Author name code: gudiksen ADS astronomy entries on 2022-09-14 author:"Gudiksen, Boris V." ------------------------------------------------------------------------ Title: Chromospheric emission from nanoflare heating in RADYN simulations Authors: Bakke, H.; Carlsson, M.; Rouppe van der Voort, L.; Gudiksen, B. V.; Polito, V.; Testa, P.; De Pontieu, B. Bibcode: 2022A&A...659A.186B Altcode: 2022arXiv220111961B Context. Heating signatures from small-scale magnetic reconnection events in the solar atmosphere have proven to be difficult to detect through observations. Numerical models that reproduce flaring conditions are essential in understanding how nanoflares may act as a heating mechanism of the corona.
Aims: We study the effects of non-thermal electrons in synthetic spectra from 1D hydrodynamic RADYN simulations of nanoflare heated loops to investigate the diagnostic potential of chromospheric emission from small-scale events.
Methods: The Mg II h and k, Ca II H and K, Ca II 854.2 nm, and Hα and Hβ chromospheric lines were synthesised from various RADYN models of coronal loops subject to electron beams of nanoflare energies. The contribution function to the line intensity was computed to better understand how the atmospheric response to the non-thermal electrons affects the formation of spectral lines and the detailed shape of their spectral profiles.
Results: The spectral line signatures arising from the electron beams highly depend on the density of the loop and the lower cutoff energy of the electrons. Low-energy (5 keV) electrons deposit their energy in the corona and transition region, producing strong plasma flows that cause both redshifts and blueshifts of the chromospheric spectra. Higher-energy (10 and 15 keV) electrons deposit their energy in the lower transition region and chromosphere, resulting in increased emission from local heating. Our results indicate that effects from small-scale events can be observed with ground-based telescopes, expanding the list of possible diagnostics for the presence and properties of nanoflares. Title: Accelerated particle beams in a 3D simulation of the quiet Sun Authors: Frogner, L.; Gudiksen, B. V.; Bakke, H. Bibcode: 2020A&A...643A..27F Altcode: 2020arXiv200514483F Context. Observational and theoretical evidence suggest that beams of accelerated particles are produced in flaring events of all sizes in the solar atmosphere, from X-class flares to nanoflares. Current models of these types of particles in flaring loops assume an isolated 1D atmosphere.
Aims: A more realistic environment for modelling accelerated particles can be provided by 3D radiative magnetohydrodynamics codes. Here, we present a simple model for particle acceleration and propagation in the context of a 3D simulation of the quiet solar atmosphere, spanning from the convection zone to the corona. We then examine the additional transport of energy introduced by the particle beams.
Methods: The locations of particle acceleration associated with magnetic reconnection were identified by detecting changes in magnetic topology. At each location, the parameters of the accelerated particle distribution were estimated from local conditions. The particle distributions were then propagated along the magnetic field, and the energy deposition due to Coulomb collisions with the ambient plasma was computed.
Results: We find that particle beams originate in extended acceleration regions that are distributed across the corona. Upon reaching the transition region, they converge and produce strands of intense heating that penetrate the chromosphere. Within these strands, beam heating consistently dominates conductive heating below the bottom of the transition region. This indicates that particle beams qualitatively alter the energy transport even outside of active regions. Title: A comprehensive three-dimensional radiative magnetohydrodynamic simulation of a solar flare Authors: Cheung, M. C. M.; Rempel, M.; Chintzoglou, G.; Chen, F.; Testa, P.; Martínez-Sykora, J.; Sainz Dalda, A.; DeRosa, M. L.; Malanushenko, A.; Hansteen, V.; De Pontieu, B.; Carlsson, M.; Gudiksen, B.; McIntosh, S. W. Bibcode: 2019NatAs...3..160C Altcode: 2018NatAs...3..160C Solar and stellar flares are the most intense emitters of X-rays and extreme ultraviolet radiation in planetary systems1,2. On the Sun, strong flares are usually found in newly emerging sunspot regions3. The emergence of these magnetic sunspot groups leads to the accumulation of magnetic energy in the corona. When the magnetic field undergoes abrupt relaxation, the energy released powers coronal mass ejections as well as heating plasma to temperatures beyond tens of millions of kelvins. While recent work has shed light on how magnetic energy and twist accumulate in the corona4 and on how three-dimensional magnetic reconnection allows for rapid energy release5,6, a self-consistent model capturing how such magnetic changes translate into observable diagnostics has remained elusive. Here, we present a comprehensive radiative magnetohydrodynamics simulation of a solar flare capturing the process from emergence to eruption. The simulation has sufficient realism for the synthesis of remote sensing measurements to compare with observations at visible, ultraviolet and X-ray wavelengths. This unifying model allows us to explain a number of well-known features of solar flares7, including the time profile of the X-ray flux during flares, origin and temporal evolution of chromospheric evaporation and condensation, and sweeping of flare ribbons in the lower atmosphere. Furthermore, the model reproduces the apparent non-thermal shape of coronal X-ray spectra, which is the result of the superposition of multi-component super-hot plasmas8 up to and beyond 100 million K. Title: Radiative MHD Simulation of a Solar Flare Authors: Cheung, Mark; Rempel, Matthias D.; Chintzoglou, Georgios; Chen, Feng; Testa, Paola; Martinez-Sykora, Juan; Sainz Dalda, Alberto; DeRosa, Marc L.; Malanushenko, Anna; Hansteen, Viggo; Carlsson, Mats; De Pontieu, Bart; Gudiksen, Boris; McIntosh, Scott W. Bibcode: 2019AAS...23431005C Altcode: We present a radiative MHD simulation of a solar flare. The computational domain captures the near-surface layers of the convection zone and overlying atmosphere. Inspired by the observed evolution of NOAA Active Region (AR) 12017, a parasitic bipolar region is imposed to emerge in the vicinity of a pre-existing sunspot. The emergence of twisted magnetic flux generates shear flows that create a pre-existing flux rope underneath the canopy field of the sunspot. Following erosion of the overlying bootstrapping field, the flux rope erupts. Rapid release of magnetic energy results in multi-wavelength synthetic observables (including X-ray spectra, narrowband EUV images, Doppler shifts of EUV lines) that are consistent with flare observations. This works suggests the super-position of multi-thermal, superhot (up to 100 MK) plasma may be partially responsible for the apparent non-thermal shape of coronal X-ray sources in flares. Implications for remote sensing observations of other astrophysical objects is also discussed. This work is an important stepping stone toward high-fidelity data-driven MHD models. Title: On the Origin of the Magnetic Energy in the Quiet Solar Chromosphere Authors: Martínez-Sykora, Juan; Hansteen, Viggo H.; Gudiksen, Boris; Carlsson, Mats; De Pontieu, Bart; Gošić, Milan Bibcode: 2019ApJ...878...40M Altcode: 2019arXiv190404464M The presence of magnetic field is crucial in the transport of energy through the solar atmosphere. Recent ground-based and space-borne observations of the quiet Sun have revealed that magnetic field accumulates at photospheric heights, via a local dynamo or from small-scale flux emergence events. However, most of this small-scale magnetic field may not expand into the chromosphere due to the entropy drop with height at the photosphere. Here we present a study that uses a high-resolution 3D radiative MHD simulation of the solar atmosphere with non-gray and non-LTE radiative transfer and thermal conduction along the magnetic field to reveal that (1) the net magnetic flux from the simulated quiet photosphere is not sufficient to maintain a chromospheric magnetic field (on average), (2) processes in the lower chromosphere, in the region dominated by magnetoacoustic shocks, are able to convert kinetic energy into magnetic energy, (3) the magnetic energy in the chromosphere increases linearly in time until the rms of the magnetic field strength saturates at roughly 4-30 G (horizontal average) due to conversion from kinetic energy, (4) and that the magnetic features formed in the chromosphere are localized to this region. Title: Emission of Joule heating events in simulations of the solar corona Authors: Kanella, Charalambos; Gudiksen, Boris V. Bibcode: 2019A&A...621A..95K Altcode: Context. Nanoscale events in cooperation with steady heating from a slow heating mechanism, such as slow-burning current-sheets, could be able to heat the corona; however, their observational traces are hard to detect via current instrumentation. After we locate heating events in magnetohydrodynamic (MHD) simulations and synthesise observational data, we extract observational signatures of small-scale events.
Aims: Our mission is threefold. The first goal is to observe the manifestation of small-scale events via three observational tools: intensity maps of three extreme ultraviolet (EUV) filters in the Atmospheric Imaging Assembly (AIA) instrument with resolution better than that in AIA images, emission measure (EM) analysis, and time-lag maps. The second goal is to identify the reason why we cannot quantify the energy release from observed events. The third goal is to study the differences between the radiation from isolated heating events and that from the whole corona.
Methods: We employed a three-dimensional magnetohydrodynamic (3D-MHD) simulation using the Bifrost code. We simulated the atmosphere of a network embedded in the quiet Sun (QS), and we identified 3D heating events in the corona in several time-steps. Then we synthesised the three observational tools for two cases. First, we considered information from the total column mass in the corona, and then we considered only regions that exhibit heating events.
Results: We report on the differences between the two regions of investigation, which also consist of the evidence to justify why observers cannot identify small-scale heating events in observations. We found that the combination of multiple heating events at different cooling phases along the line of sight gives the impression of thin elongated threads of events. For this reason, the EM as a function of temperature has a multi-thermal distribution. Both the radiation and the emission measure of the isolated heating events have values at least ten times lower than the signal calculated from the total corona. We also found that heating events move together with diffuse emission from the slow heating mechanism, and for this reason we cannot differentiate between the two. In addition, we find that the frequency of heating events and their intensity affect the EM distribution as a function of temperature. We also find that the filter's intensity, EM, and time-lag maps of heating events are different to those incorporating information from the total column mass of the corona. However, the two regions have, on average, comparable values, which are slightly smaller than the analytical cooling timescales calculated for an optically thin and radiation-dominated atmosphere. Title: Non-thermal electrons from solar nanoflares Authors: Bakke, Helle; Frogner, Lars; Gudiksen, Boris Vilhelm Bibcode: 2018arXiv181112404B Altcode: Context. We introduce a model for including accelerated particles in pure magnetohydrodynamics (MHD) simulations of the solar atmosphere. Aims. We show that the method is viable and produces results that enhance the realism of MHD simulations of the solar atmosphere. Methods. The acceleration of high-energy electrons in solar flares is an accepted fact, but is not included in the most advanced 3D simulations of the solar atmosphere. The effect of the acceleration is not known, and here we introduce a simple method to account for the ability of the accelerated electrons to move energy from the reconnection sites and into the dense transition zone and chromosphere. Results. The method was only run for a short time and with low reconnection energies, but this showed that the reconnection process itself changes, and that there is a clear effect on the observables at the impact sites of the accelerated electrons. Further work will investigate the effect on the reconnection sites and the impact sites in detail. Title: Non-thermal electrons from solar nanoflares. In a 3D radiative MHD simulation Authors: Bakke, H.; Frogner, L.; Gudiksen, B. V. Bibcode: 2018A&A...620L...5B Altcode: Context. We introduce a model for including accelerated particles in pure magnetohydrodynamics (MHD) simulations of the solar atmosphere.
Aims: We show that the method is viable and produces results that enhance the realism of MHD simulations of the solar atmosphere.
Methods: The acceleration of high-energy electrons in solar flares is an accepted fact, but is not included in the most advanced 3D simulations of the solar atmosphere. The effect of the acceleration is not known, and here we introduce a simple method to account for the ability of the accelerated electrons to move energy from the reconnection sites and into the dense transition zone and chromosphere.
Results: The method was only run for a short time and with low reconnection energies, but this showed that the reconnection process itself changes, and that there is a clear effect on the observables at the impact sites of the accelerated electrons. Further work will investigate the effect on the reconnection sites and the impact sites in detail. Title: Investigating 4D coronal heating events in magnetohydrodynamic simulations Authors: Kanella, Charalambos; Gudiksen, Boris V. Bibcode: 2018A&A...617A..50K Altcode: 2018arXiv180604495K Context. One candidate model for heating the solar corona is magnetic reconnection that embodies Ohmic dissipation of current sheets. When numerous small-scale magnetic reconnection events occur, then it is possible to heat the corona; if ever observed, these events would have been the speculated nanoflares.
Aims: Because of the limitations of current instrumentation, nanoflares cannot be resolved. But their importance is evaluated via statistics by finding the power-law index of energy distribution. This method is however biased for technical and physical reasons. We aim to overcome limitations imposed by observations and statistical analysis. This way, we identify, and study these small-scale impulsive events.
Methods: We employed a three-dimensional magnetohydrodynamic (3D MHD) simulation using the Bifrost code. We also employed a new technique to identify the evolution of 3D joule heating events in the corona. Then, we derived parameters describing the heating events in these locations, studied their geometrical properties and where they occurred with respect to the magnetic field.
Results: We report on the identification of heating events. We obtain the distribution of duration, released energy, and volume. We also find weak power-law correlation between these parameters. In addition, we extract information about geometrical parameters of 2D slices of 3D events, and about the evolution of resolved joule heating compared to the total joule heating and magnetic energy in the corona. Furthermore, we identify relations between the location of heating events and the magnetic field.
Conclusions: Even though the energy power index is less than 2, when classifying the energy release into three categories with respect to the energy release (pico-, nano-, and micro-events), we find that nano-events release 82% of the resolved energy. This percentage corresponds to an energy flux larger than that needed to heat the corona. Although no direct conclusions can be drawn, it seems that the most popular population among small-scale events is the one that contains nano-scale energetic events that are short lived with small spatial extend. Generally, the locations and size of heating events are affected by the magnitude of the magnetic field. Title: Disentangling flows in the solar transition region Authors: Zacharias, P.; Hansteen, V. H.; Leenaarts, J.; Carlsson, M.; Gudiksen, B. V. Bibcode: 2018A&A...614A.110Z Altcode: 2018arXiv180407513Z Context. The measured average velocities in solar and stellar spectral lines formed at transition region temperatures have been difficult to interpret. The dominant redshifts observed in the lower transition region naturally leads to the question of how the upper layers of the solar (and stellar) atmosphere can be maintained. Likewise, no ready explanation has been made for the average blueshifts often found in upper transition region lines. However, realistic three-dimensional radiation magnetohydrodynamics (3D rMHD) models of the solar atmosphere are able to reproduce the observed dominant line shifts and may thus hold the key to resolve these issues.
Aims: These new 3D rMHD simulations aim to shed light on how mass flows between the chromosphere and corona and on how the coronal mass is maintained. These simulations give new insights into the coupling of various atmospheric layers and the origin of Doppler shifts in the solar transition region and corona.
Methods: The passive tracer particles, so-called corks, allow the tracking of parcels of plasma over time and thus the study of changes in plasma temperature and velocity not only locally, but also in a co-moving frame. By following the trajectories of the corks, we can investigate mass and energy flows and understand the composition of the observed velocities.
Results: Our findings show that most of the transition region mass is cooling. The preponderance of transition region redshifts in the model can be explained by the higher percentage of downflowing mass in the lower and middle transition region. The average upflows in the upper transition region can be explained by a combination of both stronger upflows than downflows and a higher percentage of upflowing mass. The most common combination at lower and middle transition region temperatures are corks that are cooling and traveling downward. For these corks, a strong correlation between the pressure gradient along the magnetic field line and the velocity along the magnetic field line has been observed, indicating a formation mechanism that is related to downward propagating pressure disturbances. Corks at upper transition region temperatures are subject to a rather slow and highly variable but continuous heating process.
Conclusions: Corks are shown to be an essential tool in 3D rMHD models in order to study mass and energy flows. We have shown that most transition region plasma is cooling after having been heated slowly to upper transition region temperatures several minutes before. Downward propagating pressure disturbances are identified as one of the main mechanisms responsible for the observed redshifts at transition region temperatures.

The movie associated to Fig. 3 is available at http://www.aanda.org Title: Two-dimensional Radiative Magnetohydrodynamic Simulations of Partial Ionization in the Chromosphere. II. Dynamics and Energetics of the Low Solar Atmosphere Authors: Martínez-Sykora, Juan; De Pontieu, Bart; Carlsson, Mats; Hansteen, Viggo H.; Nóbrega-Siverio, Daniel; Gudiksen, Boris V. Bibcode: 2017ApJ...847...36M Altcode: 2017arXiv170806781M We investigate the effects of interactions between ions and neutrals on the chromosphere and overlying corona using 2.5D radiative MHD simulations with the Bifrost code. We have extended the code capabilities implementing ion-neutral interaction effects using the generalized Ohm’s law, I.e., we include the Hall term and the ambipolar diffusion (Pedersen dissipation) in the induction equation. Our models span from the upper convection zone to the corona, with the photosphere, chromosphere, and transition region partially ionized. Our simulations reveal that the interactions between ionized particles and neutral particles have important consequences for the magnetothermodynamics of these modeled layers: (1) ambipolar diffusion increases the temperature in the chromosphere; (2) sporadically the horizontal magnetic field in the photosphere is diffused into the chromosphere, due to the large ambipolar diffusion; (3) ambipolar diffusion concentrates electrical currents, leading to more violent jets and reconnection processes, resulting in (3a) the formation of longer and faster spicules, (3b) heating of plasma during the spicule evolution, and (3c) decoupling of the plasma and magnetic field in spicules. Our results indicate that ambipolar diffusion is a critical ingredient for understanding the magnetothermodynamic properties in the chromosphere and transition region. The numerical simulations have been made publicly available, similar to previous Bifrost simulations. This will allow the community to study realistic numerical simulations with a wider range of magnetic field configurations and physics modules than previously possible. Title: Realistic radiative MHD simulation of a solar flare Authors: Rempel, Matthias D.; Cheung, Mark; Chintzoglou, Georgios; Chen, Feng; Testa, Paola; Martinez-Sykora, Juan; Sainz Dalda, Alberto; DeRosa, Marc L.; Viktorovna Malanushenko, Anna; Hansteen, Viggo H.; De Pontieu, Bart; Carlsson, Mats; Gudiksen, Boris; McIntosh, Scott W. Bibcode: 2017SPD....4840001R Altcode: We present a recently developed version of the MURaM radiative MHD code that includes coronal physics in terms of optically thin radiative loss and field aligned heat conduction. The code employs the "Boris correction" (semi-relativistic MHD with a reduced speed of light) and a hyperbolic treatment of heat conduction, which allow for efficient simulations of the photosphere/corona system by avoiding the severe time-step constraints arising from Alfven wave propagation and heat conduction. We demonstrate that this approach can be used even in dynamic phases such as a flare. We consider a setup in which a flare is triggered by flux emergence into a pre-existing bipolar active region. After the coronal energy release, efficient transport of energy along field lines leads to the formation of flare ribbons within seconds. In the flare ribbons we find downflows for temperatures lower than ~5 MK and upflows at higher temperatures. The resulting soft X-ray emission shows a fast rise and slow decay, reaching a peak corresponding to a mid C-class flare. The post reconnection energy release in the corona leads to average particle energies reaching 50 keV (500 MK under the assumption of a thermal plasma). We show that hard X-ray emission from the corona computed under the assumption of thermal bremsstrahlung can produce a power-law spectrum due to the multi-thermal nature of the plasma. The electron energy flux into the flare ribbons (classic heat conduction with free streaming limit) is highly inhomogeneous and reaches peak values of about 3x1011 erg/cm2/s in a small fraction of the ribbons, indicating regions that could potentially produce hard X-ray footpoint sources. We demonstrate that these findings are robust by comparing simulations computed with different values of the saturation heat flux as well as the "reduced speed of light". Title: Identification of coronal heating events in 3D simulations Authors: Kanella, Charalambos; Gudiksen, Boris V. Bibcode: 2017A&A...603A..83K Altcode: 2017arXiv170302808K Context. The solar coronal heating problem has been an open question in the science community since 1939. One of the proposed models for the transport and release of mechanical energy generated in the sub-photospheric layers and photosphere is the magnetic reconnection model that incorporates Ohmic heating, which releases a part of the energy stored in the magnetic field. In this model many unresolved flaring events occur in the solar corona, releasing enough energy to heat the corona.
Aims: The problem with the verification and quantification of this model is that we cannot resolve small scale events due to limitations of the current observational instrumentation. Flaring events have scaling behavior extending from large X-class flares down to the so far unobserved nanoflares. Histograms of observable characteristics of flares show powerlaw behavior for energy release rate, size, and total energy. Depending on the powerlaw index of the energy release, nanoflares might be an important candidate for coronal heating; we seek to find that index.
Methods: In this paper we employ a numerical three-dimensional (3D)-magnetohydrodynamic (MHD) simulation produced by the numerical code Bifrost, which enables us to look into smaller structures, and a new technique to identify the 3D heating events at a specific instant. The quantity we explore is the Joule heating, a term calculated directly by the code, which is explicitly correlated with the magnetic reconnection because it depends on the curl of the magnetic field.
Results: We are able to identify 4136 events in a volume 24 × 24 × 9.5 Mm3 (I.e., 768 × 786 × 331 grid cells) of a specific snapshot. We find a powerlaw slope of the released energy per second equal to αP = 1.5 ± 0.02, and two powerlaw slopes of the identified volume equal to αV = 1.53 ± 0.03 and αV = 2.53 ± 0.22. The identified energy events do not represent all the released energy, but of the identified events, the total energy of the largest events dominate the energy release. Most of the energy release happens in the lower corona, while heating drops with height. We find that with a specific identification method large events can be resolved into smaller ones, but at the expense of the total identified energy releases. The energy release that cannot be identified as an event favors a low energy release mechanism.
Conclusions: This is the first step to quantitatively identify magnetic reconnection sites and measure the energy released by current sheet formation. Title: Chromospheric and Coronal Wave Generation in a Magnetic Flux Sheath Authors: Kato, Yoshiaki; Steiner, Oskar; Hansteen, Viggo; Gudiksen, Boris; Wedemeyer, Sven; Carlsson, Mats Bibcode: 2016ApJ...827....7K Altcode: 2016arXiv160608826K Using radiation magnetohydrodynamic simulations of the solar atmospheric layers from the upper convection zone to the lower corona, we investigate the self-consistent excitation of slow magneto-acoustic body waves (slow modes) in a magnetic flux concentration. We find that the convective downdrafts in the close surroundings of a two-dimensional flux slab “pump” the plasma inside it in the downward direction. This action produces a downflow inside the flux slab, which encompasses ever higher layers, causing an upwardly propagating rarefaction wave. The slow mode, excited by the adiabatic compression of the downflow near the optical surface, travels along the magnetic field in the upward direction at the tube speed. It develops into a shock wave at chromospheric heights, where it dissipates, lifts the transition region, and produces an offspring in the form of a compressive wave that propagates further into the corona. In the wake of downflows and propagating shock waves, the atmosphere inside the flux slab in the chromosphere and higher tends to oscillate with a period of ν ≈ 4 mHz. We conclude that this process of “magnetic pumping” is a most plausible mechanism for the direct generation of longitudinal chromospheric and coronal compressive waves within magnetic flux concentrations, and it may provide an important heat source in the chromosphere. It may also be responsible for certain types of dynamic fibrils. Title: Physics & Diagnostics of the Drivers of Solar Eruptions Authors: Cheung, Mark; Rempel, Matthias D.; Martinez-Sykora, Juan; Testa, Paola; Hansteen, Viggo H.; Viktorovna Malanushenko, Anna; Sainz Dalda, Alberto; DeRosa, Marc L.; De Pontieu, Bart; Carlsson, Mats; Chen, Feng; McIntosh, Scott W.; Gudiksen, Boris Bibcode: 2016SPD....47.0607C Altcode: We provide an update on our NASA Heliophysics Grand Challenges Research (HGCR) project on the ‘Physics & Diagnostics of the Drivers of Solar Eruptions’. This presentation will focus on results from a data-inspired, 3D radiative MHD model of a solar flare. The model flare results from the interaction of newly emerging flux with a pre-existing active region. Synthetic observables from the model reproduce observational features compatible with actual flares. These include signatures of coronal magnetic reconnection, chromospheric evaporation, EUV flare arcades, sweeping motion of flare ribbons and sunquakes. Title: Structures in the Outer Solar Atmosphere Authors: Fletcher, L.; Cargill, P. J.; Antiochos, S. K.; Gudiksen, B. V. Bibcode: 2016mssf.book..231F Altcode: No abstract at ADS Title: A publicly available simulation of an enhanced network region of the Sun Authors: Carlsson, Mats; Hansteen, Viggo H.; Gudiksen, Boris V.; Leenaarts, Jorrit; De Pontieu, Bart Bibcode: 2016A&A...585A...4C Altcode: 2015arXiv151007581C Context. The solar chromosphere is the interface between the solar surface and the solar corona. Modelling of this region is difficult because it represents the transition from optically thick to thin radiation escape, from gas-pressure domination to magnetic-pressure domination, from a neutral to an ionised state, from MHD to plasma physics, and from near-equilibrium (LTE) to non-equilibrium conditions.
Aims: Our aim is to provide the community with realistic simulations of the magnetic solar outer atmosphere. This will enable detailed comparison of existing and upcoming observations with synthetic observables from the simulations, thereby elucidating the complex interactions of magnetic fields and plasma that are crucial for our understanding of the dynamic outer atmosphere.
Methods: We used the radiation magnetohydrodynamics code Bifrost to perform simulations of a computational volume with a magnetic field topology similar to an enhanced network area on the Sun.
Results: The full simulation cubes are made available from the Hinode Science Data Centre Europe. The general properties of the simulation are discussed, and limitations are discussed.

The Hinode Science Data Centre Europe (http://www.sdc.uio.no/search/simulations). Title: Time Dependent Nonequilibrium Ionization of Transition Region Lines Observed with IRIS Authors: Martínez-Sykora, Juan; De Pontieu, Bart; Hansteen, Viggo H.; Gudiksen, Boris Bibcode: 2016ApJ...817...46M Altcode: 2015arXiv151200865M The properties of nonstatistical equilibrium ionization of silicon and oxygen ions are analyzed in this work. We focus on five solar targets (quiet Sun; coronal hole; plage; quiescent active region, AR; and flaring AR) as observed with the Interface Region Imaging Spectrograph (IRIS). IRIS is best suited for this work owing to the high cadence (up to 0.5 s), high spatial resolution (up to 0.″32), and high signal-to-noise ratios for O IV λ1401 and Si IV λ1402. We find that the observed intensity ratio between lines of three times ionized silicon and oxygen ions depends on their total intensity and that this correlation varies depending on the region observed (quiet Sun, coronal holes, plage, or active regions) and on the specific observational objects present (spicules, dynamic loops, jets, microflares, or umbra). In order to interpret the observations, we compare them with synthetic profiles taken from 2D self-consistent radiative MHD simulations of the solar atmosphere, where the statistical equilibrium or nonequilibrium treatment of silicon and oxygen is applied. These synthetic observations show vaguely similar correlations to those in the observations, I.e., between the intensity ratios and their intensities, but only in the nonequilibrium case do we find that (some of) the observations can be reproduced. We conclude that these lines are formed out of statistical equilibrium. We use our time-dependent nonequilibrium ionization simulations to describe the physical mechanisms behind these observed properties. Title: Numerical Modeling of the Solar Chromosphere and Corona: What Has Been Done? What Should Be Done? Authors: Hansteen, V.; Carlsson, M.; Gudiksen, B. Bibcode: 2015ASPC..498..141H Altcode: A number of increasingly sophisticated numerical simulations spanning the solar atmosphere from below the photosphere in the convection zone to far above in the corona have shed considerable insight into the role of the magnetic field in the structure and energetics of the Sun's outer layers. This development is strengthened by the wealth of observational data now coming on-line from both ground and space based observatories. In this talk we will concentrate on the successes and failures of the modeling effort thus far and discuss the inclusion of various effects not traditionally considered in the MHD description such as time dependent ionization, non-LTE radiative transfer, and generalized Ohm's law. Title: IRIS observations and 3D `realistic' MHD models of the solar chromosphere Authors: Hansteen, V.; Carlsson, M.; Gudiksen, B. Bibcode: 2015hsa8.conf...19H Altcode: The Interface Region Imaging Spectrograph (IRIS) is a NASA ``Small Explorer'' mission. It was launched in late June 2013 and since then it has obtained spectra and images from the outer solar atmosphere at unprecedented spatial and temporal resolution. Its primary goal is to probe the photosphere-corona interface: the source region of outer atmosphere heating and dynamics and a region that has an extremely complicated interplay between plasma, radiation and magnetic field. The scientific justification for IRIS hinges on the capabilities of 3D magnetohydrodynamic models to allow the confident interpretation of observed data. The interplay between observations and modeling is discussed, illustrated with examples from recent IRIS observations. Title: Structures in the Outer Solar Atmosphere Authors: Fletcher, L.; Cargill, P. J.; Antiochos, S. K.; Gudiksen, B. V. Bibcode: 2015SSRv..188..211F Altcode: 2014SSRv..tmp...52F; 2014arXiv1412.7378F The structure and dynamics of the outer solar atmosphere are reviewed with emphasis on the role played by the magnetic field. Contemporary observations that focus on high resolution imaging over a range of temperatures, as well as UV, EUV and hard X-ray spectroscopy, demonstrate the presence of a vast range of temporal and spatial scales, mass motions, and particle energies present. By focusing on recent developments in the chromosphere, corona and solar wind, it is shown that small scale processes, in particular magnetic reconnection, play a central role in determining the large-scale structure and properties of all regions. This coupling of scales is central to understanding the atmosphere, yet poses formidable challenges for theoretical models. Title: Synthesized Spectra of Optically Thin Emission Lines Authors: Olluri, K.; Gudiksen, B. V.; Hansteen, V. H.; De Pontieu, B. Bibcode: 2015ApJ...802....5O Altcode: In recent years realistic 3D numerical models of the solar atmosphere have become available. The models attempt to recreate the solar atmosphere and mimic observations in the best way, in order to make it possible to couple complicated observations with physical properties such as the temperatures, densities, velocities, and magnetic fields. We here present a study of synthetic spectra created using the Bifrost code in order to assess how well they fit with previously taken solar data. A study of the synthetic intensity, nonthermal line widths, Doppler shifts, and correlations between any two of these three components of the spectra first assuming statistical equilibrium is made, followed by a report on some of the effects nonequilibrium ionization will have on the synthesized spectra. We find that the synthetic intensities compare well with the observations. The synthetic observations depend on the assumed resolution and point-spread function (PSF) of the instrument, and we find a large effect on the results, especially for intensity and nonthermal line width. The Doppler shifts produce the reported persistent redshifts for the transition region (TR) lines and blueshifts for the upper TR and corona lines. The nonthermal line widths reproduce the well-known turnoff point around (2-3) × 105 K, but with much lower values than those observed. The nonthermal line widths tend to increase with decreasing assumed instrumental resolution, also when nonequilibrium ionization is included. Correlations between the nonthermal line width of any two TR line studies as reported by Chae et al. are reproduced, while the correlations of intensity to line width are reproduced only after applying a PSF to the data. Doppler shift correlations reported by Doschek for the TR lines and correlations of Doppler shift to nonthermal line width of the Fe xii 19.5 line reported by Doschek et al. are reproduced. Title: Non-equilibrium Ionization Effects on the Density Line Ratio Diagnostics of O IV Authors: Olluri, K.; Gudiksen, B. V.; Hansteen, V. H. Bibcode: 2013ApJ...767...43O Altcode: The dynamic timescales in the solar atmosphere are shorter than the ionization and recombination times of many ions used for line ratio diagnostics of the transition region and corona. The long ionization and recombination times for these ions imply that they can be found far from their equilibrium temperatures, and spectroscopic investigations require more care before being trusted in giving correct information on local quantities, such as density and temperature. By solving the full time-dependent rate equations for an oxygen model atom in the three-dimensional numerical model of the solar atmosphere generated by the Bifrost code, we are able to construct synthetic intensity maps and study the emergent emission. We investigate the method of electron density diagnostics through line ratio analysis of the O IV 140.1 nm to the 140.4 nm ratio, the assumptions made in carrying out the diagnostics, and the different interpretations of the electron density. The results show big discrepancies between emission in statistical equilibrium and emission where non-equilibrium (NEQ) ionization is treated. Deduced electron densities are up to an order of magnitude higher when NEQ effects are accounted for. The inferred electron density is found to be a weighted mean average electron density along the line of sight and has no relation to the temperature of emission. This study shows that numerical modeling is essential for electron density diagnostics and is a valuable tool when the ions used for such studies are expected to be out of ionization equilibrium. Though this study has been performed on the O IV ion, similar results are also expected for other transition region ions. Title: Non-equilibrium Ionization in the Bifrost Stellar Atmosphere Code Authors: Olluri, K.; Gudiksen, B. V.; Hansteen, V. H. Bibcode: 2013AJ....145...72O Altcode: The chromosphere and transition region have for the last 20 years been known to be quite dynamic layers of the solar atmosphere, characterized by timescales shorter than the ionization equilibrium timescales of many of the ions dominating emission in these regions. Due to the fast changes in the properties of the atmosphere, long ionization and recombination times can lead these ions to being found far from their equilibrium temperatures. A number of the spectral lines that we observe can therefore not be expected a priori to reflect information about local quantities such as the density or temperature, and interpreting observations requires numerical modeling. Modeling the ionization balance is computationally expensive and has earlier only been done in one dimension. However, one-dimensional models can primarily be used to investigate the possible importance of a physical effect, but cannot verify or disprove the importance of that effect in the fully three-dimensional solar atmosphere. Here, using the atomic database package DIPER, we extend one-dimensional methods and implement a solver for the rate equations of the full three-dimensional problem, using the numerical code Bifrost. We present our implementation and report on a few test cases. We also report on studies of the important C IV and Fe XII ions in a semi-realistic two-dimensional solar atmosphere model, focusing on differences between statistical equilibrium and non-equilibrium ionization results. Title: Non-equilibrium ionization in 3D numerical models Authors: Olluri, Kosovare; Gudiksen, Boris; Hansteen, Viggo Bibcode: 2012decs.confE.118O Altcode: The dynamic timescales in the chromosphere and transition region have been observed to be much smaller then the ionization equilibration timescales of many ions found in the region. Due to the fast changes in the properties of the atmosphere, long ionization- and recombination times may lead to ions being found far from their equilibrium temperatures. Spectroscopic investigations therefore needs to be interpreted with the help of numerical modeling in order to produce reliable results. By solving the rate equations within a realistic MHD simulation of the solar atmosphere, we are able to follow the ionization balance, and study the non equilibrium effects of the emitting gas. Due top lack of computation power, this has previously been done in simple 1D, but because of the many free parameters in these models, their conclusions are not free of uncertainties. The resent development in computing technology and atmospheric modeling makes it possible to study the full 3D effect of non equilibrium ionization. With the solar atmosphere model Bifrost, we have a 3D platform for calculating and following the ionization degree of important atoms of high abundances in the solar atmosphere. We will present our implementation, and a study of the carbon IV 1549 Å , Iron XII 195 Å, Oxygen IV 1399 Å and 1401 Å lines in 2D. Title: State of the art single fluid MHD numerical modeling of the coupled solar atmosphere Authors: Gudiksen, Boris Bibcode: 2012decs.confE.115G Altcode: Modeling the solar atmosphere has for a long time been known to be a very complex problem. The wealth of observational features identified in solar observations have multiplied with increasing spatial, temporal and spectral resolution. To explain the high quality of space and ground based observations, models must be very sophisticated and be able to treat a number of physical regimes, where the dominating terms in the equations change drastically. Numerical simulations are now able to explain some, but certainly not all of the observed features. The numerical complexity of solving the equations governing the physics of the solar atmosphere is very high, and a number of different numerical techniques must be used in order to create a coherent picture of the connected solar atmosphere. We are now at a level where simulations have to include a much larger range in vertical extend than has been previously done. The wealth of numerical problems arising when doing so has lead to a number of numerical codes that are specialized to deal with a specific problem, and which now are being augmented to handle a larger range of problems. Hopefully with time we will have a number of numerical codes that are sophisticated enough to deal reliably with the whole solar atmosphere. I will give a review of some the codes that have been able to produce results from a fully connected solar model. Title: Non-equilibrium ionization in 3D numerical models Authors: Olluri, Kosovare; Gudiksen, Boris; Hansteen, Viggoh Bibcode: 2012decs.confE.117O Altcode: The dynamic timescales in the chromosphere and transition region have been observed to be much smaller then the ionization equilibration timescales of many ions found in the region. Due to the fast changes in the properties of the atmosphere, long ionization- and recombination times may lead to ions being found far from their equilibrium temperatures. Spectroscopic investigations therefore needs to be interpreted with the help of numerical modeling in order to produce reliable results. By solving the rate equations within a realistic MHD simulation of the solar atmosphere, we are able to follow the ionization balance, and study the non equilibrium effects of the emitting gas. Due top lack of computation power, this has previously been done in simple 1D, but because of the many free parameters in these models, their conclusions are not free of uncertainties. The resent development in computing technology and atmospheric modeling makes it possible to study the full 3D effect of non equilibrium ionization. With the solar atmosphere model Bifrost, we have a 3D platform for calculating and following the ionization degree of important atoms of high abundances in the solar atmosphere. We will present our implementation, and a study of the carbon IV 1549 Å , Iron XII 195 Å, Oxygen IV 1399 Å and 1401 Å lines in 2D. Title: The stellar atmosphere simulation code Bifrost. Code description and validation Authors: Gudiksen, B. V.; Carlsson, M.; Hansteen, V. H.; Hayek, W.; Leenaarts, J.; Martínez-Sykora, J. Bibcode: 2011A&A...531A.154G Altcode: 2011arXiv1105.6306G Context. Numerical simulations of stellar convection and photospheres have been developed to the point where detailed shapes of observed spectral lines can be explained. Stellar atmospheres are very complex, and very different physical regimes are present in the convection zone, photosphere, chromosphere, transition region and corona. To understand the details of the atmosphere it is necessary to simulate the whole atmosphere since the different layers interact strongly. These physical regimes are very diverse and it takes a highly efficient massively parallel numerical code to solve the associated equations.
Aims: The design, implementation and validation of the massively parallel numerical code Bifrost for simulating stellar atmospheres from the convection zone to the corona.
Methods: The code is subjected to a number of validation tests, among them the Sod shock tube test, the Orzag-Tang colliding shock test, boundary condition tests and tests of how the code treats magnetic field advection, chromospheric radiation, radiative transfer in an isothermal scattering atmosphere, hydrogen ionization and thermal conduction. Results.Bifrost completes the tests with good results and shows near linear efficiency scaling to thousands of computing cores. Title: On the minimum temperature of the quiet solar chromosphere Authors: Leenaarts, J.; Carlsson, M.; Hansteen, V.; Gudiksen, B. V. Bibcode: 2011A&A...530A.124L Altcode: 2011arXiv1104.5081L
Aims: We aim to provide an estimate of the minimum temperature of the quiet solar chromosphere.
Methods: We perform a 2D radiation-MHD simulation spanning the upper convection zone to the lower corona. The simulation includes non-LTE radiative transfer and an equation-of-state that includes non-equilibrium ionization of hydrogen and non-equilibrium H2 molecule formation. We analyze the reliability of the various assumptions made in our model in order to assess the realism of the simulation.
Results: Our simulation contains pockets of cool gas with down to 1660 K from 1 Mm up to 3.2 Mm height. It overestimates the radiative heating, and contains non-physical heating below 1660 K. Therefore we conclude that cool pockets in the quiet solar chromosphere might have even lower temperatures than in the simulation, provided that there exist areas in the chromosphere without significant magnetic heating. We suggest off-limb molecular spectroscopy to look for such cool pockets and 3D simulations including a local dynamo and a magnetic carpet to investigate Joule heating in the quiet chromosphere. Title: Three-dimensional surface convection simulations of metal-poor stars. The effect of scattering on the photospheric temperature stratification Authors: Collet, R.; Hayek, W.; Asplund, M.; Nordlund, Å.; Trampedach, R.; Gudiksen, B. Bibcode: 2011A&A...528A..32C Altcode: 2011arXiv1101.3265C Context. Three-dimensional (3D) radiative hydrodynamic model atmospheres of metal-poor late-type stars are characterized by cooler upper photospheric layers than their one-dimensional counterparts. This property of 3D model atmospheres can dramatically affect the determination of elemental abundances from temperature-sensitive spectral features, with profound consequences on galactic chemical evolution studies.
Aims: We investigate whether the cool surface temperatures predicted by 3D model atmospheres of metal-poor stars can be ascribed to approximations in the treatment of scattering during the modelling phase.
Methods: We use the Bifrost code to construct 3D model atmospheres of metal-poor stars and test three different ways to handle scattering in the radiative transfer equation. As a first approach, we solve iteratively the radiative transfer equation for the general case of a source function with a coherent scattering term, treating scattering in a correct and consistent way. As a second approach, we solve the radiative transfer equation in local thermodynamic equilibrium approximation, neglecting altogether the contribution of continuum scattering to extinction in the optically thin layers; this has been the default mode in our previous 3D modelling as well as in present Stagger-Code models. As our third and final approach, we treat continuum scattering as pure absorption everywhere, which is the standard case in the 3D modelling by the CO5BOLD collaboration.
Results: For all simulations, we find that the second approach produces temperature structures with cool upper photospheric layers very similar to the case in which scattering is treated correctly. In contrast, treating scattering as pure absorption leads instead to significantly hotter and shallower temperature stratifications. The main differences in temperature structure between our published models computed with the Stagger- and Bifrost codes and those generated with the CO5BOLD code can be traced to the different treatments of scattering.
Conclusions: Neglecting the contribution of continuum scattering to extinction in optically thin layers provides a good approximation to the full, iterative solution of the radiative transfer equation in metal-poor stellar surface convection simulations, and at a much lower computational cost. Our results also demonstrate that the cool temperature stratifications predicted for metal-poor late-type stars by previous models by our collaboration are not an artifact of the approximated treatment of scattering. Title: Radiative transfer with scattering for domain-decomposed 3D MHD simulations of cool stellar atmospheres. Numerical methods and application to the quiet, non-magnetic, surface of a solar-type star Authors: Hayek, W.; Asplund, M.; Carlsson, M.; Trampedach, R.; Collet, R.; Gudiksen, B. V.; Hansteen, V. H.; Leenaarts, J. Bibcode: 2010A&A...517A..49H Altcode: 2010arXiv1007.2760H
Aims: We present the implementation of a radiative transfer solver with coherent scattering in the new BIFROST code for radiative magneto-hydrodynamical (MHD) simulations of stellar surface convection. The code is fully parallelized using MPI domain decomposition, which allows for large grid sizes and improved resolution of hydrodynamical structures. We apply the code to simulate the surface granulation in a solar-type star, ignoring magnetic fields, and investigate the importance of coherent scattering for the atmospheric structure.
Methods: A scattering term is added to the radiative transfer equation, requiring an iterative computation of the radiation field. We use a short-characteristics-based Gauss-Seidel acceleration scheme to compute radiative flux divergences for the energy equation. The effects of coherent scattering are tested by comparing the temperature stratification of three 3D time-dependent hydrodynamical atmosphere models of a solar-type star: without scattering, with continuum scattering only, and with both continuum and line scattering.
Results: We show that continuum scattering does not have a significant impact on the photospheric temperature structure for a star like the Sun. Including scattering in line-blanketing, however, leads to a decrease of temperatures by about 350 K below log10 τ5000 ⪉ -4. The effect is opposite to that of 1D hydrostatic models in radiative equilibrium, where scattering reduces the cooling effect of strong LTE lines in the higher layers of the photosphere. Coherent line scattering also changes the temperature distribution in the high atmosphere, where we observe stronger fluctuations compared to a treatment of lines as true absorbers. Title: On the nature of coronal loops above the quiet sun network Authors: Bingert, S.; Zacharias, P.; Peter, H.; Gudiksen, B. V. Bibcode: 2010AdSpR..45..310B Altcode: The structure and dynamics of a box in a stellar corona can be modeled employing a 3D MHD model for different levels of magnetic activity. Depending on the magnetic flux through the surface the nature of the resulting coronal structures can be quite different. We investigate a model of an active region for two sunspots surrounded by magnetic field patches comparable in magnetic flux to the sunspots. The model results in emission from the model corona being concentrated in loop structures. In Gudiksen and Nordlund (2005) the loops seen in EUV and X-ray emission outline the magnetic field, following the general paradigm. However, in our model, where the magnetic field is far from a force-free state, the loops seen in X-ray emission do not follow the magnetic field lines. This result is of interest especially for loops as found in areas where the magnetic field emerging from active regions interacts with the surrounding network. Title: Chromospheric heating and structure as determined from high resolution 3D simulations . Authors: Carlsson, M.; Hansteen, V. H.; Gudiksen, B. V. Bibcode: 2010MmSAI..81..582C Altcode: 2010arXiv1001.1546C We have performed 3D radiation MHD simulations extending from the convection zone to the corona covering a box 16 Mm3 at 32 km spatial resolution. The simulations show very fine structure in the chromosphere with acoustic shocks interacting with the magnetic field. Magnetic flux concentrations have a temperature lower than the surroundings in the photosphere but higher in the low chromosphere. The heating is there mostly through ohmic dissipation preferentially at the edges of the flux concentrations. The magnetic field is often wound up around the flux concentrations. When acoustic waves travel up along the field this topology leads to swirling motions seen in chromospheric diagnostic lines such as the calcium infrared triplet. Title: Photospheric Motions and Their Effects on the Corona: A Numerical Approach Authors: Gomes de Jesus, Leandro Filipe; Gudiksen, Boris Vilhelm Bibcode: 2009ApJ...704..705G Altcode: 2009arXiv0908.4174G; 2009ApJ...704..705F We perform a number of numerical simulations of the solar corona with the aim of understanding how it responds to different conditions in the photosphere. By changing parameters which govern the motion of the plasma at the photosphere, we study the behavior of the corona, in particular, the effects on the current density generated. A magnetohydrodynamics code is used to run simulations, using a 20 × 20 × 20 Mm3 box with timespans ranging from one hundred to several hundreds of minutes. All the experiments show a fast initial increase of the current density, followed by a stabilization around an asymptotic value which depends on the photospheric conditions. These asymptotic average current densities as well as the turnover points are discussed. Title: Coronal dynamics and heating theories Authors: Gudiksen, Boris V. Bibcode: 2009AdSpR..43..108G Altcode: A large number of coronal heating theories have been proposed and most of them can be labeled as AC or DC heating theories. Here a short description of these two main theories is given, and the results of a DC heating model simulation is explained in more detail. As a result of that model, arguments are given for putting emphasis on launching a very fast spectrograph, ideally a imaging spectrograph as soon as possible. Title: On the Nature of Coronal Loops Authors: Bingert, S.; Zacharias, P.; Peter, H.; Gudiksen, B. Bibcode: 2008ESPM...12.3.29B Altcode: The structure and dynamics of a box in a stellar corona can be modeled employing a 3D MHD model for different levels of magnetic activity.

Depending on the magnetic flux through the surface the nature of the resulting coronal structures can be quite different.

We will compare two different models of an active region, one for two basically isolated sunspots, and another one for two sunspots surrounded by magnetic field patches similar to the chromospheric network.

The current paradigm is that these loops follow magnetic field lines as pearls on a string, and thus the majority of present corona models describe structures following the field lines.

Our study challenges this paradigm by showing through a three-dimensional model that coronal structures in complex magnetic field geometries might appear loop-like while they are not aligned with the magnetic field.

Using a forward model approach, both models result in emission from the corona being concentrated in loop structures.

In the first case the loops seen in EUV and X-ray emission are following the magnetic field.

However, in the second case, where the magnetic field is far from a force-free state, the loops seen in X-ray emission do not follow the magnetic field, but are more related to the current sheets formed in response to the footpoint motions of the magnetic field.

This result is of interest especially for loops as found in areas where the magnetic field emerging from active regions interacts with the surrounding network or in the complex magnetic structures within chromospheric network patches. Title: On the nature of coronal loops Authors: Peter, H.; Bingert, S.; Gudiksen, B. V. Bibcode: 2008AGUSMSP41C..05P Altcode: No abstract at ADS Title: Topological Dissipation & The Solar Corona Authors: Gudiksen, B. V. Bibcode: 2007ASPC..369..269G Altcode: Reconnection in the solar corona has to take place, as was convincingly shown by tet{Parker72}, the question remains if it is sufficient to heat the corona. One of the major problems in coronal physics, is modeling reconnection. Reconnection is the basis of most heating models, in spite the fact that we really don't know how reconnection works. Simulating reconnection with realistic parameters is highly problematic and the solar corona has a parameter space not well explored. Here I try to give a hint of what conclusions one can reach about reconnection from large scale simulations of the solar corona. A model of the solar corona with a numerical diffusion reproduces a number of observables, and seem to reproduce the corona well, only using minimal assumptions. The overall well reproduced corona, means that it is highly likely that reconnection does not differ much from the diffusion scheme of the numerical code. That means that reconnection in the solar corona transfers most of the liberated magnetic energy into heat locally and mechanisms such as waves and high energy particles can not carry the a significant part of the energy released in reconnection. Title: 3D Numerical Models of the Chromosphere, Transition Region, and Corona Authors: Hansteen, V. H.; Carlsson, M.; Gudiksen, B. Bibcode: 2007ASPC..368..107H Altcode: 2007arXiv0704.1511H A major goal in solar physics has during the last five decades been to find how energy flux generated in the solar convection zone is transported and dissipated in the outer solar layers. Progress in this field has been slow and painstaking. However, advances in computer hardware and numerical methods, vastly increased observational capabilities and growing physical insight seem finally to be leading towards understanding. Here we present exploratory numerical MHD models that span the entire solar atmosphere from the upper convection zone to the lower corona. These models include non-grey, non-LTE radiative transport in the photosphere and chromosphere, optically thin radiative losses as well as magnetic field-aligned heat conduction in the transition region and corona. Title: Heating the solar corona. Authors: Gudiksen, B. V. Bibcode: 2007MmSAI..78..293G Altcode: The heating mechanism at work in the solar corona has been unknown since the temperature of the corona was discovered in the late nineteen thirties. Here I will present results from a model which we believe is the first model which allows forward modeling of observational signatures, and can fit several observational features of the solar corona. If this model proves to be a correct representation of the solar corona, the question of the coronal heating mechanism will finally be solved. Title: Connections: Photosphere -- Chromosphere - Corona Authors: Gudiksen, B. V. Bibcode: 2006ASPC..354..331G Altcode: The chromosphere is not only the region where the atmosphere goes from being optically thick to optically thin, but also the region where the dynamics changes from being controlled by the plasma to being controlled by the magnetic field. The magnetic field changes from being concentrated in small regions to being space filling. This expansion has traditionally been modeled by the magnetic funnel or wine-glass picture. For several reasons it is hard to gain any information about the magnetic field in this region, so this model remains unconfirmed. Three recent methods to acquire magnetic field information from this interesting region will be reviewed, and I will argue that the results from such investigations will require that we heavily revise the simplistic magnetic funnel picture. Title: Forward Modeling of the Corona of the Sun and Solar-like Stars: From a Three-dimensional Magnetohydrodynamic Model to Synthetic Extreme-Ultraviolet Spectra Authors: Peter, Hardi; Gudiksen, Boris V.; Nordlund, Åke Bibcode: 2006ApJ...638.1086P Altcode: 2005astro.ph..3342P A forward model is described in which we synthesize spectra from an ab initio three-dimensional MHD simulation of an outer stellar atmosphere, where the coronal heating is based on braiding of magnetic flux due to photospheric footpoint motions. We discuss the validity of assumptions such as ionization equilibrium and investigate the applicability of diagnostics like the differential emission measure inversion. We find that the general appearance of the synthesized corona is similar to the solar corona and that, on a statistical basis, integral quantities such as average Doppler shifts or differential emission measures are reproduced remarkably well. The persistent redshifts in the transition region, which have puzzled theorists since their discovery, are explained by this model as caused by the flows induced by the heating through braiding of magnetic flux. While the model corona is only slowly evolving in intensity, as is observed, the amount of structure and variability in Doppler shift is very large. This emphasizes the need for fast coronal spectroscopic observations, as the dynamical response of the corona to the heating process manifests itself in a comparably slow evolving coronal intensity but rapid changes in Doppler shift. Title: Coronal dynamics and heating theories Authors: Gudiksen, B. V.; Nordlund, Aa. Bibcode: 2006cosp...36.3545G Altcode: 2006cosp.meet.3545G The solar corona has been modeled as a collection of single hydrostatic loops and as a hydrostatic plane parallel atmosphere but these models have had serious problems reproducing the observations made of the solar corona The favored coronal heating models rely on large gradients in wave speed for AC models and gradients in the magnetic field for DC models and both provide an energy release that has no reason to be uniform across the magnetic field and so the heating function at play in the solar corona is most likely intermittent in both space and time and we must therefore embrace a dynamic model of the corona This conclusion is supported by high cadence high resolution observations of the chromosphere and transition region which show a very dynamic atmosphere I will concentrate on a 3D MHD simulation of the solar atmosphere from the photosphere to the low corona and will show that even for a quiescent active region and even though the observed intensity of the loops is close to constant the loops are not in a static equilibrium The corona is very dynamic and images made from the simulation of doppler shifts show much more time dependence and intermittency than does images showing only intensity Title: Coronal Heating Through Braiding of Magnetic Field Lines Synthesized Coronal EUV Emission and Magnetic Structure Authors: Peter, H.; Gudiksen, B. V.; Nordlund, A. Bibcode: 2005ESASP.596E..14P Altcode: 2005ccmf.confE..14P No abstract at ADS Title: EUV Emission from a 3D MHD Coronal Model: Temporal Variability in a Synthesized Corona Authors: Peter, H.; Gudiksen, B. V.; Nordlund, Å. Bibcode: 2005ESASP.592..527P Altcode: 2005soho...16E..98P; 2005ESASP.592E..98P No abstract at ADS Title: The Structure of the Base of the Corona Authors: Bingert, S.; Peter, H.; Gudiksen, B.; Nordlund, Ake Bibcode: 2005ESASP.592..471B Altcode: 2005ESASP.592E..84B; 2005soho...16E..84B No abstract at ADS Title: 3D Numerical Models of Quiet Sun Coronal Heating Authors: Hansteen, V. H.; Gudiksen, B. Bibcode: 2005ESASP.592..483H Altcode: 2005soho...16E..87H; 2005ESASP.592E..87H No abstract at ADS Title: DC Heating - Is it Enough? (Invited) Authors: Gudiksen, B. V. Bibcode: 2005ESASP.592..165G Altcode: 2005soho...16E..25G; 2005ESASP.592E..25G No abstract at ADS Title: Erratum: ``An AB Initio Approach to Solar Coronal Loops'' (ApJ, 618, 1031 [2005]) Authors: Gudiksen, Boris Vilhelm; Nordlund, Åke Bibcode: 2005ApJ...623..597G Altcode: Because of an error at the Press, incorrect versions of Figures 4 (top and bottom panels), 5, 7, and 9 were published. In all these figures, a dotted or dash-dotted line appeared as a solid line. The correct figures appear below. Figures 4 (middle panel), 6, 8, and 10 are also reproduced here for comparison purposes. The Press sincerely regrets these errors. Title: Erratum: ``An AB Initio Approach to the Solar Coronal Heating Problem'' (ApJ, 618, 1020 [2005]) Authors: Gudiksen, Boris Vilhelm; Nordlund, Åke Bibcode: 2005ApJ...623..600G Altcode: Because of an error at the Press, an incorrect version of Figure 5 was published, in which what should be a dash-dotted line (showing convective flux) appears as a solid line. The correct version appears below. The Press sincerely regrets the error. Title: Tackling the coronal heating problem using 3D MHD coronal simulations with spectral synthesis Authors: Peter, H.; Gudiksen, B. V.; Nordlund, A. Bibcode: 2005ESASP.560...59P Altcode: 2005csss...13...59P No abstract at ADS Title: Dynamo action in M-dwarfs Authors: Dorch, S. B. F.; Gudiksen, B. V.; Ludwig, H. -G. Bibcode: 2005ESASP.560..515D Altcode: 2005csss...13..515D; 2004astro.ph..9219D Magnetic activity in M-dwarfs present enigmatic questions: On the one hand they have higher field strengths and larger filling factors than the magnetic field on the Sun, on the other hand, they are fully convective and their atmospheres are more neutral, hence they do not have an undershoot layer for magnetic flux storage and as we show here, cannot have small-scale dynamo action in their photospheres either. We present a discussion of these facts and propose a new numerical model to investigate M-dwarf magnetism. Title: An AB Initio Approach to Solar Coronal Loops Authors: Gudiksen, Boris Vilhelm; Nordlund, Åke Bibcode: 2005ApJ...618.1031G Altcode: 2004astro.ph..7267G Data from recent numerical simulations of the solar corona and transition region are analyzed, and the magnetic field connections between the low corona and the photosphere are found to be close to those of a potential field. The field line-to-field line displacements follow a power-law distribution with typical displacements of just a few Mm. Three loops visible in simulated TRACE filters are analyzed in detail and found to have significantly different heating rates and distributions thereof, one of them showing a small-scale heating event. The dynamical structure is complicated, even though all the loops are visible in a single filter along most of their lengths. The loops are nonstatic and are in the process of evolving into loops with very different characteristics. Differential emission measure (DEM) curves along one of the loops illustrate that DEM curves have to be treated carefully if physical characteristics are to be extracted. Title: An Ab Initio Approach to the Solar Coronal Heating Problem Authors: Gudiksen, Boris Vilhelm; Nordlund, Åke Bibcode: 2005ApJ...618.1020G Altcode: 2004astro.ph..7266G We present an ab initio approach to the solar coronal heating problem by modeling a small part of the solar corona in a computational box using a three-dimensional MHD code including realistic physics. The observed solar granular velocity pattern and its amplitude and vorticity power spectra, as reproduced by a weighted Voronoi tessellation method, are used as a boundary condition that generates a Poynting flux in the presence of a magnetic field. The initial magnetic field is a potential extrapolation of a SOHO/MDI high-resolution magnetogram, and a standard stratified atmosphere is used as a thermal initial condition. Except for the chromospheric temperature structure, which is kept nearly fixed, the initial conditions are quickly forgotten because the included Spitzer conductivity and radiative cooling function have typical timescales much shorter than the time span of the simulation. After a short initial start-up period, the magnetic field is able to dissipate (3-4)×106ergscm-2s-1 in a highly intermittent corona, maintaining an average temperature of ~106 K, at coronal density values for which simulated images of the TRACE 171 and 195 Å passbands reproduce observed photon count rates. Title: Analysis of Synthetic EUV Spectra from 3d Models of the Corona Authors: Bingert, S.; Peter, H.; Gudiksen, B.; Nordlund, A.; Dobler, W. Bibcode: 2004ESASP.575..348B Altcode: 2004soho...15..348B No abstract at ADS Title: Synthetic EUV Spectra from 3D MHD Coronal Simulations: Coronal Heating Through Magnetic Braiding Authors: Peter, H.; Gudiksen, B. V.; Nordlund, Å. Bibcode: 2004ESASP.575...50P Altcode: 2004soho...15...50P No abstract at ADS Title: Coronal Heating through Braiding of Magnetic Field Lines Authors: Peter, Hardi; Gudiksen, Boris V.; Nordlund, Åke Bibcode: 2004ApJ...617L..85P Altcode: 2004astro.ph..9504P Cool stars such as our Sun are surrounded by a million degree hot outer atmosphere, the corona. For more than 60 years, the physical nature of the processes heating the corona to temperatures well in excess of those on the stellar surface have remained puzzling. Recent progress in observational techniques and numerical modeling now opens a new window to approach this problem. We present the first coronal emission-line spectra synthesized from three-dimensional numerical models describing the evolution of the dynamics and energetics as well as of the magnetic field in the corona. In these models the corona is heated through motions on the stellar surface that lead to a braiding of magnetic field lines inducing currents that are finally dissipated. These forward models enable us to synthesize observed properties such as (average) emission-line Doppler shifts or emission measures in the outer atmosphere, which until now have not been understood theoretically, even though many suggestions have been made in the past. As our model passes these observational tests, we conclude that the flux braiding mechanism is a prime candidate for being the dominant heating process of the magnetically closed corona of the Sun and solar-like stars. 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: 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: An Ab Initio Approach to the Solar Coronal Heating Problem Authors: Gudiksen, B. V.; Nordlund, Å. Bibcode: 2004IAUS..219..488G Altcode: No abstract at ADS Title: The coronal heating problem Authors: Gudiksen, Boris V. Bibcode: 2004PhDT.......169G Altcode: The heating of the solar corona has been investigated during four of decades and several mechanisms able to produce heating have been proposed. It has until now not been possible to produce quantitative estimates that would establish any of these heating mechanism as the most important in the solar corona. In order to investigate which heating mechanism is the most important, a more detailed approach is needed.

In this thesis, the heating problem is approached "ab initio";, using well observed facts and including realistic physics in a 3D magneto-hydrodynamic simulation of a small part of the solar atmosphere. The "engine" of the heating mechanism is the solar photospheric velocity field, that braids the magnetic field into a configuration where energy has to be dissipated. The initial magnetic field is taken from an observation of a typical magnetic active region scaled down to fit inside the computational domain. The driving velocity field is generated by an algorithm that reproduces the statistical and geometrical fingerprints of solar granulation. Using a standard model atmosphere as the thermal initial condition, the simulation goes through a short startup phase, where the initial thermal stratification is quickly forgotten, after which the simulation stabilizes in statistical equilibrium. In this state, the magnetic field is able to dissipate the same amount of energy as is estimated to be lost through radiation, which is the main energy loss mechanism in the solar corona.

The simulation produces heating that is intermittent on the smallest resolved scales and hot loops similar to those observed through narrow band filters in the ultra violet. Other observed characteristics of the heating are reproduced, as well as a coronal temperature of roughly one million K. Because of the ab initio approach, the amount of heating produced in these simulations represents a lower limit to coronal heating and the conclusion is that such heating of the corona is unavoidable. Title: Dark cores in sunspot penumbral filaments Authors: Scharmer, Göran B.; Gudiksen, Boris V.; Kiselman, Dan; Löfdahl, Mats G.; Rouppe van der Voort, Luc H. M. Bibcode: 2002Natur.420..151S Altcode: Sunspot umbrae-the dark central regions of the spots-are surrounded by brighter filamentary penumbrae, the existence of which remains largely inexplicable. The penumbral filaments contain magnetic fields with varying inclinations and are associated with flowing gas, but discriminating between theoretical models has been difficult because the structure of the filaments has not hitherto been resolved. Here we report observations of penumbral filaments that reveal dark cores inside them. We cannot determine the nature of these dark cores, but their very existence provides a crucial test for any model of penumbrae. Our images also reveal other very small structures, in line with the view that many of the fundamental physical processes in the solar photosphere occur on scales smaller than 100km. Title: Bulk Heating and Slender Magnetic Loops in the Solar Corona Authors: Gudiksen, Boris Vilhelm; Nordlund, Åke Bibcode: 2002ApJ...572L.113G Altcode: The heating of the solar corona and the puzzle of the slender high reaching magnetic loops seen in observations from the Transition Region and Coronal Explorer (TRACE) has been investigated through three-dimensional numerical simulations and found to be caused by the well-observed plasma flows in the photosphere displacing the footpoints of magnetic loops in a nearly potential configuration. It is found that even the small convective displacements cause magnetic dissipation sufficient to heat the corona to temperatures of the order of a million K. The heating is intermittent in both space and time-at any one height and time it spans several orders of magnitude, and localized heating causes transonic flows along field lines, which explains the observed nonhydrostatic stratification of loops that are bright in emission measure. Title: Bright loops in the solar corona Authors: Gudiksen, Boris V.; Nordlund, Aake Bibcode: 2002astro.ph..3167G Altcode: The heating of the solar corona and the puzzle of the slender high reaching magnetic loops seen in observations from the Transition Region And Coronal Explorer(TRACE) has been investigated through 3D numerical simulations, and found to be caused by the well observed plasma flows in the photosphere displacing the footpoints of magnetic loops in a nearly potential configuration. It is found that even the small convective displacements cause magnetic dissipation sufficient to heat the corona to temperatures of the order of a million Kelvin. The heating is intermittent in both space and time - at any one height and time it spans several orders of magnitude, and localized heating causes transonic flows along field lines, which explains the observed non-hydrostatic equilibrium of loops that are bright in emission measure. Title: Bulk and Loop Heating of the Solar Corona Authors: Gudiksen, Boris Bibcode: 2002smra.progE...7G Altcode: No abstract at ADS Title: Flux-loss of buoyant ropes interacting with convective flows Authors: Dorch, S. B. F.; Gudiksen, B. V.; Abbett, W. P.; Nordlund, Å. Bibcode: 2001A&A...380..734D Altcode: 2001astro.ph.10205D We present 3-d numerical magneto-hydrodynamic simulations of a buoyant, twisted magnetic flux rope embedded in a stratified, solar-like model convection zone. The flux rope is given an initial twist such that it neither kinks nor fragments during its ascent. Moreover, its magnetic energy content with respect to convection is chosen so that the flux rope retains its basic geometry while being deflected from a purely vertical ascent by convective flows. The simulations show that magnetic flux is advected away from the core of the flux rope as it interacts with the convection. The results thus support the idea that the amount of toroidal flux stored at or near the bottom of the solar convection zone may currently be underestimated.