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Small-scale dynamos are ubiquitous in a broad range of turbulent flows with large-scale shear, ranging from solar and galactic magnetism to accretion disks, cosmology and structure formation. Using high-resolution direct numerical simulations we show that in non-helically forced turbulence with zero mean magnetic field, large-scale shear supports small-scale dynamo action, i.e., the dynamo growth rate increases with shear and shear enhances or even produces turbulence, which, in turn, further increases the dynamo growth rate. When the production rates of turbulent kinetic energy due to shear and forcing are comparable, we find scalings for the growth rate $\gamma$ of the small-scale dynamo and the turbulent velocity $u_{\rm rms}$ with shear rate $S$ that are independent of the magnetic Prandtl number: $\gamma \propto |S|$ and $u_{\rm rms} \propto |S|^{2/3}$. For large fluid and magnetic Reynolds numbers, $\gamma$, normalized by its shear-free value, depends only on shear. Having compensated for shear-induced effects on turbulent velocity, we find that the normalized growth rate of the small-scale dynamo exhibits the scaling, $\widetilde{\gamma}\propto |S|^{2/3}$, arising solely from the induction equation for a given velocity field., Comment: Improved version submitted to the Astrophysical Journal Letters, 6 pages, 5 figures

We develop a two-scale formalism to determine global magnetic helicity spectra in systems where the local magnetic helicity has opposite signs on both sides of the equator, giving rise to cancelation with conventional methods. We verify this approach using first a synthetic one-dimensional magnetic field and then two-dimensional slices from a three-dimensional alpha effect-type dynamo-generated magnetic field with forced turbulence of opposite helicity above and below the midplane of the domain. We then apply this formalism to global solar synoptic vector magnetograms. To improve the statistics, data from three consecutive Carrington rotations (2161--2163) are combined into a single map. We find that the spectral magnetic helicity representative of the northern hemisphere is negative at all wavenumbers and peaks at ~ 0.06 Mm^{-1} (scales around 100 Mm). There is no evidence of bihelical magnetic fields that are found in three-dimensional turbulence simulations of helicity-driven alpha effect-type dynamos., Comment: 9 pages, 10 figures, published in ApJ

We consider a scale-invariant helical magnetic field generated during inflation. We show that, if the mean magnetic helicity density of such a field is measured, it can be used to determine a lower bound on the duration of inflation. Upper bounds can be used to derive constraints on the minimal duration of inflation if one assumes that the magnetic field generated during inflation is helical. Using three-dimensional simulations, we show that an initially scale-invariant field develops, which is similar both with and without magnetic helicity. In the fully helical case, however, the magnetic field appears to have a more pronounced folded structure., Comment: 19 pages, 7 figures, JCAP accepted; results unchanged, discussions added, references added and updated, typos fixed

In the presence of strong density stratification, hydromagnetic turbulence attains qualitatively new properties: the formation of magnetic flux concentrations. We review here the theoretical foundations of this mechanism in terms of what is now called the negative effective magnetic pressure instability. We also present direct numerical simulations of forced turbulence in strongly stratified layers and discuss the qualitative and quantitative similarities with corresponding mean-field simulations. Finally, the relevance to sunspot formation is discussed., Comment: 23 pages, 13 figures, special issue "Focus on Turbulence in Astrophysical and Laboratory Plasmas" of New Journal of Physics, published

Recent direct numerical simulations (DNS) of large-scale turbulent dynamos in strongly stratified layers have resulted in surprisingly sharp bipolar structures at the surface. Here we present new DNS of helically and non-helically forced turbulence with and without rotation and compare with corresponding mean-field simulations (MFS) to show that these structures are a generic outcome of a broader class of dynamos in density-stratified layers. The MFS agree qualitatively with the DNS, but the period of oscillations tends to be longer in the DNS. In both DNS and MFS, the sharp structures are produced by converging flows at the surface and might be driven in nonlinear stage of evolution by the Lorentz force associated with the large-scale dynamo-driven magnetic field if the dynamo number is at least 2.5 times supercritical., Comment: 13 pages, 25 figures, 3 tables

We perform numerical simulations of decaying hydrodynamic and magnetohydrodynamic turbulence. We classify our time-dependent solutions by their evolutionary tracks in parametric plots between instantaneous scaling exponents. We find distinct classes of solutions evolving along specific trajectories toward points on a line of self-similar solutions. These trajectories are determined by the underlying physics governing individual cases, while the infrared slope of the initial conditions plays only a limited role. In the helical case, even for a scale-invariant initial spectrum (inversely proportional to wavenumber k), the solution evolves along the same trajectory as for a Batchelor spectrum (proportional to k^4., Comment: 5 pages, 4 figures, with 3 pages supplemental material, published in PRL

Simulations show for the first time how the magnetic fields that produce solar flares can extend out of the Sun by acquiring a twist., Comment: 2 pages, 2 figures, "Viewpoint" article on arXiv:1601.00749 by Chatterjee et al., to be published in Physics. Edited by Jessica Thomas

We consider strongly stratified forced turbulence in a plane-parallel layer with helicity and corresponding large-scale dynamo action in the lower part and non-helical turbulence in the upper. The magnetic field is found to develop strongly concentrated bipolar structures near the surface. They form elongated bands with a sharp interface between opposite polarities. Unlike earlier experiments with imposed magnetic field, the inclusion of rotation does not strongly suppress the formation of these structures. We perform a systematic numerical study of this phenomenon by varying magnetic Reynolds number, scale separation ratio, and Coriolis number. We focus on the formation of a current sheet between bipolar regions where reconnection of oppositely oriented field lines occurs. We determine the reconnection rate by measuring either the inflow velocity in the vicinity of the current sheet or by measuring the electric field in the reconnection region. We demonstrate that for large Lundquist numbers, S>10^3, the reconnection rate is nearly independent of S in agreement with results of recent numerical simulations performed by other groups in simpler settings., Comment: 11 pages, 14 figures

We investigate dynamo action in global compressible solar-like convective dynamos in the framework of mean-field theory. We simulate a solar-type star in a wedge-shaped spherical shell, where the interplay between convection and rotation self-consistently drives a large-scale dynamo. To analyze the dynamo mechanism we apply the test-field method for azimuthally ($\phi$) averaged fields to determine the 27 turbulent transport coefficients of the electromotive force, of which six are related to the $\alpha$ tensor. This method has previously been used either in simulations in Cartesian coordinates or in the geodynamo context and is applied here for the first time to fully compressible simulations of solar-like dynamos. We find that the $\phi\phi$-component of the $\alpha$ tensor does not follow the profile expected from that of kinetic helicity. The turbulent pumping velocities significantly alter the effective mean flows acting on the magnetic field and therefore challenge the flux transport dynamo concept. All coefficients are significantly affected by dynamically important magnetic fields. Quenching as well as enhancement are being observed. This leads to a modulation of the coefficients with the activity cycle. The temporal variations are found to be comparable to the time-averaged values and seem to be responsible for a nonlinear feedback on the magnetic field generation. Furthermore, we quantify the validity of the Parker-Yoshimura rule for the equatorward propagation of the mean magnetic field in the present case., Comment: 21 pages, 21 figures, published

We report a systematic strengthening of the local solar surface or fundamental $f$-mode $1$-$2$ days prior to the emergence of an active region (AR) in the same (corotating) location. Except for a possibly related increase in the kurtosis of the magnetic field, no indication can be seen in the magnetograms at that time. Our study is motivated by earlier numerical findings of Singh et al. (2014) which showed that, in the presence of a nonuniform magnetic field that is concentrated a few scale heights below the surface, the $f$-mode fans out in the diagnostic $k\omega$ diagram at high wavenumbers. Here we explore this possibility using data from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory and show for six isolated ARs, 11130, 11158, 11242, 11105, 11072, and 11768, that at large latitudinal wavenumbers (corresponding to horizontal scales of around 3000 km), the $f$-mode displays strengthening about two days prior to AR formation and thus provides a new precursor for AR formation. Furthermore, we study two ARs, 12051 and 11678, apart from a magnetically quiet patch lying next to AR~12529, to demonstrate the challenges in extracting such a precursor signal when a newly forming AR emerges in a patch that lies in close proximity of one or several already existing ARs which are expected to pollute neighboring patches. We then discuss plausible procedures for extracting precursor signals from regions with crowded environments. The idea that the $f$-mode is perturbed days before any visible magnetic activity occurs at the surface can be important in constraining dynamo models aimed at understanding the global magnetic activity of the Sun., Comment: 12 pages, 14 figures, version accepted for publication in the Astrophysical Journal

The effect of kinetic helicity (velocity--vorticity correlation) on turbulent momentum transport is investigated. The turbulent kinetic helicity (pseudoscalar) enters the Reynolds stress (mirrorsymmetric tensor) expression in the form of a helicity gradient as the coupling coefficient for the mean vorticity and/or the angular velocity (axial vector), which suggests the possibility of mean-flow generation in the presence of inhomogeneous helicity. This inhomogeneous helicity effect, which was previously confirmed at the level of a turbulence- or closure-model simulation, is examined with the aid of direct numerical simulations of rotating turbulence with non-uniform helicity sustained by an external forcing. The numerical simulations show that the spatial distribution of the Reynolds stress is in agreement with the helicity-related term coupled with the angular velocity, and that a large-scale flow is generated in the direction of angular velocity. Such a large-scale flow is not induced in the case of homogeneous turbulent helicity. This result confirms the validity of the inhomogeneous helicity effect in large-scale flow generation and suggests that a vortex dynamo is possible even in incompressible turbulence where there is no baroclinicity effect., Comment: 15pages, 11 figures

We use high resolution direct numerical simulations (DNS) to show that helical turbulence can generate significant large-scale fields even in the presence of strong small-scale dynamo action. During the kinematic stage, the unified large/small-scale dynamo grows fields with a shape-invariant eigenfunction, with most power peaked at small scales or large $k$, as in \citet{SB14}. Nevertheless, the large-scale field can be clearly detected as an excess power at small $k$ in the negatively polarized component of the energy spectrum for a forcing with positively polarized waves. Its strength $bar{B}$, relative to the total rms field $B_{rms}$, decreases with increasing magnetic Reynolds number, $R_m$. However, as the Lorentz force becomes important, the field generated by the unified dynamo orders itself by saturating on successively larger scales. The magnetic integral scale for the positively polarized waves, characterizing the small-scale field, increases significantly from the kinematic stage to saturation. This implies that the small-scale field becomes as coherent as possible for a given forcing scale, which averts the $R_m$-dependent quenching of $\bar{B}/B_rms$. These results are obtained for $1024^3$ DNS with magnetic Prandtl numbers of $P_m=0.1$ and $10$. For $P_m=0.1$, $\bar{B}/B_{rms}$ grows from about $0.04$ to about $0.4$ at saturation, aided in the final stages by helicity dissipation. For $P_m=10$, $\bar{B}/B_{rms}$ grows from much less than 0.01 to values of the order the $0.2$. Our results confirm that there is a unified large/small-scale dynamo in helical turbulence., Comment: 8 pages, 7 figures. Published in mnras

Solar magnetic activity shows both smooth secular changes, such as the Grand Modern Maximum, and quite abrupt drops that are denoted as Grand Minima. Direct numerical simulations (DNS) of convection driven dynamos offer one way of examining the mechanisms behind these events. In this work, we analyze a solution of a solar-like DNS that has been evolved for roughly 80 magnetic cycles of 4.9 years, during which epochs of irregular behavior are detected. The emphasis of our analysis is to find physical causes for such behavior. The DNS employed is a semi-global (wedge) magnetoconvection model. For data analysis we use Ensemble Empirical Mode Decomposition (EEMD) and phase dispersion ($D^2$) methods. A special property of the DNS is the existence of multiple dynamo modes at different depths and latitudes. The dominant mode is solar-like. This mode is accompanied by a higher frequency mode near the surface and a low-frequency mode in the bottom of the convection zone. The overall behavior of the dynamo solution is very complex exhibiting variable cycle lengths, epochs of disturbed and even ceased surface activity, and strong short-term hemispherical asymmetries. Surprisingly, the most prominent suppressed surface activity epoch is actually a global magnetic energy maximum. We interpret the overall irregular behavior to be due to the interplay of the different dynamo modes showing different equatorial symmetries, especially the smoother part of the irregular variations being related to the variations of the mode strengths, evolving with different and variable cycle lengths. The abrupt low activity epoch in the dominant dynamo mode near the surface is related to a strong maximum of the bottom toroidal field strength, which causes abrupt disturbances especially in the differential rotation profile via the suppression of the Reynolds stresses., Comment: 24 pages, 16 figures, Astronomy and Astrophysics, accepted for publication

We study the evolution of primordial magnetic fields in an expanding cosmic plasma. For this purpose we present a comprehensive theoretical model to consider the evolution of MHD turbulence that can be used over a wide range of physical conditions, including cosmological and astrophysical applications. We model different types of decaying cosmic MHD turbulence in the expanding universe and characterize the large-scale magnetic fields in such a medium. Direct numerical simulations of freely decaying MHD turbulence are performed for different magnetogenesis scenarios: magnetic fields generated during cosmic inflation as well as electroweak and QCD phase transitions in the early universe. Magnetic fields and fluid motions are strongly coupled due to the high Reynolds number in the early universe. Hence, we abandon the simple adiabatic dilution model to estimate magnetic field amplitudes in the expanding universe and include turbulent mixing effects on the large-scale magnetic field evolution. Numerical simulations have been carried out for non-helical and helical magnetic field configurations. The numerical results show the possibility of inverse transfer of energy in magnetically dominated non-helical MHD turbulence. On the other hand, decay properties of helical turbulence depend on whether the turbulent magnetic field is in a weakly or a fully helical state. Our results show that primordial magnetic fields can be considered as a seed for the observed large-scale magnetic fields in galaxies and clusters. Bounds on the magnetic field strength are obtained and are consistent with the upper and lower limits set by observations of extragalactic magnetic fields., Comment: 20 pages, 6 figures; Invited talk given at "Turbulent Mixing and Beyond" Workshop, 4-9 August 2014, ICTP, Italy; v. 3 matches version published in Physica Scripta

The small-scale magnetic field is ubiquitous at the solar surface---even at high latitudes. From observations we know that this field is uncorrelated (or perhaps even weakly anticorrelated) with the global sunspot cycle. Our aim is to explore the origin, and particularly the cycle dependence of such a phenomenon using three-dimensional dynamo simulations. We adopt a simple model of a turbulent dynamo in a shearing box driven by helically forced turbulence. Depending on the dynamo parameters, large-scale (global) and small-scale (local) dynamos can be excited independently in this model. Based on simulations in different parameter regimes, we find that, when only the large-scale dynamo is operating in the system, the small-scale magnetic field generated through shredding and tangling of the large-scale magnetic field is positively correlated with the global magnetic cycle. However, when both dynamos are operating, the small-scale field is produced from both the small-scale dynamo and the tangling of the large-scale field. In this situation, when the large-scale field is weaker than the equipartition value of the turbulence, the small-scale field is almost uncorrelated with the large-scale magnetic cycle. On the other hand, when the large-scale field is stronger than the equipartition value, we observe an anticorrelation between the small-scale field and the large-scale magnetic cycle. This anticorrelation can be interpreted as a suppression of the small-scale dynamo. Based on our studies we conclude that the observed small-scale magnetic field in the Sun is generated by the combined mechanisms of small-scale dynamo and tangling of the large-scale field., Comment: Accepted for publication in ApJ; minor revision and a new figure added in this version

We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and most challenging of these problems is turbulence. Yet, despite these advances, the extreme parameter regimes encountered in space physics and astrophysics (as in atmospheric and oceanic physics) still preclude direct numerical simulation. Numerical models must take a Large Eddy Simulation (LES) approach, explicitly computing only a fraction of the active dynamical scales. The success of such an approach hinges on how well the model can represent the subgrid-scales (SGS) that are not explicitly resolved. In addition to the parameter regime, heliophysical and astrophysical applications must also face an equally daunting challenge: magnetism. The presence of magnetic fields in a turbulent, electrically conducting fluid flow can dramatically alter the coupling between large and small scales, with potentially profound implications for LES/SGS modeling. In this review article, we summarize the state of the art in LES modeling of turbulent magnetohydrodynamic (MHD) flows. After discussing the nature of MHD turbulence and the small-scale processes that give rise to energy dissipation, plasma heating, and magnetic reconnection, we consider how these processes may best be captured within an LES/SGS framework. We then consider several specific applications in heliophysics and astrophysics, assessing triumphs, challenges, and future directions., Comment: 51 pages, 6 figures (Figs 2, 3, and 4 color), accepted to Space Science Reviews (in press). The paper is a product of a workshop on "LES Modeling in MHD Turbulence" held in Boulder, CO in May, 2013, sponsored by the Geophysical Turbulence Program at the National Center for Atmospheric Research

The effects of a non-gradient flux term originating from the motion of convective elements with entropy perturbations of either sign are investigated and incorporated into a modified version of stellar mixing length theory (MLT). Such a term, first studied by Deardorff in the meteorological context, might represent the effects of cold intense downdrafts caused by the rapid cooling in the granulation layer at the top of the convection zone of late-type stars. Such intense downdrafts were first seen in the strongly stratified simulations of Stein & Nordlund in the late 1980s. These downdrafts transport heat nonlocally, a phenomenon referred to as entropy rain. Moreover, the Deardorff term can cause upward enthalpy transport even in a weakly Schwarzschild-stably stratified layer. In that case, no giant cell convection would be excited. This is interest in view of recent observations, which could be explained if the dominant flow structures were of small scale even at larger depths. To study this possibility, three distinct flow structures are examined: one in which convective structures have similar size and mutual separation at all depths, one in which the separation increases with depth, but their size is still unchanged, and one in which both size and separation increase with depth, which is the standard flow structure. It is concluded that the third possibility with fewer and thicker downdrafts in deeper layers remains most plausible, but it may be unable to explain the suspected absence of large-scale flows with speeds and scales expected from MLT., Comment: 19 pages, 9 figures, Astrophysical J. (in press)

We explore the effects of an outer stably stratified coronal envelope on rotating turbulent convection, differential rotation, and large-scale dynamo action in spherical wedge models of the Sun. We solve the compressible magnetohydrodynamic equations in a two-layer model with unstable stratification below the surface, representing the convection zone, and a stably stratified coronal envelope above. The interface represents a free surface. We compare our model to models that have no coronal envelope. The presence of a coronal envelope is found to modify the Reynolds stress and the $\Lambda$ effect resulting in a weaker and non-cylindrical differential rotation. This is related to the reduced latitudinal temperature variations that are caused by and dependent on the angular velocity. Some simulations develop a near-surface shear layer that we can relate to a sign change in the meridional Reynolds stress term in the thermal wind balance equation. Furthermore, the presence of a free surface changes the magnetic field evolution since the toroidal field is concentrated closer to the surface. In all simulations, however, the migration direction of the mean magnetic field can be explained by the Parker--Yoshimura rule, which is consistent with earlier findings. A realistic treatment of the upper boundary in spherical dynamo simulations is crucial for the dynamics of the flow and magnetic field evolution., Comment: 16 pages, 13 figures, Astronomy and Astrophysics, published

We adopt an isotropic representation of the Fourier-transformed two-point correlation tensor of the magnetic field to estimate the magnetic energy and helicity spectra as well as current helicity spectra of two individual active regions (NOAA 11158 and NOAA 11515) and the change of the spectral indices during their development as well as during the solar cycle. The departure of the spectral indices of magnetic energy and current helicity from 5/3 are analyzed, and it is found that it is lower than the spectral index of the magnetic energy spectrum. Furthermore, the fractional magnetic helicity tends to increase when the scale of the energy-carrying magnetic structures increases. The magnetic helicity of NOAA 11515 violates the expected hemispheric sign rule, which is interpreted as an effect of enhanced field strengths at scales larger than 30-60Mm with opposite signs of helicity. This is consistent with the general cycle dependence, which shows that around the solar maximum the magnetic energy and helicity spectra are steeper, emphasizing the large-scale field., Comment: 10 pages, 15 Figures, ApJ in press

This work presents an extensive study of the previously discovered formation of bipolar flux concentrations in a two-layer model. We interpret the formation process in terms of negative effective magnetic pressure instability (NEMPI), which is a possible mechanism to explain the origin of sunspots. In our simulations, we use a Cartesian domain of isothermal stratified gas that is divided into two layers. In the lower layer, turbulence is forced with transverse nonhelical random waves, whereas in the upper layer no flow is induced. A weak uniform magnetic field is imposed in the entire domain at all times. In this study we vary the stratification by changing the gravitational acceleration, magnetic Reynolds number, strength of the imposed magnetic field, and size of the domain to investigate their influence on the formation process. Bipolar magnetic structure formation takes place over a large range of parameters. The magnetic structures become more intense for higher stratification until the density contrast becomes around $100$ across the turbulent layer. For the Reynolds numbers considered, magnetic flux concentrations are generated at magnetic Prandtl number between 0.1 and 1. The magnetic field in bipolar regions increases with higher imposed field strength until the field becomes comparable to the equipartition field strength of the turbulence. A larger horizontal extent enables the flux concentrations to become stronger and more coherent. The size of the bipolar structures turns out to be independent of the domain size. In the case of bipolar region formation, we find an exponential growth of the large-scale magnetic field, which is indicative of a hydromagnetic instability. Additionally, the flux concentrations are correlated with strong large-scale downward and converging flows. These findings imply that NEMPI is responsible for magnetic flux concentrations., Comment: 15 pages, 13 figures, Astronomy and Astrophysics, published

The generation of large-scale magnetic field in the kinematic regime in the absence of an alpha-effect is investigated by following two different approaches, namely the test-field method and multiscale stability theory relying on the homogenisation technique. We show analytically that the former, applied for the evaluation of magnetic eddy diffusivities, yields results that fully agree with the latter. Our computations of the magnetic eddy diffusivity tensor for the specific instances of the parity-invariant flow-IV of G.O. Roberts and the modified Taylor-Green flow in a suitable range of parameter values confirm the findings of previous studies, and also explain some of their apparent contradictions. The two flows have large symmetry groups; this is used to considerably simplify the eddy diffusivity tensor. Finally, a new analytic result is presented: upon expressing the eddy diffusivity tensor in terms of solutions to auxiliary problems for the adjoint operator, we derive relations between magnetic eddy diffusivity tensors that arise for opposite small-scale flows v(x) and -v(x)., Comment: 29 pp., 19 figures, 42 references

In a paper of 1978, Eugene Parker postulated the need for hydraulic downward motion to explain magnetic flux concentrations at the solar surface. A similar process has recently also been seen in simplified (e.g., isothermal) models of flux concentrations from the negative effective magnetic pressure instability. We study the effects of partial ionization near the radiative surface on the formation of such magnetic flux concentrations. We first obtain one-dimensional (1D) equilibrium solutions using either a Kramers-like opacity or the ${\rm H}^{-}$ opacity. The resulting atmospheres are then used as initial conditions in two-dimensional (2D) models where flows are driven by an imposed gradient force resembling a localized negative pressure in the form of a blob. To isolate the effects of partial ionization and radiation, we ignore turbulence and convection. In 1D models, due to partial ionization, an unstable stratification forms always near the surface. We show that the extrema in the specific entropy profiles correspond to the extrema in degree of ionization. In the 2D models without partial ionization, flux concentrations form close to the height where the blob is placed. In models with partial ionization, such flux concentrations form at the surface much above the blob. This is due to the corresponding unstable layer in specific entropy. With ${\rm H}^{-}$ opacity, flux concentrations are weaker due to the stably stratified deeper parts. We demonstrate that, together with density stratification, the imposed source of negative pressure drives the formation of flux concentrations. We find that the inclusion of partial ionization affects entropy profiles causing the strong flux concentrations to form closer to the surface. We speculate that turbulence is needed to limit the strength of flux concentrations and homogenize the specific entropy to a more nearly marginal stratification., Comment: 11 pages, 13 figures, submitted to A&A

Recent work by Mitra et al. (2014) has shown that in strongly stratified forced two-layer turbulence with helicity and corresponding large-scale dynamo action in the lower layer, a magnetic field occurs in the upper layer in the form of sharply bounded bipolar magnetic spots. Here we extend this model to spherical wedge geometry covering the northern hemisphere up to 75{\deg} latitude and an azimuthal extent of 180{\deg}. The kinetic helicity and therefore also the large-scale magnetic field are strongest at low latitudes. For moderately strong stratification, several bipolar spots form that fill eventually the full longitudinal extent. At early times, the polarity of spots reflects the orientation of the underlying azimuthal field, as expected from {\Omega}-shaped flux loops. At late times their tilt changes such that there is a radial field of opposite orientation at different latitudes separated by about 10{\deg}. Our model demonstrates the spontaneous formation of spots of sizes much larger than the pressure scale height. Their tendency to produce filling factors close to unity is argued to be reminiscent of highly active stars. We confirm that strong stratification and strong scale separation are essential ingredients behind magnetic spot formation, which appears to be associated with downflows at larger depths., Comment: 12 pages, 14 figures

Nonlinear mean-field models of the solar dynamo show long-term variability, which may be relevant to different states of activity inferred from long-term radiocarbon data. This paper is aimed to probe the dynamo hysteresis predicted by the recent mean-field models of Kitchatinov \& Olemskoy (2010) with direct numerical simulations. We perform three-dimensional simulations of large-scale dynamos in a shearing box with helically forced turbulence. As initial condition, we either take a weak random magnetic field or we start from a snapshot of an earlier simulation. Two quasi-stable states are found to coexist in a certain range of parameters close to the onset of the large-scale dynamo. The simulations converge to one of these states depending on the initial conditions. When either the fractional helicity or the magnetic Prandtl number is increased between successive runs above the critical value for onset of the dynamo, the field strength jumps to a finite value. However, when the fractional helicity or the magnetic Prandtl number is then decreased again, the field strength stays at a similar value (strong field branch) even below the original onset. We also observe intermittent decaying phases away from the strong field branch close to the point where large-scale dynamo action is just possible. The dynamo hysteresis seen previously in mean-field models is thus reproduced by 3D simulations. Its possible relation to distinct modes of solar activity such as grand minima is discussed., Comment: Published in ApJ

We present results from four convectively-driven stellar dynamo simulations in spherical wedge geometry. All of these simulations produce cyclic and migrating mean magnetic fields. Through detailed comparisons we show that the migration direction can be explained by an $\alpha\Omega$ dynamo wave following the Parker--Yoshimura rule. We conclude that the equatorward migration in this and previous work is due to a positive (negative) $\alpha$ effect in the northern (southern) hemisphere and a negative radial gradient of $\Omega$ outside the inner tangent cylinder of these models. This idea is supported by a strong correlation between negative radial shear and toroidal field strength in the region of equatorward propagation., Comment: 6 pages, 5 figures, published in ApJ Letters

Using direct numerical simulations (DNS) we verify that in the kinematic regime, a turbulent helical dynamo grows in such a way that the magnetic energy spectrum remains to high precision shape-invariant, i.e., at each wavenumber $k$ the spectrum grows with the same growth rate. Signatures of large-scale dynamo action can be identified through the excess of magnetic energy at small $k$, of one of the two oppositely polarized constituents. Also a suitably defined planar average of the magnetic field can be chosen such that its rms value isolates the strength of the mean field. However, these different means of analysis suggest that the strength of the large-scale field diminishes with increasing magnetic Reynolds number ${\rm Re}_{\rm M}$ like ${\rm Re}_{\rm M}^{-1/2}$ for intermediate values and like ${\rm Re}_{\rm M}^{-3/4}$ for larger ones. Both an analysis from the Kazantsev model including helicity and the DNS show that this arises due to the magnetic energy spectrum still peaking at resistive scales, even when helicity is present. As expected, the amplitude of the large-scale field increases with increasing fractional helicity, enabling us to determine the onset of large scale dynamo action and distinguishing it from that of the small-scale dynamo. Our DNS show that, contrary to earlier results for smaller scale separation (only 1.5 instead of now 4), the small-scale dynamo can still be excited at magnetic Prandtl numbers of 0.1 and only moderate values of the magnetic Reynolds numbers ($\sim 160$)., Comment: 12 pages, 10 figures, Version accepted in MNRAS

Late-type stars rotate differentially owing to anisotropic turbulence in their outer convection zones. The rotation is called solar-like (SL) when the equator rotates fastest and anti-solar (AS) otherwise. Hydrodynamic simulations show a transition from SL to AS rotation as the influence of rotation on convection is reduced, but the opposite transition occurs at a different point in the parameter space. The system is bistable, i.e., SL and AS rotation profiles can both be stable. We study the effect of a dynamo-generated magnetic field on the large-scale flows, particularly on the possibility of bistable behavior of differential rotation. We solve the hydromagnetic equations numerically in a rotating spherical shell for a set of different radiative conductivities controlling the relative importance of convection. In agreement with earlier findings, our models display SL rotation profiles when the rotational influence on convection is strong and a transition to AS when the rotational influence decreases. We find that dynamo-generated magnetic fields help to produce SL differential rotation compared to the hydrodynamic simulations. We do not observe any bistable states of differential rotation. In the AS cases we get coherent single-cell meridional circulation, whereas in SL cases we get multi-cellular patterns. In both cases, we obtain poleward circulation near the surface with a magnitude close to that observed in the Sun. Moreover, both differential rotation and meridional circulation have significant magnetic cycle-related variations that are similar in strength to those of the Sun. Purely hydrodynamic simulations of differential rotation and meridional circulation are shown to be of limited relevance as magnetic fields, self-consistently generated by dynamo action, significantly affect the flows., Comment: Accepted for publication in A&A

We show that in the presence of a harmonically varying magnetic field the fundamental or $f$-mode in a stratified layer is altered in such a way that it fans out in the diagnostic $k\omega$ diagram, but with mode power also within the fan. In our simulations, the surface is defined by a temperature and density jump in a piecewise isothermal layer. Unlike our previous work (Singh et al. 2014) where a uniform magnetic field was considered, we employ here a nonuniform magnetic field together with hydromagnetic turbulence at length scales much smaller than those of the magnetic fields. The expansion of the $f$-mode is stronger for fields confined to the layer below the surface. In some of those cases, the $k\omega$ diagram also reveals a new class of low frequency vertical stripes at multiples of twice the horizontal wavenumber of the background magnetic field. We argue that the study of the $f$-mode expansion might be a new and sensitive tool to determining subsurface magnetic fields with longitudinal periodicity., Comment: 6 pages, 4 figures, submitted to Astrophysical Journal Letters

Hydromagnetic turbulence affects the evolution of large-scale magnetic fields through mean-field effects like turbulent diffusion and the $\alpha$ effect. For stronger fields, these effects are usually suppressed or quenched, and additional anisotropies are introduced. Using different variants of the test-field method, we determine the quenching of the turbulent transport coefficients for the forced Roberts flow, isotropically forced non-helical turbulence, and rotating thermal convection. We see significant quenching only when the mean magnetic field is larger than the equipartition value of the turbulence. Expressing the magnetic field in terms of the equipartition value of the {\it quenched} flows, we obtain for the quenching exponents of the turbulent magnetic diffusivity about 1.3, 1.1, and 1.3 for Roberts flow, forced turbulence, and convection, respectively. However, when the magnetic field is expressed in terms of the equipartition value of the unquenched flows these quenching exponents become about 4, 1.5, and 2.3, respectively. For the $\alpha$ effect, the exponent is about 1.3 for the Roberts flow and 2 for convection in the first case, but 4 and 3, respectively, in the second. In convection, the quenching of turbulent pumping follows the same power law as turbulent diffusion, while for the coefficient describing the $\bf \Omega \times \bf J$ effect nearly the same quenching exponent is obtained as for $\alpha$. For forced turbulence, turbulent diffusion proportional to the second derivative along the mean magnetic field is quenched much less, especially for larger values of the magnetic Reynolds number. However, we find that in corresponding axisymmetric mean-field dynamos with dominant toroidal field the quenched diffusion coefficients are the same for the poloidal and toroidal field constituents., Comment: Accepted for publication in ApJ

Kepler data from G-, K- and M-type stars are used to study conditions that lead to superflares with energies above $10^{34} {\rm erg}$. From the 117,661 stars included, 380 show superflares with a total of 1690 such events. We study whether parameters, like effective temperature or the rotation rate, have any effect on the superflare occurrence rate or energy. With increasing effective temperature we observe a decrease in the superflare rate, which is analogous to the previous findings of a decrease in dynamo activity with increasing effective temperature. For slowly rotating stars, we find a quadratic increase of the mean occurrence rate with the rotation rate up to a critical point, after which the rate decreases linearly. Motivated by standard dynamo theory, we study the behavior of the relative starspot coverage, approximated as the relative brightness variation. For faster rotating stars, an increased fraction of stars shows higher spot coverage, which leads to higher superflare rates. A turbulent dynamo is used to study the dependence of the Ohmic dissipation as a proxy of the flare energy on the differential rotation or shear rate. The resulting statistics of the dissipation energy as a function of dynamo number is similar to the observed flare statistics as a function of the inverse Rossby number and shows similarly strong fluctuations. This supports the idea that superflares might well be possible for solar-type G stars., Comment: 9 pages, 14 figures, published in ApJ

Using direct numerical simulations of three-dimensional hydromagnetic turbulence, either with helical or non-helical forcing, we show that the ratio of kinetic-to-magnetic energy dissipation always increases with the magnetic Prandtl number, i.e., the ratio of kinematic viscosity to magnetic diffusivity. This dependence can always be approximated by a power law, but the exponent is not the same in all cases. For non-helical turbulence, the exponent is around 1/3, while for helical turbulence it is between 0.6 and 2/3. In the statistically steady state, the rate of the energy conversion from kinetic into magnetic by the dynamo must be equal to the Joule dissipation rate. We emphasize that for both small-scale and large-scale dynamos, the efficiency of energy conversion depends sensitively on the magnetic Prandtl number, and thus on the microphysical dissipation process. To understand this behavior, we also study shell models of turbulence and one-dimensional passive and active scalar models. We conclude that the magnetic Prandtl number dependence is qualitatively best reproduced in the one-dimensional model as a result of dissipation via localized Alfven kinks., Comment: 10 pages, 11 figures, ApJ, in press

With the ultimate aim of using the fundamental or $f$-mode to study helioseismic aspects of turbulence-generated magnetic flux concentrations, we use randomly forced hydromagnetic simulations of a piecewise isothermal layer in two dimensions with reflecting boundaries at top and bottom. We compute numerically diagnostic wavenumber-frequency diagrams of the vertical velocity at the interface between the denser gas below and the less dense gas above. For an Alfv\'en-to-sound speed ratio of about 0.1, a 5% frequency increase of the $f$-mode can be measured when $k_xH_{\rm p}=3$-$4$, where $k_x$ is the horizontal wavenumber and $H_{\rm p}$ is the pressure scale height at the surface. Since the solar radius is about 2000 times larger than $H_{\rm p}$, the corresponding spherical harmonic degree would be 6000-8000. For weaker fields, a $k_x$-dependent frequency decrease by the turbulent motions becomes dominant. For vertical magnetic fields, the frequency is enhanced for $k_xH_{\rm p}\approx4$, but decreased relative to its nonmagnetic value for $k_xH_{\rm p}\approx9$., Comment: 17 pages, 22 figures, Version accepted in MNRAS

In the presence of magnetic helicity, inverse transfer from small to large scales is well known in magnetohydrodynamic (MHD) turbulence and has applications in astrophysics, cosmology, and fusion plasmas. Using high resolution direct numerical simulations of magnetically dominated self-similarly decaying MHD turbulence, we report a similar inverse transfer even in the absence of magnetic helicity. We compute for the first time spectral energy transfer rates to show that this inverse transfer is about half as strong as with helicity, but in both cases the magnetic gain at large scales results from velocity at similar scales interacting with smaller-scale magnetic fields. This suggests that both inverse transfers are a consequence of a universal mechanisms for magnetically dominated turbulence. Possible explanations include inverse cascading of the mean squared vector potential associated with local near two-dimensionality and the shallower $k^2$ subinertial range spectrum of kinetic energy forcing the magnetic field with a $k^4$ subinertial range to attain larger-scale coherence. The inertial range shows a clear $k^{-2}$ spectrum and is the first example of fully isotropic magnetically dominated MHD turbulence exhibiting weak turbulence scaling., Comment: 4 pages, 4 figures, submitted to PRL, plus 9 pages of supplemental material with 12 more figures

The Kelvin-Helmholtz instability in an ionized plasma is considered with a focus on the generation of magnetic field via the Biermann battery mechanisms. The problem is studied through direct numerical simulations of two counter-directed flows in 2D geometry. The simulations demonstrate the formation of eddies and their further interaction resulting in a large single vortex. At early stages, the generated magnetic field evolves due to the baroclinic term in the induction equation, revealing significantly different structures from the vorticity field, despite the fact that magnetic field and vorticity obey identical equations. At later times, the magnetic field exhibits complex behavior and continues to grow even after a hydrodynamic vortex has developed., Comment: 10 pages, 12 figures, To be submitted to Physics of Plasmas

We review our current understanding of galactic dynamo theory, paying particular attention to numerical simulations both of the mean-field equations and the original three-dimensional equations relevant to describing the magnetic field evolution for a turbulent flow. We emphasize the theoretical difficulties in explaining non-axisymmetric magnetic fields in galaxies and discuss the observational basis for such results in terms of rotation measure analysis. Next, we discuss nonlinear theory, the role of magnetic helicity conservation and magnetic helicity fluxes. This leads to the possibility that galactic magnetic fields may be bi-helical, with opposite signs of helicity and large and small length scales. We discuss their observational signatures and close by discussing the possibilities of explaining the origin of primordial magnetic fields., Comment: 28 pages, 15 figure, to appear in Lecture Notes in Physics "Magnetic fields in diffuse media", Eds. E. de Gouveia Dal Pino and A. Lazarian

The mean-field theory of magnetized stellar convection gives rise to the two possibility of distinct instabilities: the large-scale dynamo instability, operating in the bulk of the convection zone, and a negative effective magnetic pressure instability (NEMPI) operating in the strongly stratified surface layers. The latter might be important in connection with magnetic spot formation, but the growth rate of NEMPI is suppressed with increasing rotation rates, although recent direct numerical simulations (DNS) have shown a subsequent increase in the growth rate. We examine quantitatively whether this increase in the growth rate of NEMPI can be explained by an alpha squared mean-field dynamo, and whether both NEMPI and the dynamo instability can operate at the same time. We use both DNS and mean-field simulations (MFS) to solve the underlying equations numerically either with or without an imposed horizontal field. We use the test-field method to compute relevant dynamo coefficients. DNS show that magnetic flux concentrations are still possible up to rotation rates above which the large-scale dynamo effect produces mean magnetic fields. The resulting DNS growth rates are quantitatively well reproduced with MFS. As expected, for weak or vanishing rotation, the growth rate of NEMPI increases with increasing gravity, but there is a correction term for strong gravity and large turbulent magnetic diffusivity. Magnetic flux concentrations are still possible for rotation rates above which dynamo action takes over. For the solar rotation rate, the corresponding turbulent turnover time is about 5 hours, with dynamo action commencing in the layers beneath., Comment: 10 pages, 10 figures, submitted to A&A

We analyze the nature of dynamo action that produces horizontally averaged magnetic fields in two particular flows that were studied by Roberts (1972, Phil. Trans. R. Soc. A 271, 411), namely his flows II and III. They have zero kinetic helicity either pointwise (flow II), or on average (flow III). Using direct numerical simulations, we determine the onset conditions for dynamo action at moderate values of the magnetic Reynolds number. Using the test-field method, we show that the turbulent magnetic diffusivity is then positive for both flows. However, we demonstrate that for both flows large-scale dynamo action occurs through delayed transport. Mathematically speaking, the magnetic field at earlier times contributes to the electromotive force through the off-diagonal components of the alpha tensor such that a zero mean magnetic field becomes unstable to dynamo action. This represents a qualitatively new mean-field dynamo mechanism not previously described., Comment: 11 pages, 12 figures, submitted to MNRAS

Using one-dimensional models, we show that a helical magnetic field with an appropriate sign of helicity can compensate the Faraday depolarization resulting from the superposition of Faraday-rotated polarization planes from a spatially extended source. For radio emission from a helical magnetic field, the polarization as a function of the square of the wavelength becomes asymmetric with respect to zero. Mathematically speaking, the resulting emission occurs then either at observable or at unobservable (imaginary) wavelengths. We demonstrate that rotation measure (RM) synthesis allows for the reconstruction of the underlying Faraday dispersion function in the former case, but not in the latter. The presence of positive magnetic helicity can thus be detected by observing positive RM in highly polarized regions in the sky and negative RM in weakly polarized regions. Conversely, negative magnetic helicity can be detected by observing negative RM in highly polarized regions and positive RM in weakly polarized regions. The simultaneous presence of two magnetic constituents with opposite signs of helicity is shown to possess signatures that can be quantified through polarization peaks at specific wavelengths and the gradient of the phase of the Faraday dispersion function. Similar polarization peaks can tentatively also be identified for the bi-helical magnetic fields that are generated self-consistently by a dynamo from helically forced turbulence, even though the magnetic energy spectrum is then continuous. Finally, we discuss the possibility of detecting magnetic fields with helical and non-helical properties in external galaxies using the Square Kilometre Array., Comment: 12 pages, 12 figures, ApJ, in press (with 3-D turbulence results now included)

We compute for the first time magnetic helicity and energy spectra of the solar active region NOAA 11158 during 11-15 February 2011 at 20^o southern heliographic latitude using observational photospheric vector magnetograms. We adopt the isotropic representation of the Fourier-transformed two-point correlation tensor of the magnetic field. The sign of magnetic helicity turns out to be predominantly positive at all wavenumbers. This sign is consistent with what is theoretically expected for the southern hemisphere. The magnetic helicity normalized to its theoretical maximum value, here referred to as relative helicity, is around 4% and strongest at intermediate wavenumbers of k ~ 0.4 Mm^{-1}, corresponding to a scale of 2pi/k ~ 16 Mm. The same sign and a similar value are also found for the relative current helicity evaluated in real space based on the vertical components of magnetic field and current density. The modulus of the magnetic helicity spectrum shows a k^{-11/3} power law at large wavenumbers, which implies a k^{-5/3} spectrum for the modulus of the current helicity. A k^{-5/3} spectrum is also obtained for the magnetic energy. The energy spectra evaluated separately from the horizontal and vertical fields agree for wavenumbers below 3 Mm^{-1}, corresponding to scales above 2 Mm. This gives some justification to our assumption of isotropy and places limits resulting from possible instrumental artefacts at small scales., Comment: 6 pages, 4 figures, ApJL (accepted)

We report on turbulent dynamo simulations in a spherical wedge with an outer coronal layer. We apply a two-layer model where the lower layer represents the convection zone and the upper layer the solar corona. This setup is used to study the coronal influence on the dynamo action beneath the surface. Increasing the radial coronal extent gradually to three times the solar radius and changing the magnetic Reynolds number, we find that dynamo action benefits from the additional coronal extent in terms of higher magnetic energy in the saturated stage. The flux of magnetic helicity can play an important role in this context., Comment: 4 pages, 1 figure, To appear in proceedings of IAUS 302: Magnetic fields throughout stellar evolution (August 2013, Biarritz, France)

We report the finding of an azimuthal dynamo wave of a low-order (m=1) mode in direct numerical simulations (DNS) of turbulent convection in spherical shells. Such waves are predicted by mean field dynamo theory and have been obtained previously in mean-field models. Observational results both from photometry and Doppler imaging have revealed persistent drifts of spots for several rapidly rotating stars, but, although an azimuthal dynamo wave has been proposed as a possible mechanism responsible for this behavior, it has been judged as unlikely, as practical evidence for such waves from DNS has been lacking. The large-scale magnetic field in our DNS, which is due to self-consistent dynamo action, is dominated by a retrograde m=1 mode. Its pattern speed is nearly independent of latitude and does not reflect the speed of the differential rotation at any depth. The extrema of magnetic m=1 structures coincide reasonably with the maxima of m=2 structures of the temperature. These results provide direct support for the observed drifts being due to an azimuthal dynamo wave., Comment: 6 pages, 4 figures, submitted to ApJL