Author name code: pietarila-graham ADS astronomy entries on 2022-09-14 author:Pietarila Graham, Jonathan ------------------------------------------------------------------------ Title: Instrumental and Observational Artifacts in Quiet Sun Magnetic Flux Cancellation Functions Authors: Pietarila, A.; Pietarila Graham, J. Bibcode: 2013SoPh..282..389P Altcode: 2012arXiv1209.6388P Under the assumption that the photospheric quiet Sun magnetic field is turbulent, the cancellation function has previously been used to estimate the true, resolution-independent mean, unsigned vertical flux «|Bztrue. We show that the presence of network elements, noise, and seeing complicate the measurement of accurate cancellation functions and their power law exponents κ. Failure to exclude network elements previously led to estimates that were too low for both the cancellation exponent κ and «|Bztrue. However, both κ and «|Bztrue are overestimated due to noise in magnetograms. While no conclusive value can be derived with data from current instruments, our Hinode/SP results of κ⪅0.38 and «|Bztrue⪅270 gauss can be taken as upper bounds. Title: Not much helicity is needed to drive large-scale dynamos Authors: Pietarila Graham, Jonathan; Blackman, Eric G.; Mininni, Pablo D.; Pouquet, Annick Bibcode: 2012PhRvE..85f6406P Altcode: 2011arXiv1108.3039P Understanding the in situ amplification of large-scale magnetic fields in turbulent astrophysical rotators has been a core subject of dynamo theory. When turbulent velocities are helical, large-scale dynamos that substantially amplify fields on scales that exceed the turbulent forcing scale arise, but the minimum sufficient fractional kinetic helicity fh,C has not been previously well quantified. Using direct numerical simulations for a simple helical dynamo, we show that fh,C decreases as the ratio of forcing to large-scale wave numbers kF/kmin increases. From the condition that a large-scale helical dynamo must overcome the back reaction from any nonhelical field on the large scales, we develop a theory that can explain the simulations. For kF/kmin⩾8 we find fh,C≲3%, implying that very small helicity fractions strongly influence magnetic spectra for even moderate-scale separation. Title: Universality of the Small-scale Dynamo Mechanism Authors: Moll, R.; Pietarila Graham, J.; Pratt, J.; Cameron, R. H.; Müller, W. -C.; Schüssler, M. Bibcode: 2011ApJ...736...36M Altcode: 2011arXiv1105.0546M We quantify possible differences between turbulent dynamo action in the Sun and the dynamo action studied in idealized simulations. For this purpose, we compare Fourier-space shell-to-shell energy transfer rates of three incrementally more complex dynamo simulations: an incompressible, periodic simulation driven by random flow, a simulation of Boussinesq convection, and a simulation of fully compressible convection that includes physics relevant to the near-surface layers of the Sun. For each of the simulations studied, we find that the dynamo mechanism is universal in the kinematic regime because energy is transferred from the turbulent flow to the magnetic field from wavenumbers in the inertial range of the energy spectrum. The addition of physical effects relevant to the solar near-surface layers, including stratification, compressibility, partial ionization, and radiative energy transport, does not appear to affect the nature of the dynamo mechanism. The role of inertial-range shear stresses in magnetic field amplification is independent from outer-scale circumstances, including forcing and stratification. Although the shell-to-shell energy transfer functions have similar properties to those seen in mean-flow driven dynamos in each simulation studied, the saturated states of these simulations are not universal because the flow at the driving wavenumbers is a significant source of energy for the magnetic field. Title: Universality of the Small-Scale Dynamo Mechanism Authors: Pietarila Graham, Jonathan; Moll, R.; Pratt, J.; Cameron, R.; Mueller, W.; Schuessler, M. Bibcode: 2011SPD....42.1621P Altcode: 2011BAAS..43S.1621P We quantify possible differences between turbulent dynamo action in the Sun and the dynamo action studied in idealized simulation. For this purpose we compare Fourier-space shell-to-shell energy transfer rates of three incrementally more complex dynamo simulations: an incompressible, periodic simulation driven by random flow, a simulation of Boussinesq convection, and a simulation of fully compressible convection that includes physics relevant to the near-surface layers of the Sun. For each of the simulations studied, we find that energy is transferred from the turbulent flow to the magnetic field from length-scales in the inertial range of the energy spectrum. The addition of physical effects relevant to the solar near-surface layers, including stratification, compressibility, partial ionization, and radiative energy transport, does not appear to affect the nature of the dynamo mechanism. The role of inertial-range shear stresses in magnetic field amplification is independent from outer-scale circumstances, including forcing and stratification. Although shell-to-shell energy transfer functions have similar properties in each simulation studied, the saturated states of these simulations are not universal; the flow at the driving scales is a significant source of energy for the magnetic field. The mechanism of energy-transfer in kinematic small-scale dynamo simulations exhibits universal properties.

This work has been supported by the Max-Planck Society in the framework of the Interinstitutional Research Initiative Turbulent transport and ion heating, reconnection and electron acceleration in solar and fusion plasmas</u> of the MPI for Solar System Research, Katlenburg-Lindau, and the Institute for Plasma Physics, Garching (project MIF-IF-A-AERO8047). Title: Turbulent Small-Scale Dynamo Action in Solar Surface Simulations Authors: Pietarila Graham, Jonathan; Cameron, Robert; Schüssler, Manfred Bibcode: 2010ApJ...714.1606P Altcode: 2010ApJ...714.1606G; 2010arXiv1002.2750P We demonstrate that a magneto-convection simulation incorporating essential physical processes governing solar surface convection exhibits turbulent small-scale dynamo action. By presenting a derivation of the energy balance equation and transfer functions for compressible magnetohydrodynamics, we quantify the source of magnetic energy on a scale-by-scale basis. We rule out the two alternative mechanisms for the generation of the small-scale magnetic field in the simulations: the tangling of magnetic field lines associated with the turbulent cascade and Alfvénization of small-scale velocity fluctuations ("turbulent induction"). Instead, we find that the dominant source of small-scale magnetic energy is stretching by inertial-range fluid motions of small-scale magnetic field lines against the magnetic tension force to produce (against Ohmic dissipation) more small-scale magnetic field. The scales involved become smaller with increasing Reynolds number, which identifies the dynamo as a small-scale turbulent dynamo. Title: The small-scale solar surface dynamo Authors: Pietarila Graham, Jonathan; Danilovic, Sanja; Schuessler, Manfred Bibcode: 2010arXiv1003.0347P Altcode: The existence of a turbulent small-scale solar surface dynamo is likely, considering existing numerical and laboratory experiments, as well as comparisons of a small-scale dynamo in MURaM simulations with Hinode observations. We find the observed peaked probability distribution function (PDF) from Stokes-V magnetograms is consistent with a monotonic PDF of the actual vertical field strength. The cancellation function of the vertical flux density from a Hinode SP observation is found to follow a self-similar power law over two decades in length scales down to the ~200 km resolution limit. This provides observational evidence that the scales of magnetic structuring in the photosphere extend at least down to 20 km. From the power law, we determine a lower bound for the true quiet-Sun mean vertical unsigned flux density of ~43 G, consistent with our numerically-based estimates that 80% or more of the vertical unsigned flux should be invisible to Stokes-V observations at a resolution of 200 km owing to cancellation. Our estimates significantly reduce the order-of-magnitude discrepancy between Zeeman- and Hanle-based estimates. Title: The Small-Scale Solar Surface Dynamo (Keynote) Authors: Pietarila Graham, J.; Danilovic, S.; Schüssler, M. Bibcode: 2009ASPC..415...43P Altcode: The existence of a turbulent small-scale solar surface dynamo is likely, considering existing numerical and laboratory experiments, as well as comparisons of a small-scale dynamo in MURaM simulations with Hinode observations. We find the observed peaked probability distribution function (PDF) from Stokes-V magnetograms is consistent with a monotonic PDF of the actual vertical field strength. The cancellation function of the vertical flux density from a Hinode SP observation is found to follow a self-similar power law over two decades in length scales down to the ≈200 km resolution limit. This provides observational evidence that the scales of magnetic structuring in the photosphere extend at least down to 20 km. From the power law, we determine a lower bound for the true quiet-Sun mean vertical unsigned flux density of ≈43 G, consistent with our numerically-based estimates that 80% or more of the vertical unsigned flux should be invisible to Stokes-V observations at a resolution of 200 km owing to cancellation. Our estimates significantly reduce the order-of-magnitude discrepancy between Zeeman- and Hanle-based estimates. Title: Lagrangian-averaged model for magnetohydrodynamic turbulence and the absence of bottlenecks Authors: Pietarila Graham, Jonathan; Mininni, Pablo D.; Pouquet, Annick Bibcode: 2009PhRvE..80a6313P Altcode: 2008arXiv0806.2054P We demonstrate that, for the case of quasiequipartition between the velocity and the magnetic field, the Lagrangian-averaged magnetohydrodynamics (LAMHD) α model reproduces well both the large-scale and the small-scale properties of turbulent flows; in particular, it displays no increased (superfilter) bottleneck effect with its ensuing enhanced energy spectrum at the onset of the subfilter scales. This is in contrast to the case of the neutral fluid in which the Lagrangian-averaged Navier-Stokes α model is somewhat limited in its applications because of the formation of spatial regions with no internal degrees of freedom and subsequent contamination of superfilter-scale spectral properties. We argue that, as the Lorentz force breaks the conservation of circulation and enables spectrally nonlocal energy transfer (associated with Alfvén waves), it is responsible for the absence of a viscous bottleneck in magnetohydrodynamics (MHD), as compared to the fluid case. As LAMHD preserves Alfvén waves and the circulation properties of MHD, there is also no (superfilter) bottleneck found in LAMHD, making this method capable of large reductions in required numerical degrees of freedom; specifically, we find a reduction factor of ≈200 when compared to a direct numerical simulation on a large grid of 15363 points at the same Reynolds number. Title: Turbulent Magnetic Fields in the Quiet Sun: Implications of Hinode Observations and Small-Scale Dynamo Simulations Authors: Pietarila Graham, Jonathan; Danilovic, Sanja; Schüssler, Manfred Bibcode: 2009ApJ...693.1728P Altcode: 2008arXiv0812.2125P Using turbulent MHD simulations (magnetic Reynolds numbers up to ≈8000) and Hinode observations, we study effects of turbulence on measuring the solar magnetic field outside active regions. First, from synthetic Stokes V profiles for the Fe I lines at 6301 and 6302 Å, we show that a peaked probability distribution function (PDF) for observationally derived field estimates is consistent with a monotonic PDF for actual vertical field strengths. Hence, the prevalence of weak fields is greater than would be naively inferred from observations. Second, we employ the fractal self-similar geometry of the turbulent solar magnetic field to derive two estimates (numerical and observational) of the true mean vertical unsigned flux density. We also find observational evidence that the scales of magnetic structuring in the photosphere extend at least down to an order of magnitude smaller than 200 km: the self-similar power-law scaling in the signed measure from a Hinode magnetogram ranges (over two decades in length scales and including the granulation scale) down to the ≈200 km resolution limit. From the self-similar scaling, we determine a lower bound for the true quiet-Sun mean vertical unsigned flux density of ~50 G. This is consistent with our numerically based estimates that 80% or more of the vertical unsigned flux should be invisible to Stokes V observations at a resolution of 200 km owing to the cancellation of signal from opposite magnetic polarities. Our estimates significantly reduce the order-of-magnitude discrepancy between Zeeman- and Hanle-based estimates. Title: Spectral Line Selection for HMI Authors: Norton, A. A.; Pietarila Graham, J. D.; Ulrich, R. K.; Schou, J.; Tomczyk, S.; Liu, Y.; Lites, B. W.; López Ariste, A.; Bush, R. I.; Socas-Navarro, H.; Scherrer, P. H. Bibcode: 2006ASPC..358..193N Altcode: We present information on two spectral lines, Fe I 6173 Å and Ni I 6768 Å, that were candidates for use in the Helioseismic and Magnetic Imager (HMI) instrument. Both Fe I and Ni I profiles have clean continuum and no blends that threaten performance. The higher Landé factor of Fe I means its operational velocity range in regions of strong magnetic field is smaller than for Ne I. Fe I performs better than Ni I for vector magnetic field retrieval. Inversion results show that Fe I consistently determines field strength and flux more accurately than the Ni I line. Inversions show inclination and azimuthal errors are recovered to ≈2° above 600 Mx/cm2 for Fe I and above 1000 Mx/cm2 for Ni I. The Fe I line was recommended, and ultimately chosen, for use in HMI. Title: Inertial range scaling, Kármán-Howarth theorem, and intermittency for forced and decaying Lagrangian averaged magnetohydrodynamic equations in two dimensions Authors: Pietarila Graham, J.; Holm, D. D.; Mininni, P.; Pouquet, A. Bibcode: 2006PhFl...18d5106P Altcode: 2005physics...8173P We present an extension of the Kármán-Howarth theorem to the Lagrangian averaged magnetohydrodynamic (LAMHD-α) equations. The scaling laws resulting as a corollary of this theorem are studied in numerical simulations, as well as the scaling of the longitudinal structure function exponents indicative of intermittency. Numerical simulations for a magnetic Prandtl number equal to unity are presented both for freely decaying and for forced two-dimensional magnetohydrodynamic (MHD) turbulence, solving the MHD equations directly, and employing the LAMHD-α equations at 1/2 and 1/4 resolution. Linear scaling of the third-order structure function with length is observed. The LAMHD-α equations also capture the anomalous scaling of the longitudinal structure function exponents up to order 8.