mohammed, Amjed Bibcode: 2004PhFl...16.1020B Altcode: 2003astro.ph..6521B Evidence for non-Fickian diffusion of a passive scalar is presented using direct simulations of homogeneous isotropic turbulence. The results compare favorably with an explicitly time-dependent closure model based on the tau approximation. In the numerical experiments three different cases are considered: (i) zero mean concentration with finite initial concentration flux, (ii) an initial top hat profile for the concentration, and (iii) an imposed background concentration gradient. All cases agree in the resulting relaxation time in the tau approximation relating the triple correlation to the concentration flux. The first order smoothing approximation is shown to be inapplicable. Title: Stochastic excitation of gravity waves by overshooting convection in solar-type stars Authors: Dintrans, Boris; Brandenburg, Axel; Nordlund, Ake; Stein, R. F. Bibcode: 2004astro.ph..3093D Altcode: The excitation of gravity waves by penetrative convective plumes is investigated using 2D direct simulations of compressible convection. The oscillation field is measured by a new technique based on the projection of our simulation data onto the theoretical g-modes solutions of the associated linear eigenvalue problem. This allows us to determine both the excited modes and their corresponding amplitudes accurately. Title: The effects of spiral arms on the multi-phase ISM Authors: Shukurov, Anvar; Sarson, Graeme R.; Nordlund, Åke; Gudiksen, Boris; Brandenburg, Axel Bibcode: 2004Ap&SS.289..319S Altcode: 2002astro.ph.12260S Statistical parameters of the ISM driven by thermal energy injectionsfrom supernova explosions have been obtained from 3D, nonlinear,magnetohydrodynamic, shearing-box simulations for spiral arm andinterarm regions. The density scale height obtained for the interarm regionsis 50% larger than within the spiral arms because of thehigher gas temperature. The filling factorof the hot gas is also significantly larger between the armsand depends sensitively on magnetic field strength. Title: Helical coronal ejections and their role in the solar cycle Authors: Brandenburg, Axel; Sandin, Christer; Käpylä, Petri J. Bibcode: 2004IAUS..223...57B Altcode: 2005IAUS..223...57B; 2004astro.ph..7598B The standard theory of the solar cycle in terms of an alpha-Omega dynamo hinges on a proper understanding of the nonlinear alpha effect. Boundary conditions play a surprisingly important role in determining the magnitude of alpha. For closed boundaries, the total magnetic helicity is conserved, and since the alpha effect produces magnetic helicity of one sign in the large scale field, it must simultaneously produce magnetic helicity of the opposite sign. It is this secondary magnetic helicity that suppresses the dynamo in a potentially catastrophic fashion. Open boundaries allow magnetic helicity to be lost. Simulations are presented that allow an estimate of alpha in the presence of open or closed boundaries, either with or without solar-like differential rotation. In all cases the sign of the magnetic helicity agrees with that observed at the solar surface (negative in the north, positive in the south), where significant amounts of magnetic helicity can be ejected via coronal mass ejections. It is shown that open boundaries tend to alleviate catastrophic alpha quenching. The importance of looking at current helicity instead of magnetic helicity is emphasized and the conceptual advantages are discussed. Title: Turbulent magnetic Prandtl number and magnetic diffusivity quenching from simulations Authors: Yousef, T. A.; Brandenburg, A.; Rüdiger, G. Bibcode: 2003A&A...411..321Y Altcode: 2003astro.ph..2425Y Forced turbulence simulations are used to determine the turbulent kinematic viscosity, nut , from the decay rate of a large scale velocity field. Likewise, the turbulent magnetic diffusivity, etat, is determined from the decay of a large scale magnetic field. In the kinematic regime, when the field is weak, the turbulent magnetic Prandtl number, nut/etat, is about unity. When the field is nonhelical, etat is quenched when magnetic and kinetic energies become comparable. For helical fields the quenching is stronger and can be described by a dynamical quenching formula. Title: Is Nonhelical Hydromagnetic Turbulence Peaked at Small Scales? Authors: Haugen, Nils Erland L.; Brandenburg, Axel; Dobler, Wolfgang Bibcode: 2003ApJ...597L.141H Altcode: 2003astro.ph..3372H Nonhelical hydromagnetic turbulence without an imposed magnetic field is considered in the case where the magnetic Prandtl number is unity. The magnetic field is entirely due to dynamo action. The magnetic energy spectrum peaks at a wavenumber of about 5 times the minimum wavenumber in the domain, and not at the resistive scale, as has previously been argued. Throughout the inertial range, the spectral magnetic energy exceeds the kinetic energy by a factor of about 2.5, and both spectra are approximately parallel. At first glance, the total energy spectrum seems to be close to k-3/2, but there is a strong bottleneck effect and it is suggested that the asymptotic spectrum is k-5/3. This is supported by the value of the second-order structure function exponent that is found to be ζ2=0.70, suggesting a k-1.70 spectrum. Title: Relaxation of writhe and twist of a bi-helical magnetic field Authors: Yousef, T. A.; Brandenburg, A. Bibcode: 2003A&A...407....7Y Altcode: 2003astro.ph..3148Y In the past few years suggestions have emerged that the solar magnetic field might have a bi-helical contribution with oppositely polarized magnetic fields at large and small scales, and that the shedding of such fields may be crucial for the operation of the dynamo. It is shown that, if a bi-helical field is shed into the solar wind, positive and negative contributions of the magnetic helicity spectrum tend to mix and decay. Even in the absence of turbulence, mixing and decay can occur on a time scale faster than the resistive one provided the two signs of magnetic helicity originate from a single tube. In the presence of turbulence, positively and negatively polarized contributions mix rapidly in such a way that the ratio of magnetic helicity to magnetic energy is largest both at the largest scale and in the dissipation range. In absolute units the small scale excess of helical fields is however negligible. Title: Bottleneck effect in three-dimensional turbulence simulations Authors: Dobler, Wolfgang; Haugen, Nils Erland; Yousef, Tarek A.; Brandenburg, Axel Bibcode: 2003PhRvE..68b6304D Altcode: 2003astro.ph..3324D At numerical resolutions around 5123 and above, three-dimensional energy spectra from turbulence simulations begin to show noticeably shallower spectra than k-5/3 near the dissipation wave number (“bottleneck effect”). This effect is shown to be significantly weaker in one-dimensional spectra such as those obtained in wind tunnel turbulence. The difference can be understood in terms of the transformation between the one-dimensional and three-dimensional energy spectra under the assumption that the turbulent velocity field is isotropic. Transversal and longitudinal energy spectra are similar and can both accurately be computed from the full three-dimensional spectra. Second-order structure functions are less susceptible to the bottleneck effect and may be better suited for inferring the scaling exponent from numerical simulation data. Title: Outflows and Accretion in a Protostellar Star-disc System Authors: von Rekowski, Brigitta; Brandenburg, Axel Bibcode: 2003ANS...324...68V Altcode: 2003ANS...324..I10V No abstract at ADS Title: Decay of Magnetic Fields in the Early Universe Authors: Hindmarsh, Mark; Christensson, M.; Brandenburg, A. Bibcode: 2003sem..conf..482H Altcode: 2003astro.ph..2320H We study the evolution of a stochastic helical magnetic field generated in the early Universe after the electroweak phase transition, using standard magnetohydrodynamics (MHD). We find how the coherence length ξ, magnetic energy EM and magnetic helicity H evolve with time. We show that the self-similarity of the magnetic power spectrum alone implies that ξ ~ t1/2. This in turn implies that magnetic helicity decays as H ~ t-2s, and that the magnetic energy decays as EM ~ t-0.5-2s, where s inversely proportional to the magnetic Reynolds number ReM. These laws improve on several previous estimates. Title: Computational aspects of astrophysical MHD and turbulence Authors: Brandenburg, Axel Bibcode: 2003and..book..269B Altcode: 2003eclm.book..269B; 2001astro.ph..9497B The advantages of high-order finite difference scheme for astrophysical MHD and turbulence simulations are highlighted. A number of one-dimensional test cases are presented ranging from various shock tests to Parker-type wind solutions. Applications to magnetized accretion discs and their associated outflows are discussed. Particular emphasis is placed on the possibility of dynamo action in three-dimensional turbulent convection and shear flows, which is relevant to stars and astrophysical discs. The generation of large scale fields is discussed in terms of an inverse magnetic cascade and the consequences imposed by magnetic helicity conservation are reviewed with particular emphasis on the issue of alpha-quenching. Title: MHD simulations of small and large scale dynamos Authors: Brandenburg, A.; Haugen, N. E. L.; Dobler, W. Bibcode: 2003astro.ph..3371B Altcode: Isotropic homogeneous hydromagnetic turbulence is studied using numerical simulations at resolutions of up to 1024^3 meshpoints. It is argued that, in contrast to the kinematic regime, the nonlinear regime is characterized by a spectral magnetic power that is decreasing with increasing wavenumber, regardless of whether or not the turbulence has helicity. This means that the root-mean-square field strength converges to a limiting value at large magnetic Reynolds numbers. The total (magnetic and kinetic) energy spectrum tends to be somewhat shallower than k^{-5/3}, in agreement with the findings of other groups. In the presence of helicity, an inverse cascade develops, provided the scale separation between the size of the computational box and the scale of the energy carrying eddies exceeds a ratio of at least two. Finally, the constraints imposed by magnetic helicity conservation on mean-field theory are reviewed and new results of simulations are presented. Title: Structured outflow from a dynamo active accretion disc Authors: von Rekowski, B.; Brandenburg, A.; Dobler, W.; Dobler, W.; Shukurov, A. Bibcode: 2003A&A...398..825V Altcode: 2000astro.ph..3174V We present an axisymmetric numerical model of a dynamo active accretion disc. If the dynamo-generated magnetic field in the disc is sufficiently strong (close to equipartition with thermal energy), a fast magneto-centrifugally driven outflow develops within a conical shell near the rotation axis, together with a slower pressure driven outflow from the outer parts of the disc as well as around the axis. Our results show that a dynamo active accretion disc can contribute to driving an outflow even without any external magnetic field. The fast outflow in the conical shell is confined by the azimuthal field which is produced by the dynamo in the disc and advected to the disc corona. This part of the outflow has high angular momentum and is cooler and less dense than its surroundings. The conical shell's half-opening angle is typically about 30o near the disc and decreases slightly with height. The slow outflow is hotter and denser. Title: Doubly Helical Coronal Ejections from Dynamos and Their Role in Sustaining the Solar Cycle Authors: Blackman, Eric G.; Brandenburg, Axel Bibcode: 2003ApJ...584L..99B Altcode: 2002astro.ph.12010B Two questions about the solar magnetic field might be answered together once their connection is identified. The first is important for large-scale dynamo theory: what prevents the magnetic back-reaction forces from shutting down the dynamo cycle? The second question is, what determines the handedness of twist and writhe in magnetized coronal ejecta? Magnetic helicity conservation is important for answering both questions. Conservation implies that dynamo generation of large-scale writhed structures is accompanied by the oppositely signed twist along these structures. The latter is associated with the back-reaction force. We suggest that coronal mass ejections simultaneously liberate small-scale twist and large-scale writhe of opposite sign, helping to prevent the cycle from quenching and enabling a net magnetic flux change in each hemisphere. Solar observations and helicity spectrum measurements from our simulation of a rising flux tube support this idea. We show a new pictorial of dynamo flux generation that includes the back-reaction and magnetic helicity conservation and represents the field by a ribbon or tube rather than a line. Title: Contributions to the theory of a two-scale homogeneous dynamo experiment Authors: Rädler, Karl-Heinz; Brandenburg, Axel Bibcode: 2003PhRvE..67b6401R Altcode: 2002physics...8023R The principle of the two-scale dynamo experiment at the Forschungszentrum Karlsruhe is closely related to that of the Roberts dynamo working with a simple fluid flow which is, with respect to proper Cartesian coordinates x, y, and z, periodic in x and y and independent of z. A modified Roberts dynamo problem is considered with a flow more similar to that in the experimental device. Solutions are calculated numerically, and on this basis an estimate of the excitation condition of the experimental dynamo is given. The modified Roberts dynamo problem is also considered in the framework of the mean-field dynamo theory, in which the crucial induction effect of the fluid motion is an anisotropic α effect. Numerical results are given for the dependence of the mean-field coefficients on the fluid flow rates. The excitation condition of the dynamo is also discussed within this framework. The behavior of the dynamo in the nonlinear regime, i.e., with backreaction of the magnetic field on the fluid flow, depends on the effect of the Lorentz force on the flow rates. The quantities determining this effect are calculated numerically. The results for the mean-field coefficients and the quantities describing the backreaction provide corrections to earlier results, which were obtained under simplifying assumptions. Title: The Helicity Issue in Large Scale Dynamos Authors: Brandenburg, A. Bibcode: 2003LNP...614..402B Altcode: 2002astro.ph..7394B; 2003tmfa.conf..402B The connection between helically isotropic MHD turbulence and mean-field dynamo theory is reviewed. The nonlinearity in the mean-field theory is not yet well established, but detailed comparison with simulations begin to help select viable forms of the nonlinearity. The crucial discriminant is the magnetic helicity, which is known to evolve only on a slow resistive time scale in the limit of large magnetic Reynolds number. Particular emphasis is put on the possibility of memory effects, which means that an additional explicitly time-dependent equation for the nonlinearity is solved simultaneously with the mean-field equations. This approach leads to better agreement with the simulations, while it would also produce more favorable agreement between models and stellar dynamos. Title: Ejection of Bi-Helical Magnetic Fields from the Sun Authors: Brandenburg, Axel; Blackman, Eric G. Bibcode: 2003IAUJD...3E..33B Altcode: 2003astro.ph.12543B Over the past decade the measurement of magnetic and current helicity at the solar surface has attracted significant interest. There is now general consensus that the two helicities are negative in the north and positive in the south. On the other hand the tilt of bipolar regions in the clockwise direction in the north corresponds to a positive writhe helicity. In the south the tilt is counterclockwise corresponding to negative writhe helicity. These signs of writhe helicity which are thus apposite to the twist helicity measured as current helicity are also suggested by N-shaped sigmoids in the north and S-shaped sigmoids in the south. We interpret these as bi-helical magnetic field structures which have in the north negative magnetic helicity at smaller scales and positive magnetic helicity at the largest scales and oppositely in the south. This is also what is expected and required from dynamo theory in order that the dynamo cycle is able to reverse the entire field in a time as short as 11 years. The generation and evolution of bi-helical fields is studied using hydromagnetic turbulence simulations both for the convection zone and the solar wind. Title: On the generation of internal gravity waves by penetrative convection Authors: Dintrans, B.; Brandenburg, A.; Nordlund, Å.; Stein, R. F. Bibcode: 2003sf2a.conf..511D Altcode: 2003sf2a.confE.216D Gravity waves propagating in the radiative zones of solar-type stars are suspected to play a major role in the transport processes. However, the problem of their excitation remains open as a simple kappa-mechanism based on hydrogen and helium ionization zones is not applicable here. One possibility concerns the excitation by overshooting convection from neighboring convection zones. Strong downward plumes are known to penetrate substantial distances into the adjacent stable zone so that internal gravity waves can be randomly generated. We will present results coming from 2D-simulations of overshooting convection, for which a new detection method based on the anelastic subspace allows us to precisely measure internal waves which are stochastically excited. Title: Stochastic Excitation of Gravity Waves by Overshooting Convection in Solar-Type Stars Authors: Dintrans, Boris; Brandenburg, Axel; Nordlund, Åke; Stein, Robert F. Bibcode: 2003Ap&SS.284..237D Altcode: The excitation of gravity waves by penetrative convective plumes is investigated using 2D direct simulations of compressible convection. The oscillation field is measured by a new technique based on the projection of our simulation data onto the theoretical g-modes solutions of the associated linear eigenvalue problem. This allows us to determine both the excited modes and their corresponding amplitudes accurately. Title: How magnetic helicity ejection helps large scale dynamos Authors: Brandenburg, A.; Blackman, E. G.; Sarson, G. R. Bibcode: 2003AdSpR..32.1835B Altcode: 2003astro.ph..5374B There is mounting evidence that the ejection of magnetic helicity from the solar surface is important for the solar dynamo. Observations suggest that in the northern hemisphere the magnetic helicity flux is negative. We propose that this magnetic helicity flux is mostly due to small scale magnetic fields; in contrast to the more systematic large scale field of the 11 year cycle, whose helicity flux may be of opposite sign, and may be excluded from the observational interpretation. Using idealized simulations of MHD turbulence as well as a simple two-scale model, we show that shedding small scale (helical) field has two important effects. (i) The strength of the large scale field reaches the observed levels. (ii) The evolution of the large scale field proceeds on time scales shorter than the resistive time scale, as would otherwise be enforced by magnetic helicity conservation. In other words, the losses ensure that the solar dynamo is always in the near-kinematic regime. This requires, however, that the ratio of small scale to large scale losses cannot be too small, for otherwise the large scale field in the near-kinematic regime will not reach the observed values. Title: Helical Surface Structures Authors: Brandenburg, A.; Blackman, E. G. Bibcode: 2003IAUS..210..233B Altcode: 2002astro.ph.12019B Over the past few years there has been growing interest in helical magnetic field structures seen at the solar surface, in coronal mass ejections, as well as in the solar wind. Although there is a great deal of randomness in the data, on average the extended structures are mostly left-handed on the northern hemisphere and right-handed on the southern. Surface field structures are also classified as dextral (= right bearing) and sinistral (= left bearing) occurring preferentially in the northern and southern hemispheres respectively. Of particular interest here is a quantitative measurement of the associated emergence rates of helical structures, which translate to magnetic helicity fluxes. In this review, we give a brief survey of what has been found so far and what is expected based on models. Particular emphasis is put on the scale dependence of the associated fields and an attempt is made to estimate the helicity flux of the mean field vs. fluctuating field. Title: Magnetic helicity and the solar dynamo Authors: Brandenburg, Axel; Blackman, Eric G. Bibcode: 2002ESASP.506..805B Altcode: 2002ESPM...10..805B; 2002svco.conf..805B Over the past few years there has been growing interest in helical magnetic field structures seen at the solar surface, in coronal mass ejections, as well as in the solar wind. Although there is a great deal of randomness in the data, on average the extended structures are mostly left-handed on the northern hemisphere and right-handed on the southern. Surface field structures are also classified as dextral (=right bearing) and sinistral (=left bearing) occurring preferentially in the northern and southern hemispheres respectively. Of particular interest here is a quantitative measurement of the associated emergence rates of helical structures, which translate to magnetic helicity fluxes. In this review, we give a brief survey of what has been found so far and what is expected based on models. Particular emphasis is put on the scale dependence of the associated fields and an attempt is made to estimate the helicity flux of the mean field vs. fluctuating field. Title: Dynamic Nonlinearity in Large-Scale Dynamos with Shear Authors: Blackman, Eric G.; Brandenburg, Axel Bibcode: 2002ApJ...579..359B Altcode: 2002astro.ph..4497B We supplement the mean field dynamo growth equation with the total magnetic helicity evolution equation. This provides an explicitly time-dependent model for α-quenching in dynamo theory. For dynamos without shear, this approach accounts for the observed large-scale field growth and saturation in numerical simulations. After a significant kinematic phase, the dynamo is resistively quenched, i.e., the saturation time depends on the microscopic resistivity. This is independent of whether or not the turbulent diffusivity is resistively quenched. We find that the approach is also successful for dynamos that include shear and exhibit migratory waves (cycles). In this case, however, whether or not the cycle period remains of the order of the dynamical timescale at large magnetic Reynolds numbers does depend on how the turbulent magnetic diffusivity quenches. Since this is unconstrained by magnetic helicity conservation, the diffusivity is currently an input parameter. Comparison with current numerical experiments suggests a turbulent diffusivity that depends only weakly on the magnetic Reynolds number, but higher resolution simulations are needed. Title: Magnetoconvection and dynamo coefficients. II. Field-direction dependent pumping of magnetic field Authors: Ossendrijver, M.; Stix, M.; Brandenburg, A.; Rüdiger, G. Bibcode: 2002A&A...394..735O Altcode: 2002astro.ph..2299O We study the pumping of magnetic flux in three-dimensional compressible magnetoconvection in the context of stellar dynamos. The simulation domain represents a rectangular section from the lower part of a stellar convection zone plus the underlying stably stratified layer, with a total depth of up to five pressure scale heights. Once convection has attained a statistically stationary state, a magnetic field is introduced. The magnetic field is subsequently modified by the convective motions, and the resulting pumping effects are isolated by calculating various coefficients of the expansion of the electromotive force, /line{u}x{b}, in terms of components of the mean magnetic field. The dependence of the pumping effects on rotation, latitude and other parameters is studied. First numerical evidence is found for the existence of pumping effects in the horizontal directions. Evidence is found that the pumping effects act differently on different components of the mean magnetic field. Latitudinal pumping is mainly equatorward for a toroidal field, and can be poleward for a poloidal field. Longitudinal pumping is mainly retrograde for the radial field but prograde for the latitudinal field. The pumping effect in the vertical direction is found to be dominated by the diamagnetic effect, equivalent to a predominating downward advection with a maximum speed in the turbulent case of about 10% of the rms convective velocity. Where possible, an attempt is made to identify the physical origin of the effect. Finally, some consequences of the results for stellar dynamos are discussed. Title: Hydromagnetic turbulence in computer simulations Authors: Brandenburg, A.; Dobler, W. Bibcode: 2002CoPhC.147..471B Altcode: 2001astro.ph.11569B The usefulness of high-order schemes in astrophysical MHD turbulence simulations is discussed. Simple advection tests of hat profiles are used to compare schemes of different order. Higher order schemes generally need less explicit diffusion. In the case of a standing Burgers shock it is shown that the overall accuracy improves as the order of the scheme is increased. A memory efficient 3-step 2N-RK scheme is used. For cache efficiency, the entire set of equations is solved along pencils in the yz-plane. The advantage of solving for the magnetic vector potential is highlighted. Finally, results from a simulation of helical turbulence exhibiting large scale dynamo action are discussed. Title: Magnetic helicity in stellar dynamos: new numerical experiments Authors: Brandenburg, A.; Dobler, W.; Subramanian, K. Bibcode: 2002AN....323...99B Altcode: 2001astro.ph.11567B The theory of large scale dynamos is reviewed with particular emphasis on the magnetic helicity constraint in the presence of closed and open boundaries. In the presence of closed or periodic boundaries, helical dynamos respond to the helicity constraint by developing small scale separation in the kinematic regime, and by showing long time scales in the nonlinear regime where the scale separation has grown to the maximum possible value. A resistively limited evolution towards saturation is also found at intermediate scales before the largest scale of the system is reached. Larger aspect ratios can give rise to different structures of the mean field which are obtained at early times, but the final saturation field strength is still decreasing with decreasing resistivity. In the presence of shear, cyclic magnetic fields are found whose period is increasing with decreasing resistivity, but the saturation energy of the mean field is in strong super-equipartition with the turbulent energy. It is shown that artificially induced losses of small scale field of opposite sign of magnetic helicity as the large scale field can, at least in principle, accelerate the production of large scale (poloidal) field. Based on mean field models with an outer potential field boundary condition in spherical geometry, we verify that the sign of the magnetic helicity flux from the large scale field agrees with the sign of alpha. For solar parameters, typical magnetic helicity fluxes lie around 1047 Mx2 per cycle. Title: A new look at dynamo cycle amplitudes Authors: Saar, S. H.; Brandenburg, A. Bibcode: 2002AN....323..357S Altcode: 2002astro.ph..7392S We explore the dependence of the amplitude of stellar dynamo cycle variability (as seen in the Mount Wilson Ca II HK timeseries data) on other stellar parameters. We find that the fractional cycle amplitude A_cyc (i.e. the ratio of the peak-to-peak variation to the average) decreases somewhat with mean activity, increases with decreasing effective temperature, but is not correlated with inverse Rossby number Ro-1. We find that A_cyc increases with the ratio of cycle and rotational frequencies omega_cyc /Omega along two, nearly parallel branches. Title: Solar and stellar dynamos - latest developments Authors: Brandenburg, A.; Dobler, W. Bibcode: 2002AN....323..411B Altcode: 2002astro.ph..7393B Recent progress in the theory of solar and stellar dynamos is reviewed. Particular emphasis is placed on the mean-field theory which tries to describe the collective behavior of the magnetic field. In order to understand solar and stellar activity, a quantitatively reliable theory is necessary. Much of the new developments center around magnetic helicity conservation which is seen to be important in numerical simulations. Only a dynamical, explicitly time dependent theory of alpha -quenching is able to describe this behavior correctly. Title: Local and Nonlocal Magnetic Diffusion and Alpha-Effect Tensors in Shear Flow Turbulence Authors: Brandenburg, Axel; Sokoloff, Dmitry Bibcode: 2002GApFD..96..319B Altcode: 2001astro.ph.11568B Various approaches to estimate turbulent transport coefficients from numerical simulations of hydromagnetic turbulence are discussed. A quantitative comparison between the averaged magnetic field obtained from a specific three-dimensional simulation of a rotating turbulent shear flow in a slab and a simple one-dimensional alpha-omega dynamo model is given. A direct determination of transport coefficients is attempted by calculating the correlation matrix of different components of the field and its derivatives. This matrix relates the electromotive force to physically relevant parameters like the tensor components of the f-effect and the turbulent diffusivity. The f-effect operating on the toroidal field is found to be negative and of similar magnitude as the value obtained in previous work by correlating the electromotive force with the mean magnetic field. The turbulent diffusion of the toroidal field is comparable to the kinematic viscosity that was determined earlier by comparing the stress with the shear. However, the turbulent diffusion of the radial field component is smaller and can even be formally negative. The method is then modified to obtain the spectral dependence of the turbulent transport coefficients on the wavenumber. There is evidence for nonlocal behaviour in that most of the response comes from the smallest wavenumbers corresponding to the largest scale possible in the simulation. Again, the turbulent diffusion coefficient for the radial field component is small, or even negative, which is considered unphysical. However, when the diffusion tensor is assumed to be diagonal the radial component of the diffusion tensor is positive, supporting thus the relevance of a nonlocal approach. Finally, model calculations are presented using nonlocal prescriptions of the f-effect and the turbulent diffusion. We emphasize that in all cases the electromotive force exhibits a strong stochastic component which make the f-effect and the turbulent diffusion intrinsically noisy. Title: Nonlinear states of the screw dynamo Authors: Dobler, Wolfgang; Shukurov, Anvar; Brandenburg, Axel Bibcode: 2002PhRvE..65c6311D Altcode: 2001astro.ph..5484D The self-excitation of magnetic field by a spiral Couette flow between two coaxial cylinders is considered. We solve numerically the fully nonlinear, three-dimensional magnetohydrodynamic (MHD) equations for magnetic Prandtl numbers Pm (ratio of kinematic viscosity to magnetic diffusivity) between 0.14 and 10 and kinematic and magnetic Reynolds numbers up to about 2000. In the initial stage of exponential field growth (kinematic dynamo regime), we find that the dynamo switches from one distinct regime to another as the radial width δrB of the magnetic field distribution becomes smaller than the separation of the field maximum from the flow boundary. The saturation of magnetic field growth is due to a reduction in the velocity shear resulting mainly from the azimuthally and axially averaged part of the Lorentz force, which agrees with an asymptotic result for the limit of Pm<<1. In the parameter regime considered, the magnetic energy decreases with kinematic Reynolds number as Re-0.84, which is approximately as predicted by the nonlinear asymptotic theory (~Re-1). However, when the velocity field is maintained by a volume force (rather than by viscous stress) the dependence of magnetic energy on the kinematic Reynolds number is much weaker. Title: The Nonlinearity of Large Scale Dynamos Authors: Brandenburg, Axel Bibcode: 2002smra.progE...2B Altcode: No abstract at ADS Title: Effect of Hyperdiffusivity on Turbulent Dynamos with Helicity Authors: Brandenburg, Axel; Sarson, Graeme R. Bibcode: 2002PhRvL..88e5003B Altcode: 2001astro.ph.10171B In numerical studies of turbulence, hyperviscosity is often used as a tool to extend the inertial subrange and to reduce the dissipative subrange. By analogy, hyperdiffusivity (or hyperresistivity) is sometimes used in magnetohydrodynamics. The underlying assumption is that only the small scales are affected by this manipulation. In the present paper, possible side effects on the evolution of the large-scale magnetic field are investigated. It is found that for turbulent flows with helicity, hyperdiffusivity causes the dynamo-generated magnetic field to saturate at a higher level than normal diffusivity. This result is successfully interpreted in terms of magnetic helicity conservation, which also predicts that full saturation is reached only after a time comparable to the large-scale magnetic (hyper)diffusion time. Title: Global hydromagnetic non-adiabatic disc simulations Authors: von Rekowski, B.; Brandenburg, A.; Dobler, W.; Shukurov, A. Bibcode: 2002bhty.confE..23V Altcode: 2002bhty.confE..23R No abstract at ADS Title: The solar dynamo: worrying about magnetic helicity Authors: Brandenburg, A. Bibcode: 2002ocnd.confE..23B Altcode: No abstract at ADS Title: MHD inverse cascade in the early Universe Authors: Hindmarsh, Mark; Christensson, M.; Brandenburg, A. Bibcode: 2002astro.ph..1466H Altcode: We have carried out numerical simulations of freely decaying magnetohydrodynamic (MHD) turbulence in three dimensions, which can be applied to the evolution of stochastic magnetic fields in the early Universe. For helical magnetic fields an inverse cascade effect is observed in which magnetic helicity and energy is transfered from smaller scales to larger scales, accompanied by power law growth in the characteristic length scale of the magnetic field. The magnetic field quickly reaches a scaling regime with self-similar evolution, and power law behaviour at high wavenumbers. We also find power law decay in the magnetic and kinematic energies. Title: How magnetic helicity ejection can speed up large scale dynamos Authors: Brandenburg, A.; Blackman, E. Bibcode: 2002cosp...34E3053B Altcode: 2002cosp.meetE3053B There is mounting evidence that the ejection of magnetic helicity from the solar surface is of tremendous importance for the solar dynamo. Observations suggest that in the northern hemisphere the magnetic helicity flux is negative. We argue that this magnetic helicity flux is mostly due to small scale magnetic fields -- in contrast to the much more systematic large scale field of the 11 year cycle. We show, using idealized simulations of MHD turbulence as well as a simple two -scale model, that losses of small scale field can be responsible for enhancing the strength of the large scale field to observed levels. The losses of small scale field are also crucial for allowing the evolution of the large scale field to proceed on time scales shorter than the resistive time scale, that would otherwise be enforced by magnetic helicity conservation. Title: Numerical simulations of turbulent dynamos Authors: Brandenburg, Axel Bibcode: 2002HiA....12..742B Altcode: Using a periodic box calculation it is shown that, owing to helicity conservation, a large scale field can only develop on a resistive timescale. This behaviour can be reproduced by a mean-field dynamo with α and ηt quenchings that are equally strong and "catastrophic". Title: Astrophysical significance of the anisotropic kinetic alpha effect Authors: Brandenburg, A.; Rekowski, B. V. Bibcode: 2001A&A...379.1153B Altcode: 2001astro.ph..6280B The generation of large scale flows by the anisotropic kinetic alpha (AKA) effect is investigated in simulations with a suitable time-dependent space- and time-periodic anisotropic forcing lacking parity invariance. The forcing pattern moves relative to the fluid, which leads to a breaking of the Galilean invariance as required for the AKA effect to exist. The AKA effect is found to produce a clear large scale flow pattern when the Reynolds number, R, is small as only a few modes are excited in linear theory. In this case the non-vanishing components of the AKA tensor are dynamically independent of the Reynolds number. For larger values of R, many more modes are excited and the components of the AKA tensor are found to decrease rapidly with increasing value of R. However, once there is a magnetic field (imposed and of sufficient strength, or dynamo-generated and saturated) the field begins to suppress the AKA effect, regardless of the value of R. It is argued that the AKA effect is unlikely to be astrophysically significant unless the magnetic field is weak and R is small. Title: Search for non-helical disc dynamos in simulations Authors: Arlt, R.; Brandenburg, A. Bibcode: 2001A&A...380..359A Altcode: 2001astro.ph..6557A The origin of large scale magnetic fields in accretion discs is investigated. Using global three-dimensional simulations of accretion disc turbulence, a recent suggestion of Vishniac & Cho (2001, ApJ 550, 752) is re-examined, according to which large scale fields in accretion discs could be understood without explicitly invoking the usual helicity effect. Particular emphasis is placed on a certain correlation between vorticity and azimuthal velocity gradient which has been predicted to drive large scale dynamo action, independent of the presence or absence of kinetic helicity. In the global disc simulations two types of behaviours are found: those which do show this type of velocity correlation and those which do not. The former ones are typically also the cases where the resistivity is larger. The latter ones show signs typical of dynamo action based on the usual helicity effect. In the idealized simulations without rotation and just shear the above correlation is found to be particularly strong. In both cases there is, as expected, a systematic flux of magnetic helicity through the midplane. However, very little magnetic helicity leaves the domain through the top and bottom boundaries. The idealized simulations reveal that much of this systematic flux comes from the rotational component of the helicity flux and does not contribute to its divergence. Title: Burgers Turbulence and the Problem of Star Formation Authors: Brandenburg, A.; Boldyrev, S. Bibcode: 2001AAS...19914901B Altcode: 2001BAAS...33Q1528B Star forming molecular clouds are thought to be governed by supersonic, possibly super-Alfvenic turbulence. We introduce a one-dimensional Burgers model with magnetic pressure that explains sustaining of the turbulence on small scales, the turbulent shock fragmentation, and the formation of the universal density statistics,-- features characteristic of the three-dimensional supersonic turbulence. We present an analytical solution for the model and confirm it by direct numerical simulations. Title: Inverse cascade in decaying three-dimensional magnetohydrodynamic turbulence Authors: Christensson, Mattias; Hindmarsh, Mark; Brandenburg, Axel Bibcode: 2001PhRvE..64e6405C Altcode: 2000astro.ph.11321C We perform direct numerical simulations of three-dimensional freely decaying magnetohydrodynamic turbulence. For helical magnetic fields, an inverse cascade effect is observed in which power is transfered from smaller scales to larger scales. The magnetic field reaches a scaling regime with self-similar evolution, and power-law behavior at high wave numbers. We also find power-law decay in the magnetic and kinematic energies, and power-law growth in the characteristic length scale of the magnetic field. Title: Magnetohydrodynamic turbulence in warped accretion discs Authors: Torkelsson, Ulf; Ogilvie, Gordon I.; Brandenburg, Axel; Pringle, James E.; Nordlund, Åke; Stein, Robert F. Bibcode: 2001AIPC..586..681T Altcode: 2001tsra.conf..681T; 2001astro.ph..3057T Warped, precessing accretion discs appear in a range of astrophysical systems, for instance the X-ray binary Her X-1 and in the active nucleus of NGC4258. In a warped accretion disc there are horizontal pressure gradients that drive an epicyclic motion. We have studied the interaction of this epicyclic motion with the magneto-hydrodynamic turbulence in numerical simulations. We find that the turbulent stress acting on the epicyclic motion is comparable in size to the stress that drives the accretion, however an important ingredient in the damping of the epicyclic motion is its parametric decay into inertial waves. . Title: Magnetoconvection and dynamo coefficients:. Dependence of the alpha effect on rotation and magnetic field Authors: Ossendrijver, M.; Stix, M.; Brandenburg, A. Bibcode: 2001A&A...376..713O Altcode: 2001astro.ph..8274O We present numerical simulations of three-dimensional compressible magnetoconvection in a rotating rectangular box that represents a section of the solar convection zone. The box contains a convectively unstable layer, surrounded by stably stratified layers with overshooting convection. The magnetic Reynolds number, Rm, is chosen subcritical, thus excluding spontaneous growth of the magnetic field through dynamo action, and the magnetic energy is maintained by introducing a constant magnetic field into the box, once convection has attained a statistically stationary state. Under the influence of the Coriolis force, the advection of the magnetic field results in a non-vanishing contribution to the mean electric field, given by <vec{u}xvec{b}>. From this electric field, we calculate the alpha -effect, separately for the stably and the unstably stratified layers, by averaging over time and over suitably defined volumes. From the variation of alpha we derive an error estimate, and the dependence of alpha on rotation and magnetic field strength is studied. Evidence is found for rotational quenching of the vertical alpha effect, and for a monotonic increase of the horizontal alpha effect with increasing rotation. For Rm~ 30, our results for both vertical and horizontal alpha effect are consistent with magnetic quenching by a factor [1+Rm (B0/Beq)2]-1. The signs of the small-scale current helicity and of the vertical component of alpha are found to be opposite to those for isotropic turbulence. Title: The helicity constraint in turbulent dynamos with shear Authors: Brandenburg, Axel; Bigazzi, Alberto; Subramanian, Kandaswamy Bibcode: 2001MNRAS.325..685B Altcode: 2000astro.ph.11081B The evolution of magnetic fields is studied using simulations of forced helical turbulence with strong imposed shear. After some initial exponential growth, the magnetic field develops a large-scale travelling wave pattern. The resulting field structure possesses magnetic helicity, which is conserved in a periodic box by the ideal magnetohydrodynamics equations and can hence only change on a resistive time-scale. This strongly constrains the growth time of the large-scale magnetic field, but less strongly constrains the length of the cycle period. Comparing this with the case without shear, the time-scale for large-scale field amplification is shortened by a factor Q, which depends on the relative importance of shear and helical turbulence, and which also controls the ratio of toroidal to poloidal field. The results of the simulations can be reproduced qualitatively and quantitatively with a mean-field αΩ-dynamo model with alpha-effect and turbulent magnetic diffusivity coefficients that are less strongly quenched than in the corresponding α2-dynamo. Title: Thermal production of gravitinos Authors: Bolz, M.; Brandenburg, A.; Buchmüller, W. Bibcode: 2001NuPhB.606..518B Altcode: 2000hep.ph...12052B We evaluate the gravitino production rate in supersymmetric QCD at high temperature to leading order in the gauge coupling. The result, which is obtained by using the resummed gluon propagator, depends logarithmically on the gluon plasma mass. As a byproduct, a new result for the axion production rate in a QED plasma is obtained. The implications for the cosmological dark matter problem are briefly discussed, in particular the intriguing possibility that gravitinos are the dominant part of cold dark matter. Title: Magnetic Mysteries Authors: Brandenburg, A. Bibcode: 2001Sci...292.2440B Altcode: At present--some 14 billion years after the Big Bang--magnetic fields of appreciable strength are found in virtually all galaxies and also in galaxy clusters. Although weak compared with the fields at Earth's or the Sun's surface, these fields are enormous considering the scales involved and may influence the formation of stars and galaxies, the dynamics of galaxy clusters, and energy transport within galaxy clusters. Even 1 to 2 billion years after the Big Bang, such fields must already have existed at about the same strength as today. How did these fields arise? And did primordial magnetic fields exist in the early universe? Answers to these questions remain speculative, but upcoming space missions promise exciting insights. Title: The effects of vertical outflows on disk dynamos. Authors: Bardou, A.; von Rekowski, B.; Dobler, W.; Brandenburg, A.; Shukurov, A. Bibcode: 2001A&A...370..635B Altcode: 2000astro.ph.11545B We consider the effect of vertical outflows on the mean-field dynamo in a thin disk. These outflows could be due to winds or magnetic buoyancy. We analyse both two-dimensional finite-difference numerical solutions of the axisymmetric dynamo equations and a free-decay mode expansion using the thin-disk approximation. Contrary to expectations, a vertical velocity can enhance dynamo action, provided the velocity is not too strong. In the nonlinear regime this can lead to super-exponential growth of the magnetic field. Title: Evolution of highly buoyant thermals in a stratified layer Authors: Brandenburg, A.; Hazlehurst, J. Bibcode: 2001A&A...370.1092B Altcode: 2000astro.ph..8099B The buoyant rise of thermals (i.e. bubbles of enhanced entropy, but initially in pressure equilibrium) is investigated numerically in three dimensions for the case of an adiabatically stratified layer covering 6-9 pressure scale heights. It is found that these bubbles can travel to large heights before being braked by the excess pressure that builds up in order to drive the gas sideways in the head of the bubble. Until this happens, the momentum of the bubble grows as described by the time-integrated buoyancy force. This validates the simple theory of bubble dynamics whereby the mass entrainment of the bubble provides an effective braking force well before the bubble stops ascending. This is quantified by an entrainment parameter alpha which is calculated from the simulations and is found to be in good agreement with the experimental measurements. This work is discussed in the context of contact binaries whose secondaries could be subject to dissipative heating in the outermost layers. Title: The Inverse Cascade and Nonlinear Alpha-Effect in Simulations of Isotropic Helical Hydromagnetic Turbulence Authors: Brandenburg, Axel Bibcode: 2001ApJ...550..824B Altcode: 2000astro.ph..6186B A numerical model of isotropic homogeneous turbulence with helical forcing is investigated. The resulting flow, which is essentially the prototype of the α2 dynamo of mean field dynamo theory, produces strong dynamo action with an additional large-scale field on the scale of the box (at wavenumber k=1; forcing is at k=5). This large-scale field is nearly force free and exceeds the equipartition value. As the magnetic Reynolds number Rm increases, the saturation field strength and the growth rate of the dynamo increase. However, the time it takes to build up the large-scale field from equipartition to its final superequipartition value increases with magnetic Reynolds number. The large-scale field generation can be identified as being due to nonlocal interactions originating from the forcing scale, which is characteristic of the α-effect. Both α and turbulent magnetic diffusivity ηt are determined simultaneously using numerical experiments where the mean field is modified artificially. Both quantities are quenched in an Rm-dependent fashion. The evolution of the energy of the mean field matches that predicted by an α2 dynamo model with similar α and ηt quenchings. For this model an analytic solution is given that matches the results of the simulations. The simulations are numerically robust in that the shape of the spectrum at large scales is unchanged when changing the resolution from 303 to 1203 mesh points, or when increasing the magnetic Prandtl number (viscosity/magnetic diffusivity) from 1 to 100. Increasing the forcing wavenumber to 30 (i.e., increasing the scale separation) makes the inverse cascade effect more pronounced, although it remains otherwise qualitatively unchanged. Title: Large scale dynamos with helicity loss through boundaries Authors: Brandenburg, A.; Dobler, W. Bibcode: 2001A&A...369..329B Altcode: 2000astro.ph.12472B Dynamo action is investigated in simulations of locally isotropic and homogeneous turbulence in a slab between open boundaries. It is found that a ``pseudo-vacuum'' boundary condition (where the field is vertical) leads to strong helicity fluxes which significantly reduce the amplitude of the resulting large-scale field. On the other hand, if there is a conducting halo outside the dynamo-active region, the large scale field amplitude can reach larger values, but the time scale after which this field is reached increases linearly with the magnetic Reynolds number. In both cases, most of the helicity flux is found to occur on large scales. From the variety of models considered we conclude that open boundaries tend to lower the saturation field strength compared to the case with periodic boundaries. The rate at which this lower saturation field strength is attained is roughly independent of the strength of the turbulence and of the boundary conditions. For dynamos with less helicity, however, significant field strengths could be reached in a shorter time. Title: Dynamical friction of bodies orbiting in a gaseous sphere Authors: Sánchez-Salcedo, F. J.; Brandenburg, A. Bibcode: 2001MNRAS.322...67S Altcode: 2000astro.ph.10003S The dynamical friction experienced by a body moving in a gaseous medium is different from the friction in the case of a collisionless stellar system. Here we consider the orbital evolution of a gravitational perturber inside a gaseous sphere using three-dimensional simulations, ignoring however self-gravity. The results are analysed in terms of a `local' formula with the associated Coulomb logarithm taken as a free parameter. For forced circular orbits, the asymptotic value of the component of the drag force in the direction of the velocity is a slowly varying function of the Mach number in the range 1.0-1.6. The dynamical friction time-scale for free decay orbits is typically only half as long as in the case of a collisionless background, which is in agreement with E. C. Ostriker's recent analytic result. The orbital decay rate is rather insensitive to the past history of the perturber. It is shown that, similarly to the case of stellar systems, orbits are not subject to any significant circularization. However, the dynamical friction time-scales are found to increase with increasing orbital eccentricity for the Plummer model, whilst no strong dependence on the initial eccentricity is found for the isothermal sphere. Title: Further Analysis of Stellar Magnetic Cycle Periods Authors: Saar, S.; Brandenburg, A. Bibcode: 2001ASPC..248..231S Altcode: 2001astro.ph..5070S; 2001mfah.conf..231S We further investigate relationships between activity cycle periods in cool stars and rotation to include new cycle data, and explore different parameterizations of the problem. We find that relations between cycle and rotational frequencies (omega_cyc vs. Omega) and between their ratio and the inverse Rossby number (omega_cyc/Omega vs. Ro^{-1}) show many similarities, including three branches and similar rms scatter. We briefly discuss some implications for dynamo models. Title: The Solar Dynamo: Old, Recent, and New Problems Authors: Brandenburg, A. Bibcode: 2001IAUS..203..144B Altcode: 2000astro.ph.11579B There are a number of fundamental uncertainties in our understanding of the solar dynamo. What is the significance of the lower overshoot layer, does the dynamo work in the entire convection zone, why is the field oscillatory, migratory, and dipole-like? Although some of those properties can be understood in the framework of α-Ω dynamo theory, there are some basic questions whether this theory can actually work. In my talk I will present a model of helically forced turbulence that allows us to address the question what generates the large scale field (e.g. α-effect and/or inverse cascade). Next, a simulation of a convective dynamo with shear will be presented, where a large scale magnetic field is found to develop near the lower overshoot layer. Finally, comparisons will be made with dynamo action in galaxies and accretion discs. In all cases the effects of noise are rather strong, and it is the presence of large scale shear which is crucial in producing a well-defined large scale field. The importance of magnetic instabilities will be highlighted in connection with stellar dynamos, where the observed cycle periods point toward the existence of different branches of activity. Title: Helicity in Hydro and MHD Reconnection Authors: Brandenburg, Axel; Kerr, Robert M. Bibcode: 2001LNP...571..358B Altcode: 2000astro.ph.12210B; 2001qvds.conf..358B Helicity, a measure of the linkage of flux lines, has subtle and largely unknown effects upon dynamics. Both magnetic and hydrodynamic helicity are conserved for ideal systems and could suppress nonlinear dynamics. What actually happens is not clear because in a fully three-dimensional system there are additional channels whereby intense, small-scale dynamics can occur. This contribution shows one magnetic and one hydrodynamic case where for each the presence of helicity does not suppr ess small-scale intense dynamics of the type that might lead to reconnection. Title: Two-dimensional disk dynamos with vertical outflows into a halo Authors: von Rekowski, B.; Dobler, W.; Shukurov, A.; Brandenburg, A. Bibcode: 2000astro.ph.12013V Altcode: We study the effects of vertical outflows on mean-field dynamos in disks. These outflows could be due to thermal winds or magnetic buoyancy. We analyse numerical solutions of the nonlinear mean-field dynamo equations using a two-dimensional finite-difference model. Contrary to expectations, a modest vertical velocity can enhance dynamo action. This can lead to super-exponential growth of the magnetic field and to higher magnetic energies at saturation in the nonlinear regime. Title: The inverse cascade in turbulent dynamos Authors: Brandenburg, Axel Bibcode: 2000astro.ph.12112B Altcode: The emergence of a large scale magnetic field from randomly forced isotropic strongly helical flows is discussed in terms of the inverse cascade of magnetic helicity and the alpha-effect. In simulations of such flows the maximum field strength exceeds the equipartition field strength for large scale separation. However, helicity conservation controls the speed at which this final state is reached. In the presence of open boundaries magnetic helicity fluxes out of the domain are possible. This reduces the timescales of the field growth, but it also tends to reduce the maximum attainable field strength. Title: Sheared helical turbulence and the helicity constraint in large-scale dynamos Authors: Bigazzi, A.; Brandenburg, A.; Subramanian, K. Bibcode: 2000astro.ph.12240B Altcode: The effect of shear on the growth of large scale magnetic fields in helical turbulence is investigated. The resulting large-scale magnetic field is also helical and continues to evolve, after saturation of the small scale field, on a slow resistive time scale. This is a consequence of magnetic helicity conservation. Because of shear, the time scale needed to reach an equipartition-strength large scale field is shortened proportionally to the ratio of the resulting toroidal to poloidal large scale fields. Title: Magnetohydrodynamics of Accretion Disks Authors: Brandenburg, A. Bibcode: 2000eaa..bookE2226B Altcode: An ACCRETION DISK is a flat formation of gas and dust rotating about a central object and accreting matter inwards by transporting angular momentum outwards, so that the centrifugal support is gradually removed from the fluid parcels. There are three main classes of accretion disks: (i) disks around accreting compact stars (white dwarfs, neutron stars or black holes) in binary systems, (ii) disks... Title: The response of a turbulent accretion disc to an imposed epicyclic shearing motion Authors: Torkelsson, Ulf; Ogilvie, Gordon I.; Brandenburg, Axel; Pringle, James E.; Nordlund, Åke; Stein, Robert F. Bibcode: 2000MNRAS.318...47T Altcode: 2000astro.ph..5199T We excite an epicyclic motion, the amplitude of which depends on the vertical position, z, in a simulation of a turbulent accretion disc. An epicyclic motion of this kind may be caused by a warping of the disc. By studying how the epicyclic motion decays, we can obtain information about the interaction between the warp and the disc turbulence. A high-amplitude epicyclic motion decays first by exciting inertial waves through a parametric instability, but its subsequent exponential damping may be reproduced by a turbulent viscosity. We estimate the effective viscosity parameter, αv, pertaining to such a vertical shear. We also gain new information on the properties of the disc turbulence in general, and measure the usual viscosity parameter, αh, pertaining to a horizontal (Keplerian) shear. We find that, as is often assumed in theoretical studies, αv is approximately equal to αh and both are much less than unity, for the field strengths achieved in our local box calculations of turbulence. In view of the smallness (~0.01) of αv and αh we conclude that for βpgaspmag~10 the time-scale for diffusion or damping of a warp is much shorter than the usual viscous time-scale. Finally, we review the astrophysical implications. Title: Numerical simulations of turbulent dynamos Authors: Brandenburg, Axel Bibcode: 2000astro.ph.10495B Altcode: Using a periodic box calculation it is shown that, owing to helicity conservation, a large scale field can only develop on a resistive timescale. This behaviour can be reproduced by a mean-field dynamo with alpha and eta_t quenchings that are equally strong and `catastrophic'. Title: Large scale dynamos with ambipolar diffusion nonlinearity Authors: Brandenburg, A.; Subramanian, K. Bibcode: 2000A&A...361L..33B Altcode: 2000astro.ph..7450B It is shown that ambipolar diffusion as a useful model for nonlinearity leads to similar behaviour of large scale turbulent dynamos as full MHD. This is demonstrated using both direct simulations in a periodic box and a closure model for the magnetic correlation functions applicable to infinite space. Large scale fields develop via a nonlocal inverse cascade as described by the alpha -effect. However, magnetic helicity can only change on a resistive timescale, so the time it takes to organize the field into large scales increases with magnetic Reynolds number. Title: Non-linear magnetic diffusivity in mean-field electrodynamics Authors: Urpin, V.; Brandenburg, A. Bibcode: 2000MNRAS.316..684U Altcode: We consider non-linear transport and drift processes caused by an inhomogeneous magnetic field in a turbulent fluid. The coefficients of magnetic diffusivity and drift velocity are calculated by making use of the second-order correlation approximation. Transport processes in the presence of a sufficiently strong magnetic field become anisotropic with larger diffusion rate and turbulent electrical resistivity across the field than along the field. Non-linear effects also lead to a drift of the magnetic field away from the regions with a higher magnetic energy. Title: Astrophysical convection and dynamos Authors: Brandenburg, A.; Nordlund, A.; Stein, R. F. Bibcode: 2000gac..conf...85B Altcode: Convection can occur in various astrophysical settings. In this review some aspects of solar convection are highlighted. In deeper layers of the solar convection zone, rotation becomes important and can lead to effects such as downward pumping of vorticity and magnetic fields. Rotation has the tendency to partially evacuate vortex tubes making them lighter. This effect can sometimes reverse the core of a downdraft and make it buoyant. The problem of different thermal and dynamic a time scales is addressed and finally the formation of magnetic structures by convection is discussed. Title: Magnetohydrodynamic Turbulence in Accretion Discs Authors: Torkelsson, U.; Brandenburg, A.; Nordlund, A.; Stein, R. F. Bibcode: 2000IAUS..195..241T Altcode: We present results from numerical simulations of magnetohydrodynamic turbulence in accretion discs. Our simulations show that the turbulent stresses that drive the accretion are less stratified than the matter; thus, the surface layers are more strongly heated than the interior of the disc. Title: The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulence Authors: Brandenburg, A. Bibcode: 2000astu.confE..25B Altcode: No abstract at ADS Title: Discussion on Accretion Disk Turbulence Authors: Brandenburg, Axel; Gammie, Charles; Stone, Jim Bibcode: 2000astu.confE...5B Altcode: No abstract at ADS Title: The Relationship Between Vortex and Magnetic Reconnection Authors: Brandenburg, Axel; Kerr, Robert Bibcode: 2000astu.progE...3B Altcode: No abstract at ADS Title: Dynamo-generated Turbulence and Outflows from Accretion Discs Authors: Brandenburg, A. Bibcode: 2000RSPTA.358..759B Altcode: 2000RSLPT.358..759B Local hydromagnetic simulations of accretion-disc turbulence currently provide the most convincing evidence that the origin of turbulence in discs could be the Balbus-Hawley magnetorotational instability. The main results of such calculations are highlighted with particular emphasis on the generation of large-scale magnetic fields. Comparison with mean-field dynamo theory is made. This theory is then used to address the question of the launching and collimation of winds emanating from the disc surfaces. Title: Dynamo mechanisms Authors: Brandenburg, A.; Saar, S. H. Bibcode: 2000ASPC..198..381B Altcode: 2000scac.conf..381B No abstract at ADS Title: The dynamo effect in stars Authors: Brandenburg, Axel Bibcode: 2000ASSL..254....1B Altcode: 2000stas.conf....1B No abstract at ADS Title: Large scale dynamos: direct simulations Authors: Brandenburg, A. Bibcode: 2000IAUJD..14E..14B Altcode: Simulations of driven helical turbulence and of naturally driven turbulence are presented. Signs of the inverse cascade are presented and discussed in the framework of the alpha-effect. The large scale fields represent the outermost scale of the turbulent spectrum into which energy can be pumped gradually via the inverse cascade. Under somewhat idealised conditions (fully helical turbulence, no shear), these fields tend to be close to force-free and hence are not drastically felt by the turbulence, yielding fields that can saturate in superequipartition. Althought this is not realistic in real galaxies, strong field amplification by differential rotation produces toroidal flux tubes in which the field can still exceed equipartition locally. Title: Pressure-Driven Outflow and Magneto-Centrifugal Wind from a Dynamo Active Disc Authors: Dobler, Wolfgang; Brandenburg, Axel; Shukurov, Anvar Bibcode: 1999ptep.proc..347D Altcode: We present a numerical model of an accretion disc with mean-field dynamo action that develops pressure-driven collimated outflow near the rotation axis and a centrifugally driven uncollimated wind in the outer parts. The jet is collimated and confined by the azimuthal magnetic field that is produced by the dynamo in the disc and advected to the disc corona. The jet is hot and dense, but has low angular momentum. We also briefly discuss the possible generation of magnetic fields in a jet by the screw dynamo. Title: Evolution of a superbubble in a turbulent, multi-phased and magnetized ISM Authors: Korpi, M. J.; Brandenburg, A.; Shukurov, A.; Tuominen, I. Bibcode: 1999A&A...350..230K Altcode: The evolution of a superbubble is simulated using a local three-dimensional, non-ideal MHD model, which includes galactic differential rotation, an external gravitational potential, heating via supernova explosions and radiative cooling of the interstellar medium (ISM). In our model a superbubble is formed due to the clustering of supernova activity, mimicking an OB association. Supernovae are modelled as instantaneous explosions that release 10(51) erg of thermal energy and 3M_sun of gas in a small volume. We implement a superbubble with the luminosity 3 x 10(37) erg {s(-1) into an initial ISM, which is taken from our earlier calculations modelling the warm and hot phases of the ISM. The simulated ISM has a multi-phase structure with hot, dilute and warm, denser gas coexisting in pressure equilibrium; there is also some cold, dense gas in the form of clouds and filaments arising from supernova compression. The multicomponent gas is in a state of developed turbulence, with r.m.s. velocity 10 and 40{km s(-1) for the warm and hot gas, respectively. At the developed state of the simulation there is a magnetic field of 1.3muG strength having both uniform and random components. The evolution of a superbubble is rather different from that indicated by models with quasi-uniform ambient medium. The superbubble loses its spherical symmetry at very early stages of expansion. Its break-through from the disc is strongly facilitated by the nonuniformity of its environment. A superbubble which would be confined in the disc according to criteria obtained for a quasi-uniform ISM can break out to the halo. Title: Time Evolution of the Magnetic Activity Cycle Period. II. Results for an Expanded Stellar Sample Authors: Saar, Steven H.; Brandenburg, Axel Bibcode: 1999ApJ...524..295S Altcode: We further explore nondimensional relationships between the magnetic dynamo cycle period Pcyc, the rotational period Prot, the activity level (as observed in Ca II HK), and other stellar properties by expanding the stellar sample studied in the first paper in this series. We do this by adding photometric and other cycles seen in active stars and the secondaries of CV systems and by selectively adding less certain cycles from the Mount Wilson HK survey; evolved stars, long-term HK trends and secondary Pcyc are also considered. We confirm that most stars with age t>~0.1 Gyr occupy two roughly parallel branches, separated by a factor of ~6 in Pcyc, with the ratio of cycle and rotational frequencies ωcyc/Ω~Ro-0.5, where Ro is the Rossby number. Using the model of the first paper in this series, this result implies that the α effect increases with mean magnetic field (contrary to the traditional α-quenching concept) and that α and ωcyc decrease with t. Stars are not strictly segregated onto one or the other branch by activity level, though the high-ωcyc/Ω branch is primarily composed of inactive stars. The expanded data set suggests that for t>~1 Gyr, stars can have cycles on one or both branches, though among older stars, those with higher (lower) mass tend to have their primary Pcyc on the lower (upper) ωcyc/Ω branch. The Sun's ~80 yr Gleissberg cycle agrees with this scenario, suggesting that long-term activity ``trends'' in many stars may be segments of long (Pcyc~50-100 yr) cycles not yet resolved by the data. Most very active stars (Prot<3 days) appear to occupy a new, third branch with ωcyc/Ω~Ro0.4. Many RS CVn variables lie in a transition region between the two most active branches. We compare our results with various models, discuss their implications for dynamo theory and evolution, and use them to predict Pcyc for three groups: stars with long-term HK trends, stars in young open clusters, and stars that may be in Maunder-like magnetic minima. Title: Deceleration by Dynamical Friction in a Gaseous Medium Authors: Sánchez-Salcedo, F. J.; Brandenburg, A. Bibcode: 1999ApJ...522L..35S Altcode: The drag force experienced by a gravitational body moving in a straight-line trajectory through a homogeneous isothermal gaseous medium of given sound speed is investigated numerically. For perturbers with constant velocity, linear theory describes successfully the temporal evolution and magnitude of the force. The result obtained recently by E. Ostriker--that for Mach numbers \Mscr=1-2 the force is stronger in a gaseous medium than in a collisionless medium, as described by the standard Chandrasekhar formula--is confirmed. The corresponding minimum impact radius rmin for a body described with a Plummer model with core radius Rsoft is rmin/Rsoft~2.25. When \Mscr<1, the drag force is strongly suppressed, which is consistent with Ostriker's results but in disagreement with the Chandrasekhar formula. However, when the perturber is decelerated by its own wake to \Mscr<1, the effective drag force remains initially somewhat larger than the value in the case of constant velocity because it takes some time to get rid of the wake that was generated during its supersonic history. Title: Evidence for a Singularity in Ideal Magnetohydrodynamics: Implications for Fast Reconnection Authors: Kerr, Robert M.; Brandenburg, Axel Bibcode: 1999PhRvL..83.1155K Altcode: 1998physics..12017K Numerical evidence for a finite-time singularity in ideal 3D magnetohydrodynamics is presented. The simulations start from two interlocking magnetic flux rings with no initial velocity. Curvature shrinks the rings until they touch and current sheets form between them. The evidence for a singularity in a finite time tc is that the peak current density behaves like ||J||~1/\(tc-t\) for a range of sound speeds and initial conditions. For the incompressible calculations ||ω||/||J||-->const. In resistive reconnection the magnetic helicity is nearly conserved while energy is dissipated. Title: Comment on ``The sunspot as a self-excited dynamo'' Authors: Moss, David; Brandenburg, Axel Bibcode: 1999A&A...346.1009M Altcode: A recent paper claims that the well known Cowling `anti-dynamo' theorem is a ``misconception'', and that a simple axisymmetric sunspot model constitutes a counter example. We do not believe these claims to have been substantiated. Title: The influence of geometry and topology on axisymmetric mean-field dynamos Authors: Covas, Eurico; Tavakol, Reza; Tworkowski, Andrew; Brandenburg, Axel; Brooke, John; Moss, David Bibcode: 1999A&A...345..669C Altcode: 1998astro.ph.11079C We study the changes in the dynamical behaviour of axisymmetric spherical mean-field dynamo models produced by changes in their geometry and topology, by considering a two parameter family of models, ranging from a full sphere to spherical shell, torus and disc-like configurations, within a unified framework. We find that the two parameter space of the family of models considered here separates into at least three different regions with distinct characteristics for the onset of dynamo action. In two of these regions, the most easily excited fields are oscillatory, in one case with dipolar symmetry, and in the other with quadrupolar, whereas in the third region the most easily excited field is steady and quadrupolar. In the nonlinear regime, we find that topological changes can alter significantly the dynamical behaviour, whilst modest changes in geometry can produce qualitative changes, particularly for thin disc-like configurations. This is of potential importance, since the exact shapes of astrophysical bodies, especially accretion discs and galaxies, are usually not precisely known. Title: Magnetic drift processes in differentially rotating turbulence Authors: Urpin, V.; Brandenburg, A. Bibcode: 1999A&A...345.1054U Altcode: The mean electromotive force is considered in a differentially rotating fluid taking into account stretching of the turbulent magnetic field. Calculations are performed by making use of the second order correlation approximation. Non-uniformity of the angular velocity leads to specific drift processes in the azimuthal direction. Due to this drift the magnetic field can rotate with a somewhat different angular velocity than the fluid. Differential rotation can also lead in a new instability of a non-axisymmetric mean field. Regardless of the law of the differential rotation this instability can result in an exponential amplification of the field. Title: A Supernova-regulated Interstellar Medium: Simulations of the Turbulent Multiphase Medium Authors: Korpi, M. J.; Brandenburg, A.; Shukurov, A.; Tuominen, I.; Nordlund, Å. Bibcode: 1999ApJ...514L..99K Altcode: The dynamic state of the interstellar medium, heated and stirred by supernovae (SNe), is simulated using a three-dimensional, nonideal MHD model in a domain extended 0.5×0.5 kpc horizontally and 2 kpc vertically, with the gravitational field symmetric about the midplane of the domain, z=0. We include both Type I and Type II SNe, allowing the latter to cluster in regions with enhanced gas density. The system segregates into two main phases: a warm, denser phase and a hot, dilute gas in global pressure equilibrium; there is also dense, cool gas compressed into filaments, shells, and clumps by expanding SN remnants. The filling factor of the hot phase grows with height, so it dominates at z>~0.5 kpc. The multicomponent structure persists throughout the simulation, and its statistical parameters show little time variation. The warm gas is in hydrostatic equilibrium, which is supported by thermal and turbulent pressures. The multiphase gas is in a state of developed turbulence. The rms random velocity is different in the warm and hot phases, 10 and 40 km s-1, respectively, at z<~1 kpc; the turbulent cell size (twice the velocity correlation scale) is about 60 pc in the warm phase. Title: Simulations and Observations of Stellar Dynamos: Evidence for a Magnetic Alpha-Effect Authors: Brandenburg, A. Bibcode: 1999ASPC..178...13B Altcode: 1999sdnc.conf...13B No abstract at ADS Title: Magneto-Convection Authors: Stein, R. F.; Georgobiani, D.; Bercik, D. J.; Brandenburg, A.; Nordlund, Å. Bibcode: 1999ASPC..173..193S Altcode: 1999sstt.conf..193S No abstract at ADS Title: Vortex tube models for turbulent dynamo action Authors: Bigazzi, Alberto; Brandenburg, Axel; Moss, David Bibcode: 1999PhPl....6...72B Altcode: The possibility of dynamo action resulting from a pair of elongated vortex structures immersed in an electrically conducting fluid is investigated. For elongated vortex structures, the critical magnetic Reynolds number for dynamo action is about half that for the spherical rotors that have been studied previously. When applied to Kolmogorov turbulence with vortex structures of scale comparable to the dissipation length, this model can explain dynamo action only when the magnetic Prandtl number (=kinematic viscosity/magnetic diffusivity) exceeds a critical value that is larger than unity. It is argued that in astrophysical bodies where this condition is not satisfied (in stellar convection zones, for example), dynamo action must instead result from motions on all scales up to the size of the region. Title: Vortical Motions Driven by Supernova Explosions Authors: Korpi, Maarit; Brandenburg, Axel; Shukurov, Anvar; Tuominen, Ilkka Bibcode: 1999intu.conf..127K Altcode: We investigate supernova driven interstellar turbulence using local three-dimensional MHD simulations and adopting conditions corresponding to the Galaxy. Our model includes the effects of large-scale shear due to galactic differential rotation, density stratification, compressibility, magnetic fields, heating via supernova explosions and parameterized radiative cooling of the interstellar medium. We allow for multiple supernova explosions distributed randomly in the galactic disc and exponentially in the vertical direction. We found that there are two major stages governing the evolution of a supernova remnant that is isolated, i.e. does not interact with other remnants. During the first 2 Myr the explosion drives a strong shock. After the shock stage there is a cool, dense shell with a hot interior left from the remnant. During this dense shell stage large-scale shear and Coriolis force act on the remnant, but the effect of these processes was found to be rather weak. The result of an ensemble of isolated supernova explosions was a relatively wide shock spectrum in the kinetic energy. When supernova interactions, i.e. shock-shock and shock-dense shell collisions, become abundant the situation changes. In these collisions vorticity is effectively generated by the baroclinic effect. After some vorticity has been generated, the vortex stretching term can have an important role as redistributing the vorticity. Title: A Local Three-dimensional Model of the Supernova-regulated ISM Authors: Korpi, M. J.; Tuominen, I.; Brandenburg, A.; Shukurov, A. Bibcode: 1999ASPC..168..445K Altcode: 1999npim.conf..445K No abstract at ADS Title: The Dynamics of Turbulent Viscosity Authors: Torkelsson, U.; Ogilvie, G. I.; Pringle, J. E.; Brandenburg, A.; Nordlund, Å.; Stein, R. F. Bibcode: 1999ASPC..161..422T Altcode: 1999hepa.conf..422T No abstract at ADS Title: A helicity proxy from horizontal solar flow patterns Authors: Rüdiger, G.; Brandenburg, A.; Pipin, V. V. Bibcode: 1999AN....320..135R Altcode: Motivated by new observations of solar surface flow patterns of mesogranulation, theoretical computations of the horizontal diver\-gence-vorticity correlation are presented. Because of its close relation to the helicity in rotating turbulence such observations and discussions are of particular importance for the conventional dynamo theory. For the northern hemisphere we find a small, but always negative, divergence-vorticity correlation. Both an analytical Second Order Correlation Approximation for slow rotation as well as a numerical simulation (originally done for accretion disks) for fast rotation yield very similar results. Title: Time Evolution of the Magnetic Activity Cycle Period: Results for an Expanded Stellar Sample Authors: Saar, S. H.; Brandenburg, A. Bibcode: 1998AAS...193.4404S Altcode: 1998BAAS...30S1315S We explore non-dimensional relationships between the magnetic dynamo cycle period P_cyc, the rotational period P_rot, the activity level (as observed in Ca ii HK), and other stellar properties using a large stellar sample including Ca ii, photometric and other cycles in dwarfs, evolved stars, active binaries, and the secondaries of CV systems. We confirm that most stars with age t ga 0.3 Gyr occupy two roughly parallel branches, separated by a factor of ~ 6 in P_cyc, with P_rot/P_cyc ~ Ro(-0.5) , where Ro is the Rossby number. Using the simple model of Brandenburg, Saar, & Turpin (1998 ApJ 498, L51), this result implies that the alpha effect increases with mean magnetic field B, and that alpha and omega_cyc decrease with age along these branches. Stars are not strictly segregated onto one or the other branch by activity level, though the high P_rot/P_cyc branch is primarily composed of inactive stars. The expanded dataset suggests that for t ga 1 Gyr, stars can have P_cyc on one or both branches (double P_cyc stars), though among older stars, those with higher mass (F) tend to have their primary P_cyc on the low P_rot/P_cyc branch, while lower mass (K) stars occupy the high P_rot/P_cyc branch. The sun's ~ 80 year Gleissberg cycle agrees with this scenario, suggesting that long-term ``trends" in many stars may be segments of long (P_cyc ~ 50-100 yr) cycles not yet resolved by the data. Most extremely active stars (P_rot < 3 days) appear to occupy a third branch with P_rot/P_cyc ~ Ro(0.4) , where some kind of alpha -quenching may be operating. Many RS CVn variables lie in a transition region between the two most active branches. We discuss implications for dynamo theory and evolution, and compare our results with various other models. The results are also used to predict P_cyc for stars with long-term HK trends, a sample of young open cluster members, and a group which may be in the stellar analog of the Maunder minimum. Title: Simulations of an alpha-effect due to magnetic buoyancy Authors: Brandenburg, Axel; Schmitt, Dieter Bibcode: 1998A&A...338L..55B Altcode: Three-dimensional simulations of a thermally stably stratified gas with a localized layer of toroidal magnetic field are carried out. The magnetic field gives rise to a magnetic buoyancy instability. Due to the presence of rotation the resulting fluid motions are helical and lead to an alpha -effect, i.e. to a component of the electromotive force in the direction of the mean magnetic field. The value of alpha is estimated during the exponential growth phase of the instability. The mean vertical transport velocity of the magnetic field is also calculated. It is found that alpha varies with latitude and its value is positive in the northern hemisphere. Title: Mean Field Dynamos with Algebraic and Dynamic alpha-Quenchings Authors: Tworkowski, A.; Covas, E.; Tavakol, R.; Brandenburg, A. Bibcode: 1998astro.ph..8214T Altcode: Calculations for mean field dynamo models (in both full spheres and spherical shells), with both algebraic and dynamic $\alpha$--quenchings, show qualitative as well as quantitative differences and similarities in the dynamical behaviour of these models. We summarise and enhance recent results with extra examples. Overall, the effect of using a dynamic $\alpha$ appears to be complicated and is affected by the region of parameter space examined. Title: The radial disc structure around a magnetic neutron star: analytic and semi-analytic solutions Authors: Brandenburg, Axel; Campbell, Chris G. Bibcode: 1998MNRAS.298..223B Altcode: The radial structure of a thin accretion disc is calculated in the presence of a central dipole magnetic field aligned with the rotation axis. The problem is treated using a modified expression for the turbulent magnetic diffusion, which allows the angular momentum equation to be integrated analytically. The governing algebraic equations are solved iteratively between 1 and 10^4 stellar radii. An analytic approximation is provided that is valid near the disruption radius at about 100 stellar radii. At that point, which is approximately 60 per cent of the Alfven radius and typically about 30 per cent of the corotation radius, the disc becomes viscously unstable. This instability results from the fact that both radiation pressure and opacity caused by electron scattering become important. This in turn is a consequence of the magnetic field which leads to an enhanced temperature in the inner parts. This is because the magnetic field gives rise to a strongly enhanced vertically integrated viscosity, so that the viscous torque can balance the magnetic torque. Title: Turbulence and Magnetic Fields in Clusters of Galaxies Authors: Sánchez-Salcedo, F. J.; Brandenburg, A.; Shukurov, A. Bibcode: 1998Ap&SS.263...87S Altcode: 1999Ap&SS.263...87S We consider turbulence generated by galaxies moving transonically through the intracluster gas. We show that neither the gravitational drag nor the gas stripping from the galaxies are able, by themselves, to generate turbulence at a level required to feed the dynamo in the intracluster gas. Some implications for cluster radio halos are discussed. Title: New results for the Herzenberg dynamo: steady and oscillatory solutions Authors: Brandenburg, A.; Moss, D.; Soward, A. M. Bibcode: 1998RSPSA.454.1283B Altcode: No abstract at ADS Title: Time Evolution of the Magnetic Activity Cycle Period Authors: Brandenburg, Axel; Saar, Steven H.; Turpin, Christen R. Bibcode: 1998ApJ...498L..51B Altcode: We propose a new interpretation of the relationships between the dynamo cycle period (Pcyc) as observed in Ca II H and K, the rotational period (Prot), the activity level, and other stellar properties. Viewed within this framework, the data suggest that the dynamo α-parameter increases with magnetic field strength, contrary to the conventional idea of α-quenching. The data also suggest a possibly discontinuous dependence of the ratio of cycle to rotation frequency, ωcyc/Ω, as a function of Rossby number, Ro (or equivalently, activity or age). Stars evolve with ωcyc/Ω~t-0.35 (or Ro-0.7), until age t~2-3 Gyr (roughly at the Vaughan-Preston gap), where a sharp transition occurs, in which ωcyc/Ω increases by a factor of ~6. Thereafter, evolution with ωcyc/Ω~t-0.35 continues. The age at which transition occurs may be mass dependent, with K stars making the transition first. Title: Intermittent Behaviour in Axisymmetric Mean-Field Dynamo Models in Spherical Shells Authors: Tworkowski, Andrew; Tavakol, Reza; Brandenburg, Axel; Brooke, John M.; Moss, David; Tuominen, Ilkka Bibcode: 1998MNRAS.296..287T Altcode: Axisymmetric mean-field dynamo models in spherical shells are shown to be capable of producing temporally intermittent behaviour. This is of potential importance since (i) it is, as far as we are aware, the first time such behaviour has been produced internally by a mean-field dynamo model in a spherical shell, without requiring any additional assumptions or truncations, and (ii) it may be characteristic of the type of behaviour observed in the long-term record of solar activity, such as Maunder minima. We also show that these types of behaviour persist when the functional form of the alpha quenching is altered and also occur over intervals of the shell thickness and the dynamo number. Title: Magnetic fields in young galaxies due to the cross-helicity effect Authors: Brandenburg, Axel; Urpin, Vadim Bibcode: 1998A&A...332L..41B Altcode: It is shown that the cross-helicity effect facilitates rapid growth of the large scale magnetic field in young galaxies. This field then acts as a seed for the standard alpha Omega -type dynamo at later stages. This mechanism may be responsible for the relatively strong magnetic fields observed in young high redshift galaxies. Title: Exploring magnetohydrodynamic turbulence on the computer Authors: Torkelsson, Ulf; Ogilvie, Gordon I.; Brandenburg, Axel; Nordlund, A. ˚Ke; Stein, Robert F. Bibcode: 1998AIPC..431...69T Altcode: 1998apas.conf...69T Although numerical simulations have established magnetohydrodynamic turbulence as a possible candidate for the angular momentum transport mechanism in accretion discs there is still a need for a deeper understanding of the physics of the shear-induced turbulence. There are two complementary pathways to this goal, to analyze the results of a simulation at depth or to start from a simple state, whose evolution can be understood by semi-analytical methods and `extrapolate' to the turbulent state that we want to understand. We will show examples of these two approaches. Title: Magnetic and vertical shear instabilities in accretion discs Authors: Urpin, V.; Brandenburg, A. Bibcode: 1998MNRAS.294..399U Altcode: The stability properties of magnetized discs rotating with angular velocity Omega=Omega(s,z), dependent on both the radial and the vertical coordinates s and z, are considered. Such a rotation law is adequate for many astrophysical discs (e.g., galactic and protoplanetary discs, as well as accretion discs in binaries). In general, the angular velocity depends on height, even in thin accretion discs. A linear stability analysis is performed in the Boussinesq approximation, and the dispersion relation is obtained for short-wavelength perturbations. Any dependence of Omega on z can destabilize the flow. This concerns primarily small-scale perturbations for which the stabilizing effect of buoyancy is strongly suppressed due to the energy exchange with the surrounding plasma. For a weak magnetic field, instability of discs is mainly associated with vertical shear, whilst for an intermediate magnetic field the magnetic shear instability, first considered by Chandrasekhar and Velikhov, is more efficient. This instability is caused by the radial shear which is typically much stronger than the vertical shear. Therefore the growth time for the magnetic shear instability is much shorter than for the vertical shear instability. A relatively strong magnetic field can suppress both these instabilities. The vertical shear instability could be the source of turbulence in protoplanetary discs, where the conductivity is low. Title: Turbulence effects in planetesimal formation Authors: Hodgson, Lindsay S.; Brandenburg, Axel Bibcode: 1998A&A...330.1169H Altcode: The formation of planetesimals is investigated by studying the transport of dust particles in a local three-dimensional simulation of accretion disc turbulence. Heavy particles fall rapidly towards the midplane, whereas lighter particles are strongly advected by the flow. For light particles the turbulence leads to a rapid redistribution of particles such that their density per unit mass is approximately constant with height. There is no pronounced concentration of particles in vortices or anticyclones, as was suggested previously. This is partly because of the adverse effect of keplerian shear and also because in our simulation vortices are only short lived. However, if we assume the gas velocity to be frozen in time, there is a concentration of dust in ring-like structures after a few orbits. This is caused mainly by a convergence of the gas flow in those locations, rather than the presence of vortices or anticyclones. Title: Theoretical Basis of Stellar Activity Cycles Authors: Brandenburg, Axel Bibcode: 1998ASPC..154..173B Altcode: 1998csss...10..173B Numerical simulations of hydromagnetic turbulence in the presence of shear and/or convection have given us new clues as to how the solar dynamo might work. Simulations suggest that there is significant large-scale magnetic field generation at the bottom of the convection zone, where the radial shear is largest. The nature of the dynamo in the simulations seems to be qualitatively similar to an alpha Omega-dynamo. However, the origin of the effective alpha in the simulations is not thermal convection, but magnetobuoyancy and magnetic shear instabilities. This results in a negative alpha-effect. The efficiency of the alpha-effect on the one hand, and losses on the other, should increase as the field strength increases. It is argued that this could lead to an increasing ratio between cycle and rotation frequency with increasing field strength, as is indicated by the stellar cycle data of Baliunas and collaborators. Furthermore, to explain the cycle data for active stars one has to invoke another, as yet unknown, type of magnetic instability for which both alpha and the flux loss are abruptly reduced above a certain field strength. However, details of this speculation are still unclear. Title: Solar Magneto-Convection Authors: Stein, R. F.; Bercik, D. J.; Brandenburg, A.; Georgobiani, D.; Nordlund, A. Bibcode: 1998AAS...191.7417S Altcode: 1998BAAS...30..758S We present results of realistic simulations of magneto-convection near the solar surface. The simulations were performed with two magnetic field topologies - (1) a unipolar, initially vertical field, and (2) a bipolar field, where fluid entering at the base of the computational domain advects in horizontal field. As the unipolar flux is increased, the magnetic field concentrates in the intergranule lanes and develops large, dark, cool regions. These regions surround smaller areas where convection has not been suppressed. In contrast, for the bipolar case, the strongest fields appear as bright points in the intergranule lanes. Title: Axisymmetric mean field dynamos with dynamic and algebraic alpha -quenchings Authors: Covas, Eurico; Tavakol, Reza; Tworkowski, Andrew; Brandenburg, Axel Bibcode: 1998A&A...329..350C Altcode: 1997astro.ph..9062C We study axisymmetric mean field spherical and spherical shell dynamo models, with both dynamic and algebraic alpha -quenchings. Our results show that there are qualitative as well as quantitative differences and similarities between these models. Regarding similarities, both groups of models exhibit symmetric, antisymmetric and mixed modes of behaviour. As regards differences, the important feature in the full sphere models is the occurrence of chaotic behaviour in the algebraic alpha -quenching models. For the spherical shell models with dynamic alpha the main features include the possibility of multi-attractor regimes with final state sensitivity with respect to small changes in the magnitude of alpha and the initial parity. We find the effect of introducing a dynamic alpha is likely to be complicated and depend on the region of the parameter space considered, rather than a uniform change towards simplicity or complexity. Title: Disc turbulence and viscosity. Authors: Brandenburg, A. Bibcode: 1998tbha.conf...61B Altcode: 1998npad.conf...61B Three-dimensionsional simulations of hydromagnetic flows in accretion disc provide strong evidence that the turbulence in discs is driven by a magnetic instability. Some basic results of those simulations are reviewed, current shortcomings discussed, and open questions and important issues are highlighted. The main motivation behind thise simulations was imply to show tht turbulence is self-sustained. However, an important quantitative outcome has been the determination of the magnitude of the Shakura-Sunyaev viscosity parameter αSS. It is emphasized that αSS cannot be considered a constant, as it does in fact depend on a number of factors: the magnetic field strength, the height above the midplane, and the magnitude of the velocity shear - to mention just a few. Given the availability of detailed simulations, it is now possible to address specific questions, for example what are the rates of Joule and viscous heating, where is the energy deposited, what are the values of turbulent Prandtl numbers, and how efficiently does the flow disperse and mix particles? Finally, the disc simulations have significantly affected and enhanced research in dynamo theory in different fields of astrophysics, because some of the ideas (dynamo-generated turbulence) may also apply to stars and galaxies. Title: Current Sheet Formation in the Interstellar Medium: Erratum Authors: Zweibel, Ellen G.; Brandenburg, Axel Bibcode: 1997ApJ...485..920Z Altcode: In the paper "Current Sheet Formation in the Interstellar Medium" by Ellen G. Zweibel and Axel Brandenburg (ApJ, 478, 563 [1997]), the address given for Dr. Brandenburg is incorrect. It should be Department of Mathematics, University of Newcastle, Newcastle upon Tyne, NE1 7RU, England, UK. His e-mail address is Axel.Brandenburg@newcastle.ac.uk. Title: The dependence of the dynamo alpha on vorticity Authors: Brandenburg, Axel; Donner, Karl Johan Bibcode: 1997MNRAS.288L..29B Altcode: We use data from numerical simulations of dynamo-generated turbulence in the shearing box approximation to determine the dynamo alpha-effect and its dependence on the rotation law Omega(r). The data suggest that the dynamo alpha is not simply proportional to the local angular velocity Omega(r), as is usually assumed, but rather is proportional to the local vorticity omega(r)=r^-1d/dr(Omegar^2). We also find tentative evidence to support the proposition that the backreaction of the magnetic field on alpha sets in when the field reaches equipartition with the energy in the turbulent motions. Furthermore, we propose an explanation as to why the sign of alpha is found to be opposite to that in the standard picture. Title: Robustness of truncated α Ω dynamos with a dynamic α Authors: Covas, Eurico; Tworkowski, Andrew; Tavakol, Reza; Brandenburg, Axel Bibcode: 1997SoPh..172....3C Altcode: 1997astro.ph..8094C; 1997ESPM....8....3C In a recent work (Covas et al., 1996), the behaviour and the robustness of truncated α Ω dynamos with a dynamic α were studied with respect to a number of changes in the driving term of the dynamic α equation, which was considered previously by Schmalz and Stix (1991) to be of the form ∼ AΦBΦ. Here we review and extend our previous work and consider the effect of adding a quadratic quenching term of the form α|B|2. We find that, as before, such a change can have significant effects on the dynamics of the related truncated systems. We also find intervals of (negative) dynamo numbers, in the system considered by Schmalz and Stix (1991), for which there is sensitivity with respect to small changes in the dynamo number and the initial conditions, similar to what was found in our previous work. This latter behaviour may be of importance in producing the intermittent type of behaviour observed in the Sun. Title: Current Sheet Formation in the Interstellar Medium Authors: Zweibel, Ellen G.; Brandenburg, Axel Bibcode: 1997ApJ...478..563Z Altcode: There is phenomenological evidence that magnetic reconnection operates in the interstellar medium, and magnetic reconnection is also necessary for the operation of a galactic dynamo. The extremely long ohmic diffusion times of magnetic fields in typical interstellar structures suggest that reconnection occurs in two stages, with thin current layers that have relatively short resistive decay times forming by magnetohydrodynamical processes first, followed by reconnection of the fields in the layers. We propose that ambipolar drift can lead to the formation of these thin sheets in weakly ionized interstellar gas and can delineate the parameter regime in which this occurs by means of a numerical model: we find that the magnetic field cannot be too large and the medium cannot be too diffusive. Both limits are imposed by the requirement that the field be wound up about 1 time by the eddy. Title: The effect of Silk damping on primordial magnetic fields Authors: Brandenburg, Axel; Enqvist, Kari; Olesen, Poul Bibcode: 1997PhLB..392..395B Altcode: 1996hep.ph....8422B We study the effects of plasma viscosity on the dynamics of primordial magnetic fields by simulating magnetohydrodynamics in the early universe by appropriate non-linear cascade models. We find numerically that even in the presence of large kinetic viscosity, magnetic energy is transferred to large length scales. There are indications, however, that the inverse cascade stops at a given time which depends on the magnitude of viscosity. For realistic viscosities we do not find equipartition between magnetic and kinetic energies. Title: Dynamos with different formulations of a dynamic α-effect. Authors: Covas, E.; Tworkowski, A.; Brandenburg, A.; Tavakol, R. Bibcode: 1997A&A...317..610C Altcode: 1997astro.ph..8093C We investigate the behaviour of α{OMEGA} dynamos with a dynamic α, whose evolution is governed by the imbalance between a driving and a damping term. We focus on truncated versions of such dynamo models which are often studied in connection with solar and stellar variability. Given the approximate nature of such models, it is important to study how robust they are with respect to reasonable changes in the formulation of the driving and damping terms. For each case, we also study the effects of changes of the dynamo number and its sign, the truncation order and initial conditions. Our results show that changes in the formulation of the driving term have important consequences for the dynamical behaviour of such systems, with the detailed nature of these effects depending crucially on the form of the driving term assumed, the value and the sign of the dynamo number and the initial conditions. On the other hand, the change in the damping term considered here seems to produce little qualitative effect. Title: An Incoherent α-Ω Dynamo in Accretion Disks Authors: Vishniac, Ethan T.; Brandenburg, Axel Bibcode: 1997ApJ...475..263V Altcode: 1995astro.ph.10038V We use the mean-field dynamo equations to show that spatially and temporally incoherent fluctuations in the helicity in mirror-symmetric turbulence in a shearing flow can generate a large-scale, coherent magnetic field. We illustrate this effect with simulations of a few simple systems. For statistically homogeneous turbulence, we find that the dynamo growth rate is roughly τ-1/3eddyτ-2/3shearN-1/3eddyeddy/LB)2/3, where τeddy is the eddy turnover time, τ-1shear is the local shearing rate, Neddy is the number of eddies per magnetic domain, λeddy is the size of an eddy, and LB is the extent of a magnetic domain perpendicular to the mean flow direction. Even in the presence of turbulence and shear the dynamo can be stopped by turbulent dissipation if (for example) the eddy scale is close to the magnetic domain scale and τshear > τeddy. We also identify a related incoherent dynamo in a system with a stationary distribution of helicity with a high-spatial frequency and an average value of zero. In accretion disks, the incoherent dynamo can lead to axisymmetric magnetic domains the radial and vertical dimensions of which will be comparable to the disk height. This process may be responsible for dynamo activity seen in simulations of dynamo-generated turbulence involving, for example, the Balbus-Hawley instability. However, although it explains the generation of a magnetic field in numerical simulations without significant large-scale average helicity and the occasional field reversals, it also predicts that the dimensionless viscosity will scale as ~(h/r)2, which is not seen in the simulations. On the other hand, this result is consistent with phenomenological models of accretion disks, although these suggest a slightly shallower dependence on h/r. We discuss some possible resolutions to these contradictions. Title: Modelling magnetised accretion discs Authors: Brandenburg, A.; Campbell, C. Bibcode: 1997LNP...487..109B Altcode: 1997adna.conf..109B Some recent results are reviewed that lead us now to believe that accretion discs are basically always magnetised. The main components are Balbus-Hawley and Parker instabilities on the one hand and a dynamo process on the other. A mechanical model for the Balbus-Hawley instability is presented and analysed quantitatively. Three-dimensional simulations are discussed, especially the resulting magnetic field structure. Possibilities of reproducing the field by an αΩ dynamo are investigated, especially its symmetry with respect to the midplane. Title: Magnetohydrodynamic Turbulence in Accretion Discs: Towards More Realistic Models Authors: Torkelsson, U.; Brandenburg, A.; Nordlund, A.; Stein, R. F. Bibcode: 1997ASPC..121..210T Altcode: 1997apro.conf..210T; 1997IAUCo.163..210T No abstract at ADS Title: Recent developments in the theory of large-scale dynamos Authors: Brandenburg, A. Bibcode: 1997ppvs.conf..359B Altcode: Large-scale magnetic fields in the Sun Traditional αΩ dynamos The effective α in accretion disc simulations Strengths of fluctuations Quenching of α and ηt Convection with shear Forced turbulence with shear Variety of solar dynamo models Title: The dependence of the viscosity in accretion discs on the shear/vorticity ratio Authors: Abramowicz, Marek; Brandenburg, Axel; Lasota, Jean-Pierre Bibcode: 1996MNRAS.281L..21A Altcode: We estimate the Shakura-Sunyaev viscosity parameter cc for different values of the shear/vorticity ratio, w, using local simulations of dynamo-generated turbulence. We find that the time average of cc is approximately proportional to co (at least for <10). We point out that this result may have important implications for the properties of thick accretion discs, because there w is small and cc would then tend to be large. Our result may also be important for accretion discs around black holes, because o becomes large in the inner 10 Schwarzschild radii as a result of relativistic effects. Title: Large-scale magnetic fields from hydromagnetic turbulence in the very early universe Authors: Brandenburg, Axel; Enqvist, Kari; Olesen, Poul Bibcode: 1996PhRvD..54.1291B Altcode: 1996astro.ph..2031B We investigate hydromagnetic turbulence of primordial magnetic fields using magnetohydrodynamics (MHD) in an expanding universe. We present the basic, covariant MHD equations, find solutions for MHD waves in the early universe, and investigate the equations numerically for random magnetic fields in two spatial dimensions. We find the formation of magnetic structures at larger and larger scales as time goes on. In three dimensions we use a cascade (shell) model that has been rather successful in the study of certain aspects of hydrodynamic turbulence. Using such a model we find that after ~109 times the initial time the scale of the magnetic field fluctuation (in the comoving frame) has increased by 4-5 orders of magnitude as a consequence of an inverse cascade effect (i.e., transfer of energy from smaller to larger scales). Thus at large scales primordial magnetic fields are considerably stronger than expected from considerations which do not take into account the effects of MHD turbulence. Title: Testing Cowling's Antidynamo Theorem near a Rotating Black Hole Authors: Brandenburg, Axel Bibcode: 1996ApJ...465L.115B Altcode: The kinematic evolution of axisymmetric magnetic and electric fields is investigated numerically in Kerr geometry for a simplified Keplerian disk near a rotating black hole. In the cases investigated it is found that a magnetic field cannot be sustained against ohmic diffusion. In flat space this result is known as Cowling's antidynamo theorem. No support is found for the possibility that the gravitomagnetic dynamo effect of Khanna & Camenzind could lead to self-excited axisymmetric solutions. In practice, therefore, Cowling's antidynamo theorem may still hold in Kerr geometry, although here the original proof can no longer be applied. Title: Supercomputer windows into the solar convection zone Authors: Nordlund, Å.; Stein, R. F.; Brandenburg, A. Bibcode: 1996BASI...24..261N Altcode: No abstract at ADS Title: The Disk Accretion Rate for Dynamo-generated Turbulence Authors: Brandenburg, Axel; Nordlund, Ake; Stein, Robert F.; Torkelsson, Ulf Bibcode: 1996ApJ...458L..45B Altcode: Dynamo-generated turbulence is simulated in a modified shearing box approximation that removes scale invariance and allows finite accretion rates for a given distance from the central object. The effective Shakura-Sunyaev viscosity parameter, alpha SS, is estimated in three different ways using the resulting mass accretion rate, the heating rate, and the horizontal components of the Maxwell and Reynolds stress tensors. The results are still resolution dependent: doubling the resolution leads to 1.4--1.6 times larger values for the viscosity parameter. For 63 x 127 x 64 meshpoints we find that alpha SS = 0.007. Title: Magnetic structures in a dynamo simulation Authors: Brandenburg, A.; Jennings, R. L.; Nordlund, Å.; Rieutord, M.; Stein, R. F.; Tuominen, I. Bibcode: 1996JFM...306..325B Altcode: We use three-dimensional simulations to study compressible convection in a rotating frame with magnetic fields and overshoot into surrounding stable layers. The, initially weak, magnetic field is amplified and maintained by dynamo action and becomes organized into flux tubes that are wrapped around vortex tubes. We also observe vortex buoyancy which causes upward flows in the cores of extended downdraughts. An analysis of the angles between various vector fields shows that there is a tendency for the magnetic field to be parallel or antiparallel to the vorticity vector, especially when the magnetic field is strong. The magnetic energy spectrum has a short inertial range with a slope compatible with k(+1/3) during the early growth phase of the dynamo. During the saturated state the slope is compatible with k(-1). A simple analysis based on various characteristic timescales and energy transfer rates highlights important qualitative ideas regarding the energy budget of hydromagnetic dynamos. Title: The Turbulent Viscosity in Accretion Discs Authors: Torkelsson, U.; Brandenburg, A.; Nordlund, Å.; Stein, R. F. Bibcode: 1996ApL&C..34..383T Altcode: No abstract at ADS Title: Dynamo-generated turbulence in disks: value and variability of alpha. Authors: Brandenburg, A.; Nordlund, Å.; Stein, R. F.; Torkelsson, U. Bibcode: 1996bpad.conf..285B Altcode: 1996pada.conf..285B Dynamo-generated turbulence seems to be a universal mechanism for angular momentum transport in accretion disks. The authors discuss the resulting value of the viscosity parameter alpha and emphasize that this value is in general not constant. Alpha varies with the magnetic field strength which, in turn, can vary in an approximately cyclic manner. The authors also show that the stress does not vary significantly with depth, even though the density drops by a factor of about 30. Title: Galactic Magnetism: Recent Developments and Perspectives Authors: Beck, Rainer; Brandenburg, Axel; Moss, David; Shukurov, Anvar; Sokoloff, Dmitry Bibcode: 1996ARA&A..34..155B Altcode: We discuss current observational and theoretical knowledge of magnetic fields, especially the large-scale structure in the disks and halos of spiral galaxies. Among other topics, we consider the enhancement of global magnetic fields in the interarm regions, magnetic spiral arms, and representations as superpositions of azimuthal modes, emphasizing a number of unresolved questions. It is argued that a turbulent hydromagnetic dynamo of some kind and an inverse cascade of magnetic energy gives the most plausible explanation for the regular galactic magnetic fields. Primordial theory is found to be unsatisfactory, and fields of cosmological origin may not even be able to provide a seed field for a dynamo. Although dynamo theory has its own problems, the general form of the dynamo equations appears quite robust. Finally, detailed models of magnetic field generation in galaxies, allowing for factors such as spiral structure, starburts, galactic winds, and fountains, are discussed and confronted with observations. Title: An Incoherent alpha -Omega Dynamo Mechanism for Accretion Disks Authors: Vishniac, E. T.; Brandenburg, A. Bibcode: 1995AAS...18710409V Altcode: 1995BAAS...27.1435V We use the mean-field dynamo equations to show that an incoherent alpha effect in mirror-symmetric turbulence in a shearing flow can generate a large scale, coherent magnetic field. In other words, a shearing environment can create an organized magnetic field even if the time averaged helicity is zero. We illustrate this effect with simulations of a few simple systems. In accretion disks, this process can lead to axisymmetric magnetic domains whose radial and vertical dimensions will be comparable to the disk height. This process may be responsible for observations of dynamo activity seen in simulations of dynamo-generated turbulence involving, for example, the Balbus-Hawley instability. In this case the magnetic field strength will saturate at ~ (h/r)(2) times the ambient pressure in real accretion disks. The resultant dimensionless viscosity will be of the same order. In numerical simulations the azimuthal extent of the simulated annulus should be substituted for r. We compare the predictions of this model to numerical simulations previously reported by Brandenburg et al. (1995). In a radiation pressure dominated environment this estimate for viscosity should be reduced by a factor of (Pgas/Pradiation)(6) due to magnetic buoyancy. Title: Generalized entropies in a turbulent dynamo simulation Authors: Brandenburg, Axel; Klapper, Isaac; Kurths, Jürgen Bibcode: 1995PhRvE..52.4602B Altcode: A simulation of hydromagnetic turbulence exhibiting dynamo action is employed to estimate the generalized entropies, Hq, from the distribution of moments of local expansion factors of material line elements. These generalized entropies can be used to characterize the dynamics of turbulence and of nonlinear dynamo action. The value of the metric entropy, H1, is comparable to the largest Lyapunov exponent describing the divergence of trajectories in phase space, which in turn is somewhat larger than the growth rate of the magnetic energy. The value of the topological entropy, H0, is similar to the conversion rate of kinetic to magnetic energy, but larger than the growth rate of the dynamo. This is in agreement with results stating that the growth rate of the kinematic dynamo is limited by the topological entropy. The dependence of Hq on q leads to a criterion from which we infer that the degree of intermittency in our particular system is weak. Title: Chaos in accretion disk dynamos? Authors: Torkelsson, U.; Brandenburg, A. Bibcode: 1995CSF.....5.1975T Altcode: Accretion disks appear to be favourable places for dynamo action, because of their strong differential rotation. A simple estimate of the strength of an accretion disk dynamo indicates that it will be highly nonlinear. In spite of this, most studies hitherto have assumed a linear model for the dynamo. The authors investigate nonlinear, axisymmetric mean-field dynamos in accretion disks in order to study the route to chaotic solutions in certain parameter regimes. The authors find a sequence of bifurcations that lead eventually to chaos. Finally, the physical significance of these results is discussed. Title: Flux tubes and scaling in MHD dynamo simulations. Authors: Brandenburg, A. Bibcode: 1995CSF.....5.2023B Altcode: MHD simulations of compressible convection in a layer heated from below are discussed and the results analysed in various ways. The ultimate aim of these simulations is to understand the generation and evolution of the magnetic field in the Sun. The formation of flux tubes is addressed, and it is concluded that random field line stretching plays the dominant rôle, which is in contrast to vortex tubes where both shear instabilities and vortex stretching contribute almost equally to the generation of vorticity. Magnetic flux tubes occur preferentially near stagnation points, but there remains a significant flow component along the tube. Various scaling properties of the magnetic field generated in such simulations are investigated. Multifractal dimensions, cancellation exponents, and generalized power spectra are computed. While the spectra show a tendency for power law scaling, no such behavior is found for the cancellation exponent. Finally, implications for the generation of large-scale fields in the solar dynamo are discussed. Title: Galactic Fountains as Magnetic Pumps Authors: Brandenburg, A.; Moss, D.; Shukurov, A. Bibcode: 1995MNRAS.276..651B Altcode: We study a simple, kinematical model of a galactic fountain flow and show that a horizontal field in the galactic plane can be pumped into the halo to a height of several kiloparsecs. This pumping effect results from the topological structure of the flow in which the updraughts (represented by hot gas) form a connected network, whereas the downdraughts (associated with isolated cool clouds) are disconnected from each other. Such a flow traps the large-scale magnetic field in the disc and deposits it at the top of the fountain flow. Unlike previously studied models of topological pumping, in our case the flow is not constrained to a closed box and horizontal magnetic flux can leak out at the top. We find significant pumping of mean magnetic field into the halo, which can be parametrized by an advection velocity of order 1-10 km s^-1^. The resulting magnetic field strength at a height of several kiloparsecs above the galactic plane is comparable with that at the base of the flow. Title: Effects of Pressure and Resistivity on the Ambipolar Diffusion Singularity: Too Little, Too Late Authors: Brandenburg, Axel; Zweibel, Ellen G. Bibcode: 1995ApJ...448..734B Altcode: Ambipolar diffusion, or ion-neutral drift, can lead to steepening of the magnetic field profile and even to the formation of a singularity in the current density. These results are based on an approximate treatment of ambipolar drift in which the ion pressure is assumed vanishingly small and the frictional coupling is assumed to be very strong, so that the medium can be treated as a single fluid. This steepening, if it really occurs, must act to facilitate magnetic reconnection in the interstellar medium, and so could have important consequences for the structure and evolution of the galactic magnetic field on both global and local scales.

In actuality, the formation of a singularity must be prevented by physical effects omitted by the strong coupling approximation. In this paper we solve the coupled equations for charged and neutral fluids in a simple slab geometry, which was previously shown to evolve to a singularity in the strong coupling approximation. We show that both ion pressure and resistivity play a role in removing the singularity, but that, for parameters characteristic of the interstellar medium, the peak current density is nearly independent of ion pressure and scales inversely with resistivity. The current gradient length scale, however, does depend on ion pressure. In the end, effects outside the fluid approximation, such as the finite ion gyroradius, impose the strictest limit on the evolution of the magnetic profile. Title: Non-Local Transport in Turbulent MHD Convection Authors: Miesch, M.; Brandenburg, A.; Zweibel, E.; Toomre, J. Bibcode: 1995ESASP.376b.253M Altcode: 1995help.confP.253M; 1995soho....2..253M No abstract at ADS Title: Dynamo-generated Turbulence and Large-Scale Magnetic Fields in a Keplerian Shear Flow Authors: Brandenburg, Axel; Nordlund, Ake; Stein, Robert F.; Torkelsson, Ulf Bibcode: 1995ApJ...446..741B Altcode: The nonlinear evolution of magnetized Keplerian shear flows is simulated in a local, three-dimensional model, including the effects of compressibility and stratification. Supersonic flows are initially generated by the Balbus-Hawley magnetic shear instability. The resulting flows regenerate a turbulent magnetic field which, in turn, reinforces the turbulence. Thus, the system acts like a dynamo that generates its own turbulence. However, unlike usual dynamos, the magnetic energy exceeds the kinetic energy of the turbulence by a factor of 3-10. By assuming the field to be vertical on the outer (upper and lower) surfaces we do not constrain the horizontal magnetic flux. Indeed, a large-scale toroidal magnetic field is generated, mostly in the form of toroidal flux tubes with lengths comparable to the toroidal extent of the box. This large-scale field is mainly of even (i.e., quadrupolar) parity with respect to the midplane and changes direction on a timescale of ∼30 orbits, in a possibly cyclic manner. The effective Shakura-Sunyaev alpha viscosity parameter is between 0.001 and 0.005, and the contribution from the Maxwell stress is ∼3-7 times larger than the contribution from the Reynolds stress. Title: A solar dynamo in the overshoot layer: cycle period and butterfly diagram. Authors: Ruediger, G.; Brandenburg, A. Bibcode: 1995A&A...296..557R Altcode: We construct a solar dynamo model for the overshoot layer where a strong gradient in the turbulence velocity is assumed to produce the α-effect. A recent rotation law from helioseismology is adopted and meridional flows are ignored. Since in the overshoot layer the convective turnover time is long compared with the rotation period, the full structure of the alpha and turbulent diffusion tensors appearing in the expressions for the turbulent electromotive force (EMF) must be retained in the computations. The important toroidal component of α is negative in the overshoot layer. In this layer the turbulence is considered as rarefied with a "dilution factor" ɛ<1 to account for the reduced EMF due to the intermittent nature of the magnetism. The cycle period increases with decreasing ɛ, and for ɛ=~0.2-0.5 the 22yr solar cycle period is reproduced, depending on details of the model. The effect of magnetic buoyancy can increase the cycle period further. If this layer is thinner than =~30Mm, the number of toroidal field belts is too large compared to the sun. Due to the strong rotational influence on the turbulence in the presence of a sharp change of the turbulence intensity at the bottom of the convection zone, the α-effect is more concentrated to the equatorial region. This leads to more realistic butterfly diagrams. Observations indicate, however, that radial and azimuthal field components are out of phase, which is not reproduced by our model. Title: Structural stability of axisymmetric dynamo models. Authors: Tavakol, R.; Tworkowski, A. S.; Brandenburg, A.; Moss, D.; Tuominen, I. Bibcode: 1995A&A...296..269T Altcode: We examine the stability of the dynamical behaviour of axisymmetric α^2^ ω dynamo models in rotating spherical shells as well as in spheres. Overall, our results show that the spherical dynamo models are more stable in the following senses: spherical models (i) do not seem to allow chaotic behaviour and (ii) are robust with respect to changes in the functional form of α. On the other hand, spherical shell models (i) are capable of producing chaotic behaviour for certain ranges of parameter values and (ii) possess, in the combined "space" of parameters and boundary conditions, regions of complicated behaviours, in the sense that there are regimes in which small changes in either the dynamo parameters or the boundary conditions can drastically change the qualitative behaviour of the model. Finally, we discuss briefly the physical relevance of our results. Title: Multiple far-supercritical solutions for an α{LAMBDA}-dynamo. Authors: Muhli, P.; Brandenburg, A.; Moss, D.; Tuominen, I. Bibcode: 1995A&A...296..700M Altcode: We compute numerical solutions for axisymmetric, dynamically consistent mean-field dynamos in a spherical shell of conducting incompressible fluid. In the process of investigating the stability properties of solutions in the far-supercritical regime we found an unusual behaviour, with the magnetic energy decreasing discontinuously as the dynamo number is increased. A new stable solution with a more complicated field geometry emerges. In addition, a stable mixed parity state occurs at the discontinuity of the magnetic energy, between the two branches of stable pure parity solutions. For a given dynamo number there may be as many as four metastable solutions. Title: The size and dynamics of magnetic flux structures in magnetohydrodynamic turbulence Authors: Brandenburg, Axel; Procaccia, Itamar; Segel, Daniel Bibcode: 1995PhPl....2.1148B Altcode: The structures in magnetohydrodynamic (MHD) flow, flux tubes in particular, are investigated with respect to coherence in the direction of the magnetic field. A length scale, which is interpreted as the diameter of the tubes, is derived from the MHD equations. This scale implies that the tendency towards alignment of flux lines in tubes is a diffusion driven phenomenon. The dynamics of the tubes is also investigated; the major conclusion is that stronger tubes are expected to be straighter. These ideas are tested out on data from numerical simulations of turbulent MHD convection. It is also seen that alignment of flux lines increases with the strength of the tube. Possible reasons for this effect are discussed. Title: Nonaxisymmetric dynamo solutions and extended starspots on late-type stars. Authors: Moss, D.; Barker, D. M.; Brandenburg, A.; Tuominen, I. Bibcode: 1995A&A...294..155M Altcode: We have computed mean field dynamo models in a deep spherical shell, without restriction on spatial symmetries, in which the growth of the magnetic field is limited solely by the back reaction of the large scale Lorentz force on the large scale motions. A parameterization of the Reynolds stress tensor is included to describe the generation of differential rotation. We find for moderate values of the Taylor number, when the differential rotation is also small, that the stable magnetic fields are nonaxisymmetric, with the same basic topology as a "perpendicular dipole". For larger Taylor numbers, and stronger absolute differential rotation, we expect axisymmetric fields to be stable. We briefly discuss the relevance of our results to the large scale nonaxisymmetric structures and extended starspots observed on late type "active giant" and other stars. Title: Dynamo Generated Turbulence in Discs Authors: Brandenburg, A.; Nordlund, Å.; Stein, R. F.; Torkelsson, U. Bibcode: 1995LNP...462..385B Altcode: 1995ssst.conf..385B The magnetic shear instability appears to be a workable mechanism for generating turbulence in accretion discs. The magnetic field, in turn, is generated by a dynamo process that taps energy from the Keplerian shear flow. Large scale magnetic fields are generated, whose strength is comparable with, or in excess of, the turbulent kinetic energy. Such models enable us to investigate the detailed nature of turbulence in discs. We discuss in particular the possibility of generating convection, where the heat source is viscous and magnetic heating in the bulk of the disc. Title: The generation of nonaxisymmetric magnetic fields in the giant planets Authors: Moss, D.; Brandenburg, A. Bibcode: 1995GApFD..80..229M Altcode: We consider mean-field dynamo models in uniformly rotating spheres and spherical shells, with anisotropic alpha and magnetic diffusivity tensors which are functions of the inverse Rossby number, *. When we include an a-quenching nonlinearity we show that, for all values of * considered, nonaxisymmetric magnetic fields are stable to axisymmetric perturbations. However the stability of nonaxisymmetric magnetic fields is weakened for large values of *, which would make the generation of axisymmetric magnetic fields more probable. When a small amount of differential rotation is introduced, only axisymmetric dipole-like solutions are stable. We draw attention to the possibility that the nonaxisymmetric magnetic fields of Uranus and Neptune could be the result of anisotropic alpha and magnetic diffusi vity tensors. The more nearly axisymmetric magnetic fields of Jupiter and Saturn could result from their more rapid rotation, or possibly because of internal differential rotation. Title: The many incarnations of accretion disk dynamos: mixed parities and chaos for large dynamo numbers. Authors: Torkelsson, Ulf; Brandenburg, Axel Bibcode: 1994A&A...292..341T Altcode: We study nonlinear accretion disk dynamos, and demonstrate that different types of magnetic field configurations will arise depending on the dynamo number. Dynamo action is parametrised by the α-effect, whose strength is determined by a dimensionless number Calpha_. Using α-quenching as the only nonlinearity, we find for Calpha_>0 that a steady quadrupolar field is first excited. However this solution disappears before any other field configuration is excited. Thus there is a gap without any magnetic field. This is a feature of the particular nonlinearity used, and has not been observed previously in other systems. At higher dynamo numbers oscillatory dipolar and quadrupolar fields emerge, and later the quadrupolar solution bifurcates to a chaotically varying mixed parity solution. Finally, at extremely high dynamo numbers the chaotic field transforms into a steady mixed parity solution, which is dominated by an even parity component. For Calpha_<0 we first find an oscillatory dipolar field, which bifurcates to a doubly periodic mixed parity field, and later also to a chaotically varying field. Using magnetic buoyancy as the nonlinearity the gap no longer occurs. However we are not able to go to as high dynamo numbers as before. Nevertheless for the entire interval investigated, we only find a steady quadrupolar field for Calpha_>0, and an oscillatory quadrupolar or dipolar field for Calpha_<0. Title: The Formation of Sharp Structures by Ambipolar Diffusion Authors: Brandenburg, Axel; Zweibel, Ellen G. Bibcode: 1994ApJ...427L..91B Altcode: The effect of ambipolar diffusion is investigated using simple numerical models. Examples are shown where sharp structures develop around magnetic nulls. In contrast to the case of ordinary diffusion, the magnetic field topology is conserved by ambipolar diffusion. This is demonstrated in an example where differential rotation winds up an initially uniform magnetic field and brings oppositely oriented field lines close together. It is argued that ambipolar diffusion produces structures of scales small enough for reconnection to occur. Title: Reynolds stresses and differential rotation in Boussinesq convection in a rotating spherical shell. Authors: Rieutord, Michel; Brandenburg, Axel; Mangeney, Andre; Drossart, Pierre Bibcode: 1994A&A...286..471R Altcode: We consider the problem of how numerical simulations of convection in a spherical shell can be used to estimate turbulent transport coefficients that may be used in mean field theory. For this purpose we analyse data from simulations of three dimensional Boussinesq convection. The rotational influence on convection is described in terms of the {LAMBDA}-effect and anisotropic eddy conductivity. When the resulting transport coefficients are used in a mean field model, the original rotation law is recovered approximately. We thus conclude that the flow can be described in terms of a {LAMBDA}-effect. Our results are also compared with analytical theories and observations. Title: Does solar differential rotation ARISE from a large scale instability?. Authors: Tuominen, Ilkka; Brandenburg, Axel; Moss, David; Rieutord, Michel Bibcode: 1994A&A...284..259T Altcode: The suggestion by several authors that the solar differential rotation is caused by a large scale instability of the basic convective state is examined. We find that the proposed mean-field models are unstable to a Rayleigh-Benard type instability, but argue that this cannot explain the differential rotation of the Sun, because such a flow would become nonaxisymmetric. We discuss the applicability of the mean-field equations to the problem. hydrodynamics - Sun: rotation Title: Turbulent accretion disk dynamos ? Authors: Torkelsson, Ulf; Brandenburg, Axel Bibcode: 1994A&A...283..677T Altcode: We present numerical results for mean-field α^2OMEGA- dynamos in an accretion disk. We first study the linear case in both disks with constant thickness and disks with radially increasing thickness. The preferred mode is dipolar for a thick disk, but quadrupolar for a thin one. The quadrupolar mode generates a magnetic torque that transports angular momentum outwards. The role of the geometrical distribution of both the α-effect and the magnetic diffusivity in the disk is considered for thin disks. It is found that the parity of the most easily excited mode is unaffected, albeit the distribution of the magnetic field and torque change in such a way that a larger fraction of the field and the torque appears in regions with small diffusivity. For some interesting cases we study nonlinear effects like α-quenching and magnetic buoyancy. These effects can affect significantly the magnetic field distribution, compared to the linear case. A transition to chaotic behaviour is found for α-quenching when α is negative in the upper part of the disk. Title: Stellar Dynamo Models: From F to K Authors: Brandenburg, A.; Saar, S. H.; Moss, D.; Tuominen, I. Bibcode: 1994ASPC...64..357B Altcode: 1994csss....8..357B We extend the two-dimensional solar dynamo models to stars of different spectral types. Dynamo action is restricted to the overshoot layer. Title: The Evolution of Stellar Dynamo Variations. Authors: Saar, S. H.; Brandenburg, A.; Donahue, R. A.; Baliunas, S. L. Bibcode: 1994ASPC...64..468S Altcode: 1994csss....8..468S No abstract at ADS Title: Angular Momentum Loss from the Young Sun: Improved Wind and Dynamo Models Authors: Keppens, R.; Charbonneau, P.; MacGregor, K. B.; Brandenburg, A. Bibcode: 1994ASPC...64..193K Altcode: 1994csss....8..193K No abstract at ADS Title: Stellar Dynamos: The Rossby Number Dependence Authors: Brandenburg, A.; Charbonneau, P.; Kitchatinov, L. L.; Rudiger, G. Bibcode: 1994ASPC...64..354B Altcode: 1994csss....8..354B No abstract at ADS Title: Hydrodynamical simulations of the solar dynamo Authors: Brandenburg, Axel Bibcode: 1994LNP...432...73B Altcode: 1994LNPM...11...73B Hydrodynamic simulations of the solar convection zone can be used to model the generation of differential rotation and magnetic fields, and to determine mean-field transport coefficients that are needed in mean-field models. The importance of the overshoot layer beneath the solar convection zone is discussed: it is the place where the magnetic field accumulates, although most of the field regeneration can still occur in the convection zone proper. We also discuss how systematically oriented bipolar regions can emerge from the convection zone where the magnetic field is highly intermittent. Title: Solar Dynamos; Computational Background Authors: Brandenburg, A. Bibcode: 1994lspd.conf..117B Altcode: No abstract at ADS Title: Models for the Magnetic Field of M81 Authors: Moss, David; Brandenburg, Axel; Donner, Karl J.; Thomasson, Magnus Bibcode: 1993ApJ...409..179M Altcode: We study several mean field dynamo models in disk geometry in an attempt to understand the origin of the nonaxisymmetric magnetic field present in M81. There appear to be three (at least) relevant mechanisms, which are not mutually exclusive. Because field growth times are not very short compared to galactic ages, a predominantly nonaxisymmetric seed field may still give a significantly nonaxisymmetric field after times of order 10^10^ yr, even if the stable field configuration is axisymmetric. The spiral structure may give a non-axisymmetric structure to the disk turbulence, and thus to the turbulent coefficients appearing in mean field dynamo theory. Third M81 may have undergone a close encounter with a companion galaxy. A dynamical model of the interaction predicts strong, nonaxisymmetric, large-scale gas velocities in the disk plane, and these can produce nonaxisymmetric fields. In the absence of the second of these effects, our models predict that nonaxisymmetric fields will be present in the outer parts of the galaxy, together with significant axisymmetric contributions in the inner part. However, we do not find that any of these effects, taken individually, can produce dominant nonaxisymmetric field structure. If they are simultaneously present, they can reinforce one another. Further, our calculations are for a relatively thick disk (thickness to radius ratio of order 0.2), and a reduction to smaller, and plausibly more realistic, values will also favor nonaxisymmetric field generation. Title: Vertical magnetic fields above the discs of spiral galaxies. Authors: Brandenburg, A.; Donner, K. J.; Moss, D.; Shukurov, A.; Sokoloff, D. D.; Tuominen, I. Bibcode: 1993A&A...271...36B Altcode: We investigate the magnetic fields above the discs of spiral galaxies in the framework of axisymmetric nonlinear mean-field dynamo models for a disc surrounded by a spherical halo, using realistic rotation curves. We consider, in particular, NGC 4631 and NGC 891, and include turbulent diamagnetism, an anisotropy of the α effect and a galactic wind. In these model magnetic field is generated in a disc of scale height 1.5 kpc and distorted by the wind in the halo. For typical wind velocities of 50.. .200 km/s in the halo we find good qualitative agreement between the observed polarisation maps and those synthesised from the magnetic fields of our models: Poloidal synthesised fields dominate in the halo of NGC 4631, and horizontal fields in that of NGC 891. In some cases, a galactic wind can enhance dynamo action, contrary to previous expectations. Our results indicate that turbulent diamagnetism plays an important role in galactic dynamos. Title: The excitation of nonaxisymmetric magnetic fields in galaxies. Authors: Moss, D.; Brandenburg, A. Bibcode: 1993spd..conf..219M Altcode: No abstract at ADS Title: Reynolds Stresses Derived from Simulations Authors: Pulkkinen, P.; Tuominen, I.; Brandenburg, A.; Nordlund, A. Bibcode: 1993IAUS..157..123P Altcode: No abstract at ADS Title: Multifractality, near-singularities and the role of stretching in turbulence. Authors: Brandenburg, A.; Procaccia, I.; Segel, D.; Vincent, A.; Manzini, M. Bibcode: 1993spd..conf...35B Altcode: No abstract at ADS Title: Rotational effects on convection simulated at different latitudes Authors: Pulkkinen, Pentti; Tuominen, Ilkka; Brandenburg, Axel; Nordlund, Ake; Stein, Robert F. Bibcode: 1993A&A...267..265P Altcode: We simulate numerically convection inside the solar convection zone under the influence of rotation at different latitudes. The computational domain is a small rectangular box with stress-free upper and lower boundaries, and with periodicity assumed in the lateral directions. We study the transport of angular momentum, which is important for the generation of differential rotation. The sign and the latitudinal dependence of the horizontal Reynolds stress component turn out to be in good agreement with correlation measurements of sunspot proper motions and with predictions from the theory of the Lambda effect. We also investigate the other components of the Reynolds stress as well as the eddy heat flux tensor, both of which are needed in mean field models of differential rotation. Title: Simulating the Solar Dynamo Authors: Brandenburg, A. Bibcode: 1993IAUS..157..111B Altcode: No abstract at ADS Title: Chaos in Nonlinear Dynamo Models Authors: Kurths, J.; Brandenburg, A.; Feudel, U.; Jansen, W. Bibcode: 1993IAUS..157...83K Altcode: No abstract at ADS Title: Towards the Magnetic Field of M 81 Authors: Moss, D.; Brandenburg, A.; Donner, K. J.; Thomasson, M. Bibcode: 1993IAUS..157..339M Altcode: No abstract at ADS Title: Galactic Dynamos and Dynamics Authors: Donner, K. J.; Brandenburg, A.; Thomasson, M. Bibcode: 1993IAUS..157..333D Altcode: No abstract at ADS Title: Evolution of a magnetic flux tube in two-dimensional penetrative convection Authors: Jennings, R. L.; Brandenburg, A.; Nordlund, A.; Stein, R. F. Bibcode: 1992MNRAS.259..465J Altcode: Highly supercritical compressible convection is simulated in a two-dimensional domain in which the upper half is unstable to convection while the lower half is stably stratified. This configuration is an idealization of the layers near the base of the solar convection zone. Once the turbulent flow is well developed, a toroidal magnetic field Btor is introduced to the stable layer. The field's evolution is governed by an advection-diffusion-type equation, and the Lorentz force does not significantly affect the flow. After many turnover times the field is stratified such that the absolute value of Btor/rho is approximately constant in the convective layer, where rho is density, while in the stable layer this ratio decreases linearly with depth. Consequently most of the magnetic flux is stored in the overshoot layer. The inclusion of rotation leads to travelling waves which transport magnetic flux latitudinally in a manner reminiscent of the migrations seen during the solar cycle. Title: Stratification and thermodynamics in mean-field dynamos Authors: Brandenburg, Axel; Moss, David; Tuominen, Ilkka Bibcode: 1992A&A...265..328B Altcode: Previous investigations of axisymmetric incompressible mean-field dynamos are extended to the compressible case with strong stratification. It is shown that the effects of stratification, compressibility, and thermodynamics on the rotation law are small when the present results are compared with those previously obtained for incompressible models. For solar values of the Taylor number cylindrical contours of the angular velocity typically occur, even for strong stratification. The stagnation line of the meridional circulation is close to the bottom of the convection zone. In the presence of magnetic fields the meridional flow is amplified, in particular, close to the surface where the density is small and the Lorentz force per unit mass is large. The depth dependence of the magnetic energy density is not much altered by the inclusion of a density stratification. For cyclical dynamo magnetic fields thermal and magnetic energies are approximately in antiphase. The cyclic variation in luminosity is small and lags behind the variation in magnetic energy by about 1/8 of the period. Title: Stochastic effects in mean-field dynamos Authors: Moss, David; Brandenburg, Axel; Tavakol, Reza; Tuominen, Ilkka Bibcode: 1992A&A...265..843M Altcode: We investigate the effects of various forms of noise on previously studied nonlinear (alpha-squared)(omega) dynamos in a sphere or a spherical shell. We investigate the consequences of perturbing solutions of both pure and mixed parity. In the former case we find that there can be quite pronounced deviations from the pure parity, and that these seem larger nearer to the relevant bifurcation. Effects are also stronger in a shell dynamo than in the full sphere. However, the magnetic period is relatively little changed in these examples. When a 2-torus solution (of mixed parity) is perturbed, the effects on the long period variations are much greater than on the short period, but even for quite strong perturbations the solutions do not leave the neighborhood of the underlying attractor. Title: Fractal level sets and multifractal fields in direct simulations of turbulence Authors: Brandenburg, Axel; Procaccia, Itamar; Segel, Daniel; Vincent, Alain Bibcode: 1992PhRvA..46.4819B Altcode: The fractal nature of level sets and the multifractal nature of various scalar and vector fields in hydromagnetic and hydrodynamic turbulence are investigated using data of direct simulations. It turns out that fields whose evolution is governed by stretching terms (vortex stretching, magnetic-field line stretching) exhibit ``near singularities'' that result in a multifractal scaling. Such stretching terms can lead to a rapid increase in the local value of the field. Fields without rapid local increase have no multifractal scaling. Furthermore, the simulations support recent theoretical suggestions that the fractal properties of the level sets of various fields are quite insensitive to the existence of stretching. Indeed, all the fields under study (temperature, vorticity magnitude, magnetic-field magnitude) show rather universal behavior in the geometry of their level sets, consistent with a two-dimensional geometry at small scales, with a crossover to a universal fractal geometry at large scales. The dimension at large scales is compatible with the theoretical prediction of about 2.7. The most surprising result of the simulations is that it appears that the ``near singularities'' are not efficiently eliminated by viscous dissipation, but rather seem to be strongest at the Kolmogorov cutoff. The effects of the singularities do not quite penetrate into the inertial range. We offer a simple analytic model to account for this behavior. We conclude that our findings may be due to the relatively small Reynolds numbers, but may also be indicative of generic behavior at larger Reynolds numbers. We offer some thoughts about the expected scaling behavior in the inertial range in light of our findings. Title: Energy spectra in a model for convective turbulence Authors: Brandenburg, Axel Bibcode: 1992PhRvL..69..605B Altcode: The energy cascade in both hydrodynamic and hydromagnetic Boussinesq convection is investigated at large Rayleigh numbers using a scalar model for turbulence. Depending on the relative importance of direct and inverse transfer, either classical Kolmogorov k exp -5/3 spectra are derived or, if there is a strong inverse transfer of kinetic energy, a K exp -7/5 spectrum is found for the temperature fluctuation and a K exp -11/5 spectrum for the kinetic energy (Bolgiano-Obukhov scaling). Dissipative cutoff wave numbers that are consistent with these spectra are derived. Title: Dynamos in discs and halos of galaxies. Authors: Brandenburg, A.; Donner, K. J.; Moss, D.; Shukurov, A.; Sokolov, D. D.; Tuominen, I. Bibcode: 1992A&A...259..453B Altcode: The authors investigate linear and nonlinear dynamo models for a galactic disc embedded in a halo, assuming a relatively strong magnetic diffusivity and a non-vanishing α effect in the halo. They take the halo to be spherical and embedded in a vacuum. The field is assumed to be axisymmetric, but they do not impose symmetry conditions at the equatorial plane. In one parameter regime mixed parity solutions are found. However, it is argued that the regular magnetic field in the galactic halo can hardly reach a steady-state configuration during the galactic lifetime. In the regime that is observably relevant the field can have an even parity within and near the disc and an odd one in the halo. This may have implications for explaining the occurrence of a neutral sheet above the galactic plane. During certain time intervals the rotation measure of these models shows a doubly peaked azimuthal variation, which could be falsely interpreted as an indication of a bisymmetric field structure. Title: Dynamo Action in Stratified Convection with Overshoot Authors: Nordlund, Ake; Brandenburg, Axel; Jennings, Richard L.; Rieutord, Michel; Ruokolainen, Juha; Stein, Robert F.; Tuominen, Ilkka Bibcode: 1992ApJ...392..647N Altcode: Results are presented from direct simulations of turbulent compressible hydromagnetic convection above a stable overshoot layer. Spontaneous dynamo action occurs followed by saturation, with most of the generated magnetic field appearing as coherent flux tubes in the vicinity of strong downdrafts, where both the generation and destruction of magnetic field is most vigorous. Whether or not this field is amplified depends on the sizes of the magnetic Reynolds and magnetic Prandtl numbers. Joule dissipation is balanced mainly by the work done against the magnetic curvature force. It is this curvature force which is also responsible for the saturation of the dynamo. Title: The influence of boundary conditions on the excitation of disk dynamo modes Authors: Moss, David; Brandenburg, Axel Bibcode: 1992A&A...256..371M Altcode: Calculations of mean field dynamos for galaxies have largely been for two rather disparate models. The thin disk model treats the ratio of disk height to radius explicitly as a small parameter, and applies zero tangential field boundary conditions at the disk surface. In contrast, the embedded disk model calculates the magnetic field in a spherical volume, whose radius is the disk radius and with the magnetic field fitting smoothly on to a curl-free exterior field at the surface of the sphere. The disk geometry is imposed by a flat distribution of the α-effect (and maybe also of the diffusivity η. For computational reasons this model has not been applied to very thin disks, so the regions of validity of the two models are almost disjoint. Comparison between their predictions is therefore difficult. In this paper we calculate, in linear theory, galactic dynamo modes according to both thin and embedded (or "thick") disk models for a simple underlying distribution of α-effect and differential rotation, using a common numerical scheme. For the smallest attainable ratio of disk height to radius, we find the critical dynamo numbers are similar, but that there are some significant differences in field topology. Title: Magnet Convection (Invited Review) Authors: Stein, R. F.; Brandenburg, A.; Nordlund, A. Bibcode: 1992ASPC...26..148S Altcode: 1992csss....7..148S No abstract at ADS Title: Turbulent Pumping in the Solar Dynamo Authors: Brandenburg, Axel; Moss, David; Tuominen, Ilkka Bibcode: 1992ASPC...27..536B Altcode: 1992socy.work..536B No abstract at ADS Title: Lyapunov exponents for hydromagnetic convection Authors: Kurths, J.; Brandenburg, A. Bibcode: 1991PhRvA..44.3427K Altcode: We estimate the two largest Lyapunov exponents in a three-dimensional simulation of hydromagnetic convection in which there is dynamo action. It turns out that these first two exponents (from a total of 8×633) are positive and of similar magnitude. Thus we conclude that the dynamo is chaotic. Furthermore, the consideration of local exponents helps in our understanding of the relevant dynamics. We find that the downdraft flows are more chaotic than the upward motions. Likewise, the velocity and magnetic fields have more chaotic dynamics than the temperature and density fields. Title: Properties of mean field dynamos with non-axisymmetric alpha-effect Authors: Moss, D.; Brandenburg, A.; Tuominen, I. Bibcode: 1991A&A...247..576M Altcode: The influence of an azimuthally dependent alpha-effect on the properties of alpha(2) and alpha(2)Omega-dynamos in spherical geometry is investigated. Consideration is given solely to odd parity solutions in linear theory. For all the present linear models an exponentially growing mode, consisting of locked axisymmetric and nonaxisymmetric parts is found. A strong nonaxisymmetry in alpha substantially increases the linear growth rates at given dynamo number and can result in a marginal dynamo number. Some exploratory nonlinear calculations are also reported and the relevance of the present results to galactic dyanmos and to stars is briefly discussed. Title: Nonlinear nonaxisymmetric dynamo models for cool stars Authors: Moss, D.; Tuominen, I.; Brandenburg, A. Bibcode: 1991A&A...245..129M Altcode: Observational evidence for long-lived nonaxisymmetric features on the surfaces of rapidly rotating late-type giant stars (e.g., FK Comae and RS CVn stars) is beginning to be found. By analogy with sunspots, these features may be associated with large scale nonaxisymmetric magnetic field structures, generated by a dynamo operating in the convective envelopes. A nonlinear nonaxisymmetric dynamo model is described, and it is shown that for a simple 'alpha-quenching' nonlinearity together with suitable choices of underlying radial profiles of differential rotation and the alpha-effect, stable nonaxisymmetric solution can be found by numerical integration. Title: Challenges for solar dynamo theory: α-effect, differential rotation and stability. Authors: Brandenburg, A.; Tuominen, I. Bibcode: 1991NAWG.1991...26B Altcode: No abstract at ADS Title: Can the Lorentz force accelerate magnetic field expansion? Authors: Brandenburg, A.; Krause, F.; Moss, D.; Tuominen, I. Bibcode: 1991AGAb....6...32B Altcode: No abstract at ADS Title: Hydromagnetic -type dynamos with feedback from large scale motions Authors: Brandenburg, A.; Moss, D.; Rüdiger, G.; Tuominen, I. Bibcode: 1991GApFD..61..179B Altcode: Nonlinear axisymmetric mean-field -type dynamos in spherical shells of conducting incompressible fluid are computed, with differential rotation being generated by the Reynolds stress of anisotropic turbulence (A-effect). The correlation time of the turbulence is assumed to be short compared with the rotation period. In this case the angular velocity tends to be constant on cylindrical surfaces as the Taylor number, Ta, is increased (cf. the Taylor-Proudman theorem). The only magnetic feedback mechanism considered is the Lorentz force of the mean magnetic field acting on the macroscale motions (Malkus-Proctor mechanism). The Elsasser number is in this case close to unity, but grows slowly as Ta1'2. Restricting ourselves to strictly dipole-type magnetic fields we find for Ta = 108, magnetic cycles with migrating field belts close to the equator. For smaller Taylor numbers and only slightly supercritical a-effect the magnetic field is steady and the -effect becomes unimportant for the generation of toroidal field from a poloidal one. However, magnetic cycles are still possible if the -effect is sufficiently strong. In this case the field is concentrated at high latitudes. Poloidal and toroidal fields can be in antiphase with equatorward field migration only when the angular velocity increases inwards and towards the poles. The energy of the mean magnetic field generated is usually less than the energy of the turbulent convective motions. The ratio between cycle period and rotational period can reach values of around fifty. Title: The Solar Dynamo Authors: Brandenburg, Axel; Tuominen, Ilkka Bibcode: 1991LNP...380..223B Altcode: 1991IAUCo.130..223B; 1991sacs.coll..223B The traditional -dynamo as a model for the solar cycle has been successful in explaining the butterfly diagram, phase relations between poloidal and toroidal field, and polar branch migration features. Observational and theoretical achievements in recent years have however shaken this picture. The current trend is towards dynamos operating in the overshoot region of the convection zone. Nevertheless, there are many open questions and a consistent picture has not been established. In this paper we compare recent approaches and discuss remaining problems. Title: αΛ-dynamos Authors: Brandenburg, A.; Moss, D.; Rieutord, M.; Rüdiger, G.; Tuominen, I. Bibcode: 1991LNP...380..147B Altcode: 1991sacs.coll..147B; 1991IAUCo.130..147B In contrast to -dynamos, where the angular velocity is arbitrarily prescribed, we consider here -dynamos, for which the differential rotation and meridional circulation are solutions of the momentum equation. The non-diffusive parts of the Reynolds stress tensor are parameterized by the -effect. In earlier investigations we have shown that the turbulent magnetic diffusivity has to be much smaller than the eddy viscosity, otherwise the dynamo is not oscillatory or else the contours of constant angular velocity are cylindrical, contrary to observations. In the present paper we investigate the effects of compressibility. Title: The Role of Overshoot in Solar Activity - a Direct Simulation of the Dynamo Authors: Brandenburg, A.; Jennings, R. L.; Nordlund, Å.; Stein, R. F.; Tuominen, I. Bibcode: 1991LNP...380...86B Altcode: 1991IAUCo.130...86B; 1991sacs.coll...86B We investigate convective overshoot in a layer of electrically conducting fluid. The radiative conductivity is assumed to be larger in the lower part of the layer which makes it stable to convective motions, yet penetrative convection from the upper layer can occur. The numerical resolution is 633 gridpoints. We observe a dynamo effect for magnetic Reynolds numbers around one thousand when a magnetic seed field is rapidly concentrated to form flux tubes. Later the average magnetic field is expelled from the convectively unstable regions, but it accumulates in the interface between the convection zone and the radiative interior. Title: Magnetic Tubes in Overshooting Compressible Convection Authors: Jennings, R. L.; Brandenburg, A.; Nordlund, Å.; Stein, R. F.; Tuominen, I. Bibcode: 1991LNP...380...92J Altcode: 1991sacs.coll...92J; 1991IAUCo.130...92J A magnetic tube is introduced into turbulent compressible penetrative convection. After being strongly advected, most of the magnetic flux is stored in the overshoot region. With rotation there are meridional travelling waves. Title: Rotational Effects on Reynolds Stresses in the Solar Convection Zone Authors: Pulkkinen, P.; Tuominen, I.; Brandenburg, A.; Nordlund, Å.; Stein, R. F. Bibcode: 1991LNP...380...98P Altcode: 1991IAUCo.130...98P; 1991sacs.coll...98P Three-dimensional hydrodynamic simulations are carried out in a rectangular box. The angle between gravity and rotation axis is kept as an external parameter in order to study the latitude-dependence of convection. Special attention is given to the horizontal Reynolds stress and the -effect (Rüdiger, 1989). The results of the simulations are compared with observations and theory and a good agreement is found. Title: Buoyancy-limited thin shell dynamos Authors: Moss, D.; Tuominen, I.; Brandenburg, A. Bibcode: 1990A&A...240..142M Altcode: Axisymmetric nonlinear mean-field dynamos in spherical shells are investigated that attempt to model the gross effects of a dynamo operating in a thin layer at the base of a convective envelope. A form of magnetic buoyancy restricts the fields to finite amplitude. As the shell thickness decreases, the excitation conditions and spatial structure of even and odd parity modes become almost identical. For very thin shells the field forms a number of almost disjoint cells. Mixed parity solutions are found which typically evolve very slowly toward pure odd or even parity solutions. The time scale of these slow variations is of the order of a hundred global diffusion times. Title: Generation and interpretation of galactic magnetic fields Authors: Donner, K. J.; Brandenburg, A. Bibcode: 1990A&A...240..289D Altcode: We present kinematic mean-field dynamo models for galaxies consisting of a turbulent gas disc embedded in a low-conductivity spherical halo. In the cases investigated an axisymmetric mode is the dominant one. This mode can be of either even or odd parity (SO or A0, respectively). The preference of S0 or A0 modes is governed mainly by the radial profiles of the α effect and the turbulent magnetic diffusivity. If the gas disc extends into the galactic centre, the dominant mode is of A0 type and it is concentrated within the central region. If the model is changed so that induction effects are absent in the centre, the dominant mode is an axisymmetric spiral of even parity. We point out that a finite disc thickness and a low- conductivity halo will both lead to appreciable vertical magnetic fields outside the disc plane, and this may affect the interpretation of polarisation observations. We integrate the transfer equations for the three Stokes parameters I, Q, and U and produce in this way synthetic maps for the observed polarisation and rotation measures. Assuming a disc-like distribution of relativistic electrons, our models suggest that for moderate disc thickness modifications of the observed polarised emission due to fields above the plane are minor. For more extended electron distributions quite complicated polarisation patterns are obtained. Still, qualitatively the criteria distinguishing axisymmetric and bisymmetric spiral patterns remain valid. Title: Nonlinear mean-field dynamo models - Stability and evolution of three-dimensional magnetic field configurations. Authors: Raedler, K. -H.; Wiedemann, E.; Brandenburg, A.; Meinel, R.; Tuominen, I. Bibcode: 1990A&A...239..413R Altcode: The stability and evolution of three-dimensional magnetic field configurations of nonlinear mean-field dynamo models are investigated. A single stable solution showing the same symmetry is found for two models with isotropic alpha effect. A model with anisotropic alpha effect is investigated for which the marginal solution is known to be nonaxisymmetric, and a nonaxisymmetric solution is found to be the only stable one for slightly supercritical dynamo numbers. A stable axisymmetric solution is found for dynamo numbers exceeding a certain value. For even higher dynamo numbers, the nonaxisymmetric solution loses stability to the axisymmetric solution. Mixed parity solutions with periodic time dependence are found for a model with differential rotation in a parameter regime where four different modes are approximately equally excitable. Title: Behaviour of highly supercritical alpha-effect dynamos Authors: Meinel, R.; Brandenburg, A. Bibcode: 1990A&A...238..369M Altcode: The behavior of alpha-squared-dynamos is discussed for highly supercritical dynamo numbers, with alpha-quenching assumed to be the dominant nonlinearity. Particular attention is paid to a one-dimensional reduction of the dynamo equations. For sufficiently high dynamo numbers both steady and time-dependent solutions (limit cycles) are possible. The basins of attraction of these solutions depend on the dynamo number as well as on the degree of the nonlinearity assumed. For extreme nonlinearities the limit-cycle solutions, at particular time instants (turning points), closely approach the steady solutions. In this case some noise of small but finite amplitude may cause transitions between the limit-cycle and the steady solutions. This leads to an irregular time-behavior including nearly steady stages as well as reversals of the magnetic polarity. Title: The Nonlinear Solar Dynamo and Differential Rotation - a Taylor Number Puzzle Authors: Brandenburg, A.; Tuominen, I.; Moss, D.; Ruediger, G. Bibcode: 1990SoPh..128..243B Altcode: 1990IAUCo.121P.243B We consider dynamically consistent mean-field dynamos in a spherical shell of incompressible fluid. The generation of magnetic field and differential rotation is parameterized by the α- and Λ-effects, respectively. Extending previous investigations, we include now the cases of moderate and rapid rotation in the sense that the inverse Rossby number can approach or exceed unity: This can lead to disk-shapedΩ-contours, which are in better accordance with recent results of helioseismology than cylindricalΩ-contours. On the other hand, in order to obtain αω-dynamo cycles the Taylor number has to be so large, that eventually cylindrical Ω-contours become unavoidable (cf. Taylor-Proudman theorem). We discuss the different possibilities in a state diagram, where the inverse Rossby number and the relative correlation length are taken as the elementary parameters for mean-field dynamos. Title: 3-D simulation of turbulent cyclonic magneto-convection. Authors: Brandenburg, A.; Tuominen, I.; Nordlund, A.; Pulkkinen, P.; Stein, R. F. Bibcode: 1990A&A...232..277B Altcode: Results are presented of a simulation of turbulent three-dimensional magnetic convection under the influence of rotation in a fluid layer whose depth is about 1 pressure-scale hight. The approach is similar to that of Meneguzzi and Pouquet (1989), except for the assumptions that the fluid is a compressible conducting gas and there is a vanishing horizontal magnetic field at the boundaries. The results demonstrate that topological effects may be of great importance for MHD convection. It is shown that, as a consequence of topological effects, anisotropies of the alpha-effect can play a dominant role. In particular, the sign of alpha(V) can be opposite to that expected from a first-order smoothing approach. Title: Can stellar dynamos be modelled in less than three dimensions? Authors: Jennings, R.; Brandenburg, A.; Tuominen, I.; Moss, D. Bibcode: 1990A&A...230..463J Altcode: Nonlinear alpha-omega dynamos in different geometries are compared. The importance of radial structure is investigated via comparison of axisymmetric one-dimensional models with their two-dimensional counterparts. For the two-dimensional nonaxisymmetric extension of the one-dimensional model, a finite-amplitude mixed solution with nonaxisymmetric contributions is found. Title: Nonlinear dynamos with magnetic buoyancy in spherical geometry Authors: Moss, D.; Tuominen, I.; Brandenburg, A. Bibcode: 1990A&A...228..284M Altcode: Numerical solutions are computed for axisymmetric mean field dynamos of alpha-sq and alpha-sq omega type in spherical geometry. In particular, the effects of including a term in the magnetohydrodynamic equations which represents the upward advection of fields by magnetic buoyancy is studied. For the buoyancy-limited alpha-sq dynamo, it is found that, for certain parameter values, this model may have two stable solutions, of opposite parity properties with respect to the equator. In the dynamo models for smaller values of a dynamo number, odd parity solutions are stable, but, for larger values, it is the even parity solutions that are stable. These results concerning the stability of pure parity solutions are similar to those found in an earlier study in which the nonlinearity was a simple alpha-quenching. Some models are presented with both buoyancy and alpha-quenching included. The most noticeable effect of adding a buoyancy term to the alpha-quenched solutions is that the amplitude of the finite amplitude parity oscillations (tori and limit cycles) previously found is reduced. Title: Magnetic field structure in differentially rotating discs Authors: Donner, K. J.; Brandenburg, A. Bibcode: 1990GApFD..50..121D Altcode: In order to gain a better understanding of the processes that may give rise to non-axisymmetric magnetic fields in galaxies, we have calculated field decay rates for models with a realistic galactic rotation curve and including the effects of a locally enhanced turbulent magnetic diffusivity within the disc. In all cases we have studied, the differential rotation increases the decay rate of non-axisymmetric modes, whereas axisymmetric ones are unaffected. A stronger magnetic diffusivity inside the disc does not lead to a significant preference for non-axisymmetric modes. Although Elsasser's antidynamo theorem has not yet been proved for the present case of a non-spherical distribution of the magnetic diffusivity, we do not find any evidence for the theorem not to be valid in general. Title: Turbulent diffusivities derived from simulations. Authors: Brandenburg, A.; Nordlund, Å.; Pulkkinen, P.; Stein, R. F.; Tuominen, I. Bibcode: 1990fas..conf....1B Altcode: By employing direct simulations of turbulent magneto-convection the authors determine the turbulent diffusivities, such as the turbulent magnetic diffusivity, the eddy viscosity and the turbulent heat conductivity. Title: Challenges for the solar dynamo theory: α-effect, differential rotation and stability Authors: Brandenburg, Axel Bibcode: 1990PhDT.......290B Altcode: No abstract at ADS Title: Challenges for solar dynamo theory: Alpha-effect, differential rotation and stability Authors: Brandenburg, Axel Bibcode: 1990csdt.book.....B Altcode: 1990QB539.M23B73... No abstract at ADS Title: Surface Imaging of Giant Stars and Nonlinear Dynamos Authors: Tuominen, I.; Piskunov, N. E.; Moss, D.; Brandenburg, A. Bibcode: 1990ASPC....9...73T Altcode: 1990csss....6...73T Recent results of photometric cycles and surface images of active giants are discussed in terms of nonlinear 3D mean-field dynamos. The existence of mixed parity solutions with periodic and quasi-periodic time dependence is suggestive for explaining the nonaxisymmetric surface patterns observed on active giant stars. Title: Dynamos with a flat -effect distribution Authors: Brandenburg, A.; Tuominen, I.; Krause, F. Bibcode: 1990GApFD..50...95B Altcode: In order to obtain a better insight into the excitation conditions of magnetic fields in flat objects, such as galaxies, we have calculated critical dynamo numbers of different magnetic field modes for spherical dynamos with a flat -effect distribution. A simple but realistic approximation formula for the rotation curve is employed. In most cases investigated a stationary quadrupole-type solution is preferred. This is a consequence of the flat distribution of the -effect. Non-axisymmetric fields are in all cases harder to excite than axisymmetric ones. This seems to be the case particularly for flat objects in combination with a realistic rotation curve for galaxies. The question of whether non-axisymmetric (bisymmetric) fields, which are observed in some galaxies, can be explained as dynamos generated by an axisymmetric -effect is therefore still open. Title: Torsional Oscillations and the Solar Dynamo Regime Authors: Tuominen, I.; Rüdiger, G.; Brandenburg, A. Bibcode: 1990IAUS..138..387T Altcode: No abstract at ADS Title: Effect of a conducting halo on the structure of galactic magnetic fields. Authors: Donner, K. J.; Brandenburg, A. Bibcode: 1990nba..meet...85D Altcode: 1990taco.conf...85D The authors give examples of the magnetic fields generated by dynamo processes in galaxy models consisting of a turbulent disc embedded in a conducting halo. As the halo conductivity increases, the dominant marginally stable mode becomes more spatially extended and more nearly azimuthal. This is because the critical strengths of the α effect is smaller for higher halo conductivity. Title: Variation of Even and Odd Parity in the Solar Dynamo Authors: Brandenburg, A.; Meinel, R.; Moss, D.; Tuominen, I. Bibcode: 1990IAUS..138..379B Altcode: No abstract at ADS Title: Structure of dynamo generated galactic magnetic fields. Authors: Donner, K. J.; Brandenburg, A. Bibcode: 1990apsu.conf...16D Altcode: No abstract at ADS Title: IUE observations of the M dwarfs CM Draconis and Rossiter 137B : magnetic activity at saturated levels. Authors: Vilhu, O.; Ambruster, C. W.; Neff, J. E.; Linsky, J. L.; Brandenburg, A.; Ilyin, I. V.; Shakhovskaya, N. I. Bibcode: 1989A&A...222..179V Altcode: IUE observations of two active M dwarfs with known rotation rate or age and presumed to be almost totally convective are presented. The first of these stars, CM Draconis (Gl 630.1), is an old Population II binary with its components in tidally induced rapid rotation (P = 1.27 d, dM 4 + dM 4). The other one, Rossiter 137 B, forms with HD 36705 (AB Dor) a visual pair of young active stars. The activity of CM Dra is due to the forced rotation in a close binary, while Rst 137 B is assumed to rotate fast enough to generate its magnetica activity. These results are compared with those for M dwarfs, particularly AU Mic and YZ CMi, that have known rotational periods and measured ultraviolet emission line fluxes. The chromospheric-coronal saturation levels of cool dwarfs between 0.3 less than B-V less than 1.6 is determined. It is found that saturated F stars have stronger chromospheres than saturated M stars, but the opposite is true for the corona. Results of these observations seem to favor a rotation-dependent distributed dynamo generating magnetic flux in totally convective stars. Title: The stability of nonlinear dynamos and the limited role of kinematic growth rates Authors: Brandenburg, A.; Krause, F.; Meinel, R.; Moss, D.; Tuominen, I. Bibcode: 1989A&A...213..411B Altcode: The growth rate behavior of several kinematic dynamo models was investigated in the context of the observation that, as a rule, a magnetic field of a single symmetry dominates in the sun and other cosmic objects. For all dynamo models considered, it is shown that, as the dynamo numbers increase, the kinematic growth rates of fields of different parities are asymptotically equal, indicating that growth rates do not dominate the final state of the field. The possibility that the stability of different solutions of nonlinear dynamos determines the final state was then investigated. Dynamo models in spherical geometry were found in which both symmetric and antisymmetric solutions are stable. The kind of symmetry finally established depends in these cases on the initial conditions, i.e., on the history of the object. It is noted that the basic mechanism stabilizing or destabilizing different solutions is not well understood. Title: On the nonlinear stability of dynamo models Authors: Brandenburg, A.; Tuominen, I.; Moss, D. Bibcode: 1989GApFD..49..129B Altcode: The stability of nonlinear mean-field dynamo models in spherical geometry has been investigated numerically. Assuming axisymmetry and incompressibility we find stable stationary solutions of both even and odd parity over a range of four decades in the Taylor number. Furthermore, we extend studies on solutions with "mixed parity", which have been found previously for an -dynamo model, neglecting here, however, the explicit feedback on the mean motions. Plots of trajectories in phase space and Poincaré maps, showing intersections of the trajectories with certain hyperplanes in phase space, reveal that the solution lies on a torus for some of these models. Title: On the generation of non-axisymmetric magnetic fields in mean-field dynamos Authors: Brandenburg, A.; Tuominen, I.; Rädler, K. -H. Bibcode: 1989GApFD..49...45B Altcode: The magnetic fields of the Earth and other planets deviate in varying degrees from symmetry about the rotational axis. While, for example, the field of Saturn is highly symmetric, that of Uranus shows a striking asymmetry. With these observations in mind we investigate excitation conditions of axisymmetric and non-axisymmetric field modes in spherical mean-field dynamo models. In models of 2-type the marginal dynamo numbers for modes with different azimuthal dependences are close together if the -effect is concentrated in a thin layer. Preference of non-axisymmetric modes over axisymmetric ones occurs if we include weak differential rotation, anisotropies of the -effect or the -effect, the last one corresponding to a radial transport of magnetic flux. We discuss consequences of these results for planetary dynamos. Title: Solar magnetic fields and dynamo process. Authors: Brandenburg, A.; Tuominen, I. Bibcode: 1989sasf.confP.369B Altcode: 1989IAUCo.104P.369B; 1988sasf.conf..369B The authors have computed kinematic dynamo models for the Sun making realistic assumptions about the different induction effects. Recent results of helioseismology are used to infer the differential rotation. By changing the value of the angular velocity at the bottom of the convection zone in the models the authors find more or less agreement with the observations. Title: Parity selection in nonlinear dynamics. Authors: Brandenburg, A.; Tuominen, I.; Krause, F. Bibcode: 1989tndm.conf...35B Altcode: The stability of different nonlinear α-effect dynamos in spherical geometry is studied. A critical value of the dynamo number is found, above which steady hydromagnetic solutions of even and odd parity are both stable. In αω-dynamos long-term variations between even and odd parity are possible. Comparison with similar variations of the sunspot number is made. Title: Non-axisymmetric magnetic fields in turbulent gas discs. Authors: Donner, K. J.; Brandenburg, A. Bibcode: 1989dad..conf..151D Altcode: Large-scale magnetic fields could play an important role in the dynamics of astrophysical discs. Here the authors report some results showing how the structure of non-axisymmetric magnetic fields is affected by differential rotation. A turbulent disc is likely to be surrounded by a gaseous corona. The authors study in particular how the field structure in the disc is affected by surrounding gas. The results are used to discuss the origin of galactic magnetic fields. Title: Hydrodynamic Green's functions for atmospheric oscillations Authors: Brandenburg, A. Bibcode: 1988A&A...203..154B Altcode: A Green's function tensor is derived giving the response of an isothermal atmosphere to small disturbances representing deviations from a state of static stratification. A Hermitian differential operator is first derived that describes an adiabatic flow in a plane-parallel isothermal atmosphere. This operator is inverted using a Fourier transformation to give the Green's function tensor. The inverse Fourier transformation is then carried out for an axisymmetric initial condition. Different properties of g-modes and the range of validity of the anelastic approximation are discussed. An approximate, explicit solution for small bubbles is given. Title: Gravity Wave Generation by Largescale Bubbles Authors: Brandenburg, A. Bibcode: 1988IAUS..123..383B Altcode: The response of an isothermal atmosphere to small disturbances in entropy is studied taking compressible effects fully into account. The method of Green's functions is applied to solve the linearized hydrodynamic equations by Fourier transformation. A bubble may be created by perturbing the entropy within a finite volume. At first Lamb waves will be then emitted radially and the bubble undergoes a series of Brunt-Väisälä oscillations. Title: Observational Constraints for Solar-Type Dynamos Authors: Tuominen, I.; Rüdiger, G.; Brandenburg, A. Bibcode: 1988ASSL..143...13T Altcode: 1988acse.conf...13T The different phenomena of solar and stellar activity are generally considered to have its origin in the turbulent convective envelopes of these stars. The authors discuss how the problem can be treated in the framework of the mean-field concept. Title: Solar oscillations in the two year range. Authors: Brandenburg, A. Bibcode: 1988sfam.conf...34B Altcode: Oscillations of the solar magnetic field pattern are considered as global resonances. It is argued that they can be standing Alfvén waves trapped in a cavity below the convection zone. Such a cavity can be formed by a strong toroidal field in the Sun. Eigenfrequencies are estimated to be in rough agreement with the observed diagnostic power spectrum of Stenflo and Vogel (1986). Title: Variation of magnetic fields and flows during the solar cycle Authors: Brandenburg, A.; Tuominen, I. Bibcode: 1988AdSpR...8g.185B Altcode: 1988AdSpR...8..185B We have studied dynamo models with realistic assumptions for the induction effects and compare the resulting magnetic fields with observations. We make use of recent results of helioseismology to infer the differential rotation and adopt mixing length approach to get the form of the α-effect, which is in general anisotropic. Dynamo models are computed numerically using an eigenvalue method. Finally, we discuss the resulting Lorentz force, which is relevant for explaining observed flows such as the torsional waves, as a back reaction of the dynamo magnetic fields. Comparison is made in particular with Mt. Wilson/Kitt Peak magnetograms and synoptic charts showing the magnetic flux, torsional oscillation pattern, and the distribution of ephemeral regions, coronal activity, and polar faculae.