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We solve for waves in a polytropic, stratified medium with a spatially varying background magnetic field that points along a horizontal $x$-direction, and with gravity that is directed along the vertical $z$-direction. Force balance determines the magnitude of the background magnetic field, $B_0^2 \sim z^{n+1}$, where $n$ is the polytropic index. Using numerical and asymptotic methods, we deduce an accurate and explicit dispersion relation for fast pressure-driven waves: $\Omega^2 \sim K\left(2m+n\right) \left[1 + (1/M_\mathrm{A})^2 (4-2\gamma+\cos^2\theta-3\cos^4\theta)/4 \right]$. Here, $\Omega$ is the frequency, $K$ the wavenumber, $\theta$ the angle the wave-vector makes with the background magnetic field, $M_\mathrm{A}$ the Alfv\'enic Mach number, and $m$ an integer representing the eigen state. Applications of our result are in magnetoseismology and nonlinear asteroseismology., Comment: 11 pages, 5 figures

Solar flares create adverse space weather impacting space and Earth-based technologies. However, the difficulty of forecasting flares, and by extension severe space weather, is accentuated by the lack of any unique flare trigger or a single physical pathway. Studies indicate that multiple physical properties contribute to active region flare potential, compounding the challenge. Recent developments in machine learning (ML) have enabled analysis of higher-dimensional data leading to increasingly better flare forecasting techniques. However, consensus on high-performing flare predictors remains elusive. In the most comprehensive study to date, we conduct a comparative analysis of four popular ML techniques (k-nearest neighbor, logistic regression, random forest classifier, and support vector machine) by training these on magnetic parameters obtained from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) for the entirety of solar cycle 24. We demonstrate that the logistic regression and support vector machine algorithms perform extremely well in forecasting active region flaring potential. The logistic regression algorithm returns the highest true skill score of $0.967 \pm 0.018$, possibly the highest classification performance achieved with any strictly parametric study. From a comparative assessment, we establish that the magnetic properties like total current helicity, total vertical current density, total unsigned flux, R_VALUE, and total absolute twist are the top-performing flare indicators. We also introduce and analyze two new performance metrics, namely, severe and clear space weather indicators. Our analysis constrains the most successful ML algorithms and identifies physical parameters that contribute most to active region flare productivity.

The dynamic activity of the Sun, governed by its cycle of sunspots -- strongly magnetized regions that are observed on its surface -- modulate our solar system space environment creating space weather. Severe space weather leads to disruptions in satellite operations, telecommunications, electric power grids and air-traffic on polar routes. Forecasting the cycle of sunspots, however, has remained a challenging problem. We use reservoir computing -- a model-free, neural--network based machine-learning technique -- to forecast the upcoming solar cycle, sunspot cycle 25. The standard algorithm forecasts that solar cycle 25 is going to last about ten years, the maxima is going to appear in the year 2024 and the maximum number of sunspots is going to be 113 ($\pm15$). We also develop a novel variation of the standard algorithm whose forecasts for duration and peak timing matches that of the standard algorithm, but whose peak amplitude forecast is 124 ($\pm2$) -- within the upper bound of the standard reservoir computing algorithm. We conclude that sunspot cycle 25 is likely to be a weak, lower than average solar cycle, somewhat similar in strength to sunspot cycle 24., Comment: 9 pages 3 figures

We solve for waves in an isothermal, stratified medium with a magnetic field that points along a direction perpendicular to that of gravity and varies exponentially in the direction of gravity. We find exact analytical solutions for two different cases: (a) waves propagating along the direction of the magnetic field and (b) waves propagating along the direction of the gravity. In each case, we find solutions in terms of either the hypergeometric functions or their confluent cousins. We solve the resultant transcendental dispersion relation numerically. The changes in the eigenfrequencies due to a spatially inhomogeneous Alfv\'en wave speed are significant -- there are more oscillations or leaking of nodes of the eigenfunctions in regions of lower Alfv\'en speed and wave reflection from regions of larger Alfv\'en speed. Such changes in the dispersion relation and the mode structures may allow detection of magnetic fields buried in the stellar interior., Comment: Accepted for publication in the Astrophysical Journal

We study the role of turbulence in magnetic reconnection, within the framework of magneto-hydrodynamics, using three-dimensional direct numerical simulations. For small turbulent intensity we find that the reconnection rate obeys Sweet-Parker scaling. For large enough turbulent intensity reconnection rate departs significantly from Sweet-Parker behaviour, becomes almost a constant as a function of the Lundquist number. We further study energisation of test-particles in the same setup. We find that the speed of the energised particles obeys a Maxwellian distribution, whose variance also obeys Sweet-Parker scaling for small turbulent intensity but depends weakly on the Lundquist number for large turbulent intensity. Furthermore, the variance is found to increase with the strength of the reconnecting magnetic field., Comment: 9 pages, 11 figures

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

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

Accurate knowledge of time-variation in meridional flow-speed and profile is crucial for estimating a solar cycle's features, which are ultimately responsible for causing space climate variations. However, no consensus has been reached yet about the Sun's meridional circulation pattern observations and theories. By implementing an Ensemble Kalman Filter (EnKF) data assimilation in a Babcock-Leighton solar dynamo model using Data Assimilation Research Testbed (DART) framework, we find that the best reconstruction of time-variation in meridional flow-speed can be obtained when ten or more observations are used with an updating time of 15 days and a $\le 10\%$ observational error. Increasing ensemble-size from 16 to 160 improves reconstruction. Comparison of reconstructed flow-speed with "true-state" reveals that EnKF data assimilation is very powerful for reconstructing meridional flow-speeds and suggests that it can be implemented for reconstructing spatio-temporal patterns of meridional circulation., Comment: 18 pages, 6 figures, published in GRL (August 2014)

We perform direct numerical simulations of the equations of magnetohydrodynamics with external random forcing and in the presence of gravity. The domain is divided into two parts: a lower layer where the forcing is helical and an upper layer where the helicity of the forcing is zero with a smooth transition in between. At early times, a large-scale helical dynamo develops in the bottom layer. At later times the dynamo saturates, but the vertical magnetic field continues to develop and rises to form dynamic bipolar structures at the top, which later disappear and reappear. Some of the structures look similar to $\delta$ spots observed in the Sun. This is the first example of magnetic flux concentrations, owing to strong density stratification, from self-consistent dynamo simulations that generate bipolar, super-equipartition strength, magnetic structures whose energy density can exceeds the turbulent kinetic energy by even a factor of ten., Comment: Published in Monthly Notices of Royal Astronomical Society

In astrophysics, turbulent diffusion is often used in place of microphysical diffusion to avoid resolving the small scales. However, we expect this approach to break down when time and length scales of the turbulence become comparable with other relevant time and length scales in the system. Turbulent diffusion has previously been applied to the magneto-rotational instability (MRI), but no quantitative comparison of growth rates at different turbulent intensities has been performed. We investigate to what extent turbulent diffusion can be used to model the effects of small-scale turbulence on the kinematic growth rates of the MRI, and how this depends on angular velocity and magnetic field strength. We use direct numerical simulations in three-dimensional shearing boxes with periodic boundary conditions in the spanwise direction and additional random plane-wave volume forcing to drive a turbulent flow at a given length scale. We estimate the turbulent diffusivity using a mixing length formula and compare with results obtained with the test-field method. It turns out that the concept of turbulent diffusion is remarkably accurate in describing the effect of turbulence on the growth rate of the MRI. No noticeable breakdown of turbulent diffusion has been found, even when time and length scales of the turbulence become comparable with those imposed by the MRI itself. On the other hand, quenching of turbulent magnetic diffusivity by the magnetic field is found to be absent. Turbulence reduces the growth rate of the MRI in a way that is the same as microphysical magnetic diffusion., Comment: 8 pages, 9 figures, submitted to Astronomy & Astrophysics

In the presence of strong density stratification, turbulence can lead to a large-scale instability of a horizontal magnetic field if its strength is in a suitable range (within a few percent of the turbulent equipartition value). This instability is related to a suppression of the turbulent pressure so that the turbulence contribution to the mean magnetic pressure becomes negative. This results in the excitation of a negative effective magnetic pressure instability (NEMPI). This instability has so far only been studied for an imposed magnetic field. We want to know how NEMPI works when the mean magnetic field is generated self-consistently by an $\alpha^2$ dynamo, whether it is affected by global spherical geometry, and whether it can influence the properties of the dynamo itself. We adopt the mean-field approach which has previously been shown to provide a realistic description of NEMPI in direct numerical simulations. We assume axisymmetry and solve the mean-field equations with the Pencil-Code for an adiabatic stratification at a total density contrast in the radial direction of approximately 4 orders of magnitude. NEMPI is found to work when the dynamo-generated field is about 4% of the equipartition value, which is achieved through strong $\alpha$ quenching. This instability is excited in the top 5% of the outer radius provided the density contrast across this top layer is at least 10. NEMPI is found to occur at lower latitudes when the mean magnetic field is stronger. For weaker fields, NEMPI can make the dynamo oscillatory with poleward migration. NEMPI is a viable mechanism for producing magnetic flux concentrations in a strongly stratified spherical shell in which a magnetic field is generated by a strongly quenched $\alpha$ effect dynamo., Comment: published in A&A

Using direct numerical simulations, we verify that "flow IV" of Roberts (1972) exhibits dynamo action dominated by horizontally averaged large-scale magnetic field. With the test-field method we compute the turbulent magnetic diffusivity and find that it is negative and overcomes the molecular diffusivity, thus explaining quantitatively the large-scale dynamo for magnetic Reynolds numbers above $\approx8$. As expected for a dynamo of this type, but contrary to $\alpha$-effect dynamos, the two horizontal field components grow independently of each other and have arbitrary amplitude ratios and phase differences. Small length scales of the mean magnetic field are shown to be stabilized by the turbulent magnetic diffusivity becoming positive at larger wavenumbers. Oscillatory decaying or growing solutions have also been found in certain wavenumber intervals and sufficiently large values of the magnetic Reynolds number. For magnetic Reynolds numbers below $\approx0.5$ the turbulent magnetic diffusivity is confirmed to be positive, as expected for all incompressible flows. Earlier claims of a dynamo driven by a modified Taylor-Green flow through negative eddy diffusivity could not be confirmed., Comment: 7 pages, 9 figures, accepted to MNRAS

The surface layers of the Sun are strongly stratified. In the presence of turbulence with a weak mean magnetic field, a large-scale instability resulting in the formation of non-uniform magnetic structures, can be excited over the scale of many turbulent eddies or convection cells. This instability is caused by a negative contribution of turbulence to the effective (mean-field) magnetic pressure and has previously been discussed in connection with the formation of active regions and perhaps sunspots. We want to understand the effects of rotation on this instability in both two and three dimensions. We use mean-field magnetohydrodynamics in a parameter regime in which the properties of the negative effective magnetic pressure instability have previously been found to be in agreement with those of direct numerical simulations. We find that the instability is suppressed already for relatively slow rotation with Coriolis numbers (i.e. inverse Rossby numbers) around 0.2. The suppression is strongest at the equator. In the nonlinear regime, we find traveling wave solutions with propagation in the prograde direction at the equator with additional poleward migration away from the equator. The prograde rotation of the magnetic pattern near the equator is argued to be a possible explanation for the faster rotation speed of magnetic tracers found on the Sun. In the bulk of the domain, kinetic and current helicities are negative in the northern hemisphere and positive in the southern., Comment: 8 pages, 13 figures, submitted to A&A

We study spontaneous breakdown of chiral symmetry during the nonlinear evolution of the Tayler instability. We start with an initial steady state of zero helicity. Within linearized perturbation calculations, helical perturbations of this initial state have the same growth rate for either sign of helicity. Direct numerical simulations (DNS) of the fully nonlinear equations, however, show that an infinitesimal excess of one sign of helicity in the initial perturbation gives rise to a saturated helical state. We further show that this symmetry breaking can be described by weakly nonlinear finite--amplitude equations with undetermined coefficients which can be deduced solely from symmetry consideration. By fitting solutions of the amplitude equations to data from DNS we further determine the coefficients of the amplitude equations., Comment: 8 pages, 5 figures, Published on Phys. Rev. E

The negative effective magnetic pressure instability operates on scales encompassing many turbulent eddies and is here discussed in connection with the formation of active regions near the surface layers of the Sun. This instability is related to the negative contribution of turbulence to the mean magnetic pressure that causes the formation of large-scale magnetic structures. For an isothermal layer, direct numerical simulations and mean-field simulations of this phenomenon are shown to agree in many details in that their onset occurs at the same depth. This depth increases with increasing field strength, such that the maximum growth rate of this instability is independent of the field strength, provided the magnetic structures are fully contained within the domain. A linear stability analysis is shown to support this finding. The instability also leads to a redistribution of turbulent intensity and gas pressure that could provide direct observational signatures., Comment: 19 pages, 10 figures, submitted to Solar Physics

We present evidence for finite magnetic helicity density in the heliosphere and numerical models thereof, and relate it to the magnetic field properties of the dynamo in the solar convection zone. We use simulations and solar wind data to compute magnetic helicity either directly from the simulations, or indirectly using time series of the skew-symmetric components of the magnetic correlation tensor. We find that the solar dynamo produces negative magnetic helicity at small scales and positive at large scales. However, in the heliosphere these properties are reversed and the magnetic helicity is now positive at small scales and negative at large scales. We explain this by the fact that a negative diffusive magnetic helicity flux corresponds to a positive gradient of magnetic helicity, which leads to a change of sign from negative to positive values at some radius in the northern hemisphere., Comment: 7 pages, 12 Figures, accepted in Journal of Space Weather and Space Climate

The negative effective magnetic pressure instability discovered recently in direct numerical simulations (DNS) may play a crucial role in the formation of sunspots and active regions in the Sun and stars. This instability is caused by a negative contribution of turbulence to the effective mean Lorentz force (the sum of turbulent and non-turbulent contributions) and results in formation of large-scale inhomogeneous magnetic structures from initial uniform magnetic field. Earlier investigations of this instability in DNS of stably stratified, externally forced, isothermal hydromagnetic turbulence in the regime of large plasma beta are now extended into the regime of larger scale separation ratios where the number of turbulent eddies in the computational domain is about 30. Strong spontaneous formation of large-scale magnetic structures is seen even without performing any spatial averaging. These structures encompass many turbulent eddies. The characteristic time of the instability is comparable to the turbulent diffusion time, L^2/eta_t, where eta_t is the turbulent diffusivity and L is the scale of the domain. DNS are used to confirm that the effective magnetic pressure does indeed become negative for magnetic field strengths below the equipartition field. The dependence of the effective magnetic pressure on the field strength is characterized by fit parameters that seem to show convergence for larger values of the magnetic Reynolds number., Comment: 14 pages, 8 figures, submitted to special issue "Advances of European Solar Physics" in Solar Physics

The chiral symmetry breaking properties of the Tayler instability are discussed. Effective amplitude equations are determined in one case. This model has three free parameters that are determined numerically. Comparison with chiral symmetry breaking in biochemistry is made., Comment: 4 pages, 2 figures to appear in Proceedings of IAU Symp 286, Comparative Magnetic Minima, C. H. Mandrini, eds

We present the first demonstration of the negative effective magnetic pressure instability in direct numerical simulations of stably stratified, externally forced, isothermal hydromagnetic turbulence in the regime of large plasma beta. By the action of this instability, an initially uniform horizontal magnetic field forms flux concentrations whose scale is large compared to the turbulent scale. We further show that the magnetic energy of these large-scale structures is only weakly dependent on the magnetic Reynolds number, provided its value is large enough for the instability to be excited. Our results support earlier mean-field calculations and analytic work which identified this instability. Applications to the formation of active regions in the Sun are discussed., Comment: 4 pages, 5 figures, published in ApJL

We consider mean-field dynamo models with fluctuating \alpha effect, both with and without shear. The \alpha effect is chosen to be Gaussian white noise with zero mean and given covariance. We show analytically that the mean magnetic field does not grow, but, in an infinitely large domain, the mean-squared magnetic field shows exponential growth of the fastest growing mode at a rate proportional to the shear rate, which agrees with earlier numerical results of Yousef et al (2008) and recent analytical treatment by Heinemann et al (2011) who use a method different from ours. In the absence of shear, an incoherent \alpha^2 dynamo may also be possible. We further show by explicit calculation of the growth rate of third and fourth order moments of the magnetic field that the probability density function of the mean magnetic field generated by this dynamo is non-Gaussian., Comment: Mysteriously missing a line in introduction, ("Heinemann et al. (2011) have recently proposed a simple analytically tractable model ..") which has now been added

We extend earlier models of turbulent dynamos with an upper, nearly force-free exterior to spherical geometry, and study how flux emerges from lower layers to the upper ones without being driven by magnetic buoyancy. We also study how this affects the possibility of plasmoid ejection. A spherical wedge is used that includes northern and southern hemispheres up to mid-latitudes and a certain range in longitude of the Sun. In radius, we cover both the region that corresponds to the convection zone in the Sun and the immediate exterior up to twice the radius of the Sun. Turbulence is driven with a helical forcing function in the interior, where the sign changes at the equator between the two hemispheres. An oscillatory large-scale dynamo with equatorward migration is found to operate in the turbulence zone. Plasmoid ejections occur in regular intervals, similar to what is seen in earlier Cartesian models. These plasmoid ejections are tentatively associated with coronal mass ejections. The magnetic helicity is found to change sign outside the turbulence zone, which is in agreement with recent findings for the solar wind., Comment: 11 pages, 19 figures, accepted in A&A

We present a unified three-dimensional model of the convection zone and upper atmosphere of the Sun in spherical geometry. In this model, magnetic fields, generated by a helically forced dynamo in the convection zone, emerge without the assistance of magnetic buoyancy. We use an isothermal equation of state with gravity and density stratification. Recurrent plasmoid ejections, which rise through the outer atmosphere, is observed. In addition, the current helicity of the small--scale field is transported outwards and form large structures like magnetic clouds., Comment: 4 pages, 4 figures, proceedings of IAU Symp. 274, Advances in Plasma Astrophysics

Evidence for a parity-breaking nature of the magnetic buoyancy instability in a stably stratified gas is reported. In the absence of rotation, no helicity is produced, but the non-helical state is found to be unstable to small helical perturbations during the development of the instability. The parity-breaking nature of an instability in magnetohydrodynamics appears to be the first of its kind and is similar to chiral symmetry breaking in biochemistry. Applications to the production of mean fields in galaxy clusters are being discussed., Comment: consistent with the published version

A strong toroidal field can exist in form of a magnetic layer in the overshoot region below the solar convection zone. This motivates a more detailed study of the magnetic buoyancy instability with rotation. We calculate the alpha effect due to helical motions caused by a disintegrating magnetic layer in a rotating density-stratified system with angular velocity Omega making an angle theta with the vertical. We also study the dependence of the alpha effect on theta and the strength of the initial magnetic field. We carry out three-dimensional hydromagnetic simulations in Cartesian geometry. A turbulent EMF due to the correlations of the small scale velocity and magnetic field is generated. We use the test-field method to calculate the transport coefficients of the inhomogeneous turbulence produced by the layer. We show that the growth rate of the instability and the twist of the magnetic field vary monotonically with the ratio of thermal conductivity to magnetic diffusivity. The resulting alpha effect is inhomogeneous and increases with the strength of the initial magnetic field. It is thus an example of an "anti-quenched" alpha effect. The alpha effect is nonlocal, requiring around 8--16 Fourier modes to reconstruct the actual EMF based on the actual mean field., Comment: 14 pages, 19 figures 3 tables (submitted to A & A)

Magnetic helicity fluxes are investigated in a family of gauges in which the contribution from ideal magnetohydrodynamics takes the form of a purely advective flux. Numerical simulations of magnetohydrodynamic turbulence in this advective gauge family exhibit instabilities triggered by the build-up of unphysical irrotational contributions to the magnetic vector potential. As a remedy, the vector potential is evolved in a numerically well behaved gauge, from which the advective vector potential is obtained by a gauge transformation. In the kinematic regime, the magnetic helicity density evolves similarly to a passive scalar when resistivity is small and turbulent mixing is mild, i.e. when the fluid Reynolds number is not too large. In the dynamical regime, resistive contributions to the magnetic helicity flux in the advective gauge are found to be significant owing to the development of small length scales in the irrotational part of the magnetic vector potential., Comment: 11 pages, 10 figures, submitted to Physics of Plasmas

We present a natural framework for studying the persistence problem in two-dimensional fluid turbulence by using the Okubo-Weiss parameter $\Lambda$ to distinguish between vortical and extensional regions. We then use a direct numerical simulation (DNS) of the two-dimensional, incompressible Navier--Stokes equation with Ekman friction to study probability distribution functions (PDFs) of the persistence times of vortical and extensional regions by employing both Eulerian and Lagrangian measurements. We find that, in the Eulerian case, the persistence-time PDFs have exponential tails; by contrast, this PDF for Lagrangian particles, in vortical regions, has a power-law tail with an exponent $\theta=2.9\pm0.2$., Comment: consistent with the published version

We study the ability of magnetic helicity expulsion to alleviate catastrophic $\alpha$-quenching in mean field dynamos in two--dimensional spherical wedge domains. Motivated by the physical state of the outer regions of the Sun, we consider $\alpha^2\Omega$ mean field models with a dynamical $\alpha$ quenching. We include two mechanisms which have the potential to facilitate helicity expulsion, namely advection by a mean flow ("solar wind") and meridional circulation. We find that a wind alone can prevent catastrophic quenching, with the field saturating at finite amplitude. In certain parameter ranges, the presence of a large-scale meridional circulation can reinforce this alleviation. However, the saturated field strengths are typically below the equipartition field strength. We discuss possible mechanisms that might increase the saturated field., Comment: consistent with the published version

We carry out systematic and high-resolution studies of dynamo action in a shell model for magnetohydrodynamic (MHD) turbulence over wide ranges of the magnetic Prandtl number $Pr_{\rm M}$ and the magnetic Reynolds number $Re_{\rm M}$. Our study suggests that it is natural to think of dynamo onset as a nonequilibrium, first-order phase transition between two different turbulent, but statistically steady, states. The ratio of the magnetic and kinetic energies is a convenient order parameter for this transition. By using this order parameter, we obtain the stability diagram (or nonequilibrium phase diagram) for dynamo formation in our MHD shell model in the $(Pr^{-1}_{\rm M}, Re_{\rm M})$ plane. The dynamo boundary, which separates dynamo and no-dynamo regions, appears to have a fractal character. We obtain hysteretic behavior of the order parameter across this boundary and suggestions of nucleation-type phenomena., Comment: 9 pages, 9 figures

We use direct numerical simulations of forced MHD turbulence with a forcing function that produces two different signs of kinetic helicity in the upper and lower parts of the domain. We show that the mean flux of magnetic helicity from the small-scale field between the two parts of the domain can be described by a Fickian diffusion law with a diffusion coefficient that is approximately independent of the magnetic Reynolds number and about one third of the estimated turbulent magnetic diffusivity. The data suggest that the turbulent diffusive magnetic helicity flux can only be expected to alleviate catastrophic quenching at Reynolds numbers of more than several thousands. We further calculate the magnetic helicity density and its flux in the domain for three different gauges. We consider the Weyl gauge, in which the electrostatic potential vanishes, the pseudo-Lorenz gauge, where the speed of light is replaced by the sound speed, and the `resistive gauge' in which the Laplacian of the magnetic vector potential acts as resistive term. We find that, in the statistically steady state, the time-averaged magnetic helicity density and the magnetic helicity flux are the same in all three gauges., Comment: 6 pages 5 figures

We present direct numerical simulations of the equations of compressible magnetohydrodynamics in a wedge-shaped spherical shell, without shear, but with random helical forcing which has negative (positive) helicity in the northern (southern) hemisphere. We find a large-scale magnetic field that is nearly uniform in the azimuthal direction and approximately antisymmetric about the equator. Furthermore, the large-scale field in each hemisphere oscillates on nearly dynamical time scales with reversals of polarity and equatorward migration. Corresponding mean-field models also show similar migratory oscillations with a frequency that is nearly independent of the magnetic Reynolds number. This mechanism may be relevant for understanding equatorward migration seen in the solar dynamo., Comment: Consistent with the published verstion (emulateapj)