Mean-field dynamo theory has important applications in solar physics and galactic magnetism. We discuss some of the many turbulence effects relevant to the generation of large-scale magnetic fields in the solar convection zone. The mean-field description is then used to illustrate the physics of the α effect, turbulent pumping, turbulent magnetic diffusivity, and other effects on a modern solar dynamo model. We also discuss how turbulence transport coefficients are derived from local simulations of convection and then used in mean-field models.

A mean-field theory of the electrodynamics of a turbulent fluid is formulated under the assumption that the molecular electric conductivity is correlated with the turbulent velocity fluctuation in the (radial) direction, g. It is shown that for such homogeneous fluids a strong turbulence-induced field advection anti-parallel to g arises almost independently of rotation. For rotating fluids, an extra alpha effect appears with the known symmetries and with the expected maximum at the poles. Fast rotation, however, with Coriolis number exceeding unity suppresses this term. Numerical simulations of forced turbulence using the nirvana code demonstrate that the radial advection velocity, gamma, always dominates the alpha term. We show finally with simplified models that alpha(2) dynamos are strongly influenced by the radial pumping: for gamma < alpha the solutions become oscillatory, while for gamma > alpha they become highly exotic if they exist at all. In conclusion, dynamo models for slow and fast solid-body rotation on the basis of finite conductivity-velocity correlations are unlikely to work, at least for alpha(2)omega dynamos without strong shear.

Large-scale coherent magnetic fields observed in the nearby galaxies are thought to originate by a mean-field dynamo. This is governed via the turbulent electromotive force (EMF, (epsilon) over bar) generated by the helical turbulence driven by supernova (SN) explosions in the differentially rotating interstellar medium (ISM). In this paper, we aim to investigate the possibility of dynamo action by the virtue of buoyancy due to a cosmic ray (CR) component injected through the SN explosions. We do this by analysing the magnetohydrodynamic simulations of local shearing box of ISM in which the turbulence is driven via random SN explosions and the energy of the explosion is distributed in the CR and/or thermal energy components. We use the magnetic field aligned diffusion prescription for the propagation of CR. We compare the evolution of magnetic fields in the models with the CR component to our previous models that did not involve the CR. We demonstrate that the inclusion of CR component enhances the growth of dynamo slightly. We further compute the underlying dynamo coefficients using the test-field method and argue that the entire evolution of the large-scale mean magnetic field can be reproduced with an alpha - Omega dynamo model. We also show that the inclusion of CR component leads to an unbalanced turbulent pumping between magnetic field components and additional dynamo action by the Radler effect.

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Coherent magnetic fields in disc galaxies are thought to be generated by a large-scale (or mean-field) dynamo operating in their interstellar medium. A key driver of mean magnetic field growth is the turbulent electromotive force (EMF), which represents the influence of correlated small-scale (or fluctuating) velocity and magnetic fields on themean field. The EMF is usually expressed as a linear expansion in the mean magnetic field and its derivatives, with the dynamo tensors as expansion coefficients. Here, we adopt the singular value decomposition (SVD) method to directly measure these turbulent transport coefficients in a simulation of the turbulent interstellar medium that realizes a large-scale dynamo. Specifically, the SVD is used to least-square fit the time series data of the EMF with that of the mean field and its derivatives, to determine these coefficients. We demonstrate that the spatial profiles of the EMF reconstructed from the SVD coefficients match well with that taken directly from the simulation. Also, as a direct test, we use the coefficients to simulate a 1D mean-field dynamo model and find an overall similarity in the evolution of the mean magnetic field between the dynamo model and the direct simulation. We also compare the results with those which arise using simple regression and the ones obtained previously using the test-field method, to find reasonable qualitative agreement. Overall, the SVD method provides an effective post-processing tool to determine turbulent transport coefficients from simulations.

The interstellar medium of the Milky Way and nearby disk galaxies harbours large-scale coherent magnetic fields of Microgauss strength, that can be explained via the action of a mean-field dynamo. As in our previous work, we aim to quantify dynamo effects that are self-consistently emerging in realistic direct magnetohydrodynamic simulations, but we generalise our approach to the case of a non-local (non-instantaneous) closure relation, described by a convolution integral in space (time). To this end, we leverage our comprehensive simulation framework for the supernova-regulated turbulent multi-phase interstellar medium. By introducing spatially (temporally) modulated mean fields, we extend the previously used test-field method to the spectral realm -- providing the Fourier representation of the convolution kernels. The resulting spectra of the dynamo mean-field coefficients that we obtain broadly match expectations and allow to rigorously constrain the degree of scale separation in the Galactic dynamo. A surprising result is found for the diamagnetic pumping term, which increases in amplitude when going to smaller scales. Our results amount to the most comprehensive description of dynamo mean-field effects in the Galactic context to date. Surveying the relevant parameter space and quenching behaviour, this will ultimately enable the development of assumption-free sub-grid prescriptions for otherwise unresolved global galaxy simulations.

AbstractThe profile of the differential rotation together with the sign of the alpha-effect determine the dynamo wave direction. In early models of the solar dynamo the dynamo wave often leads to a poleward migration of the activity belts. Flux transport by the meridional flow or the effect of the surface shear layer are possible solutions. In a model including the corona, we show that various migrations can be obtained by varying the properties of the corona. A new dynamo of Babcock-Leighton type also leads to the correct equatorward migration by the non-linear relation between flux density and rise time of the flux.

Context . Solar dynamo models of Babcock-Leighton type typically assume the rise of magnetic flux tubes to be instantaneous. The periods of solutions with high magnetic diffusivity are too short, and their active belts do not migrate correctly. Only the low-diffusivity regime with advective meridional flows is usually considered. Aims . We here discuss these assumptions and apply a time delay in the source term of the azimuthally averaged induction equation. This delay is set to be the rise time of magnetic flux tubes, which are assumed to form at the tachocline. We study the effect of the delay, which adds a nonlinear temporal to the spacial nonlocality in the advective but particularly in the diffusive regime. Methods . We have previously obtained the rise time as a function of rotation and the magnetic field strength at the bottom of the convection zone. These results allowed us to constrain the delay in the mean-field model we used in a parameter study. Results . We identify an unknown family of solutions. These solutions show self-quenching and exhibit longer periods than their nondelayed counterparts. Additionally, we demonstrate that the nonlinear delay is responsible for the recovery of the equatorward migration of the active belts at high turbulent diffusivities. Conclusions . By introducing a nonlinear temporal nonlocality (the delay) in a Babcock-Leighton dynamo model, we were able to obtain solutions that are quantitatively comparable to the solar butterfly diagram in the diffusion-dominated regime.

It is still unknown how magnetic field-generation mechanisms could operate in low-mass dwarf galaxies. Here, we present a detailed study of a nearby pure-disk dwarf galaxy NGC 2976. Unlike previously observed dwarf objects, this galaxy possesses a clearly defined disk. For the purpose of our studies, we performed deep multi-frequency polarimetric observations of NGC 2976 with the VLA and Effelsberg radio telescopes. Additionally, we supplement them with re-imaged data from the WSRT-SINGS survey. The magnetic field morphology discovered in NGC 2976 consists of a southern polarized ridge. This structure does not seem to be due to just a pure large-scale dynamo process (possibly cosmic-ray driven) at work in this object, as indicated by the RM data and dynamo number calculations. Instead, the field of NGC 2976 is modified by past gravitational interactions and possibly also by ram pressure inside the M 81 galaxy group environment. The estimates of total (7 muG) and ordered (3 muG) magnetic field strengths, as well as degree of field order (0.46), which is similar to those observed in spirals, suggest that tidally generated magnetized gas flows can further enhance dynamo action in the object. NGC 2976 is apparently a good candidate for the efficient magnetization of its neighbourhood. It is able to provide an ordered (perhaps also regular) magnetic field into the intergalactic space up to a distance of about 5 kpc. Tidal interactions (and possibly also ram pressure) can lead to the formation of unusual magnetic field morphologies (like polarized ridges) in galaxies out of the star-forming disks, which do not follow any observed component of the interstellar medium (ISM), as observed in NGC 2976. These galaxies are able to provide ordered magnetic fields far out of their main disks.

The development of smooth particle magnetohydrodynamic (SPMHD) has significantly improved the simulation of complex astrophysical processes. However, the preservation the solenoidality of the magnetic field is still a severe problem for the MHD. A formulation of the induction equation with a vector potential would solve the problem. Unfortunately all previous attempts suffered from instabilities. In the present work, we evolve the vector potential in the Coulomb gauge and smooth the derived magnetic field for usage in the momentum equation. With this implementation we could reproduce classical test cases in a stable way. A simple test case demonstrates the possible failure of widely used direct integration of the magnetic field, even with the usage of a divergence cleaning method.

The ordered magnetic field observed via polarised synchrotron emission in nearby disc galaxies can be explained by a mean-field dynamo operating in the diffuse interstellar medium (ISM). Additionally, vertical-flux initial conditions are potentially able to influence this dynamo via the occurrence of the magnetorotational instability (MRI). We aim to study the influence of various initial field configurations on the saturated state of the mean-field dynamo. This is motivated by the observation that different saturation behaviour was previously obtained for different supernova rates. We perform direct numerical simulations (DNS) of three-dimensional local boxes of the vertically stratified, turbulent interstellar medium, employing shearing-periodic boundary conditions horizontally. Unlike in our previous work, we also impose a vertical seed magnetic field. We run the simulations until the growth of the magnetic energy becomes negligible. We furthermore perform simulations of equivalent 1D dynamo models, with an algebraic quenching mechanism for the dynamo coefficients. We compare the saturation of the magnetic field in the DNS with the algebraic quenching of a mean-field dynamo. The final magnetic field strength found in the direct simulation is in excellent agreement with a quenched alpha Omega dynamo. For supernova rates representative of the Milky Way, field losses via a Galactic wind are likely responsible for saturation. We conclude that the relative strength of the turbulent and regular magnetic fields in spiral galaxies may depend on the galaxy's star formation rate. We propose that a mean field approach with algebraic quenching may serve as a simple sub-grid scale model for galaxy evolution simulations including a prescribed feedback from magnetic fields. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

We aim to estimate the contribution of the radial component of the Lorentz force to the gas rotation in several types of galaxies. Using typical parameters for the exponential scale of synchrotron emission and the scale length of HI gas, under the assumption of equipartition between the energies of cosmic rays and total magnetic fields, we derive the Lorentz force and compare it to the gravitational force in the radial component of the momentum equation. We distinguish the different contributions between the large scale and the small-scale turbulent fields by Reynolds averaging. We compare these findings with a dynamical dynamo model. We find a possible reduction of circular gas velocity in the outermost parts and an increase inside a radius of four times the synchrotron scale length. Sufficiently localised radial reversals of the magnetic field may cause characteristic modulations in the gas rotation curve with typical amplitudes of 10-20 km s(-1). It is unlikely that the magnetic field contributes to the flat rotation in the outer parts of galaxies. If anything, it will impede the gravitationally supported rotation. demanding an even higher halo mass to explain the observed rotation profile. We speculate that this may have consequences for ram pressure stripping and the truncation of the stellar disc.

The emergence of large-scale magnetic fields observed in the diffuse interstellar medium is explained by a turbulent dynamo. The underlying transport coefficients have previously been extracted from numerical simulations. So far, this was restricted to the kinematic regime, but we aim to extend our analysis into the realm of dynamically important fields. This marks an important step on which derived mean-field models rely to explain observed equipartition-strength fields. As in previous work, we diagnose turbulent transport coefficients by means of the test-field method. We derive quenching functions for the dynamo a effect, diamagnetic pumping and turbulent diffusivity, which are compared with theoretical expectations. At late times, we observe the suppression of the vertical wind. Because this potentially affects the removal of small-scale magnetic helicity, new concerns arise about circumventing constraints imposed by the conservation of magnetic helicity at high magnetic Reynolds numbers. While present results cannot safely rule out this possibility, the issue only becomes important at late stages and is absent when the dynamo is quenched by the wind itself.

Context. Based on the rapidly increasing all-sky data of Faraday rotation measures and polarised synchrotron radiation, the Milky Way's magnetic field can now be modelled with an unprecedented level of detail and complexity.Aims. We aim to complement this phenomenological approach with a physically motivated, quantitative dynamo model - a model that moreover allows for the evolution of the system as a whole, instead of just solving the induction equation for a fixed static disc.Methods. Building on the framework of mean-field magnetohydrodynamics and extending it to the realm of a hybrid evolution, we performed three-dimensional global simulations of the Galactic disc. To eliminate free parameters, closure coefficients embodying the mean-field dynamo were calibrated against resolved local simulations of supernova-driven interstellar turbulence.Results. The emerging dynamo solutions comprise a mixture of the dominant axisymmetric S0 mode with even parity, and a subdominant A0 mode with odd parity. Notably, this superposition of modes creates a strong localised vertical field on one side of the Galactic disc. Moreover, we found significant radial pitch angles that decay with radius, which can be explained by flaring of the disc. In accordance with previous work, magnetic instabilities appear to be restricted to the calmer outer Galactic disc. Their main effect is to create strong fields at large radii such that the radial scale length of the magnetic field increases from 4 kpc (for a mean-field dynamo alone) to about 10 kpc in the hybrid models - the latter being in much better agreement with observations.Conclusions. There remain aspects (e. g., spiral arms, X-shaped halo fields, fluctuating fields) that are not captured by the current model and that will require further development towards a fully dynamical evolution. Nevertheless, we demonstrate that a hybrid modelling of the Galactic dynamo is feasible and can serve as a foundation for future efforts.

Magnetic field amplification by a fast dynamo is seen in local box simulations of SN-driven ISM turbulence, where the self-consistent emergence of large-scale fields agrees very well with its mean-field description. We accordingly derive scaling laws of the turbulent transport coef- ficients in dependence of the SN rate, density and rotation. These provide the input for global simulations of regular magnetic fields in galaxies within a mean-field MHD framework. Using a Kennicutt-Schmidt relation between the star formation (SF) rate and midplane density, we can reduce the number of free parameters in our global models. We consequently present dynamo models for different rotation curves and radial density distributions.

The helicity and a effect driven by the non-axisymmetric Tayler instability of toroidal magnetic fields in stellar radiation zones are computed. In the linear approximation, a purely toroidal field always excites pairs of modes with identical growth rates but with opposite helicity so that the net helicity vanishes. If the magnetic background field has a helical structure by an extra (weak) poloidal component then one of the modes dominates, producing a net kinetic helicity anticorrelated with the current helicity of the background field. The mean electromotive force is computed with the result that the a effect by the most rapidly growing mode has the same sign as the current helicity of the background field. The a effect is found to be too small to drive an a2 dynamo, but the excitation conditions for an aO dynamo can be fulfilled for weak poloidal fields. Moreover, if the dynamo produces its own a effect by the magnetic instability, then problems with its sign do not arise. For all cases, however, the a effect shows an extremely strong concentration to the poles so that a possible aO dynamo might only work at the polar regions. Hence, the results of our linear theory lead to a new topological problem for the existence of large-scale dynamos in stellar radiation zones on the basis of the current-driven instability of toroidal fields.

Aims. In this work the latitude-dependent stellar spot rotation is investigated based on dynamo models, and with similar analysis techniques as for real observations. The resulting surface differential rotation patterns are compared to the known input rotation law used in the calculation of the dynamo model.Methods. Snapshots of the dynamo simulations are used to measure the surface differential rotation. The maps of the magnetic pressure at the surface are treated similarly to the temperature maps obtained using Doppler imaging techniques, and a series of snapshots from the dynamo models are cross-correlated to obtain the shift of the magnetic patterns at each latitude and time point. These shifts are used to study the surface rotation pattern over a wide latitude range at different epochs during the activity cycle, and are compared to the known input rotation law.Results. Two different rotation laws are investigated, one solar-type law and one with axis-distance-dependent rotation. Three different dynamo calculations are carried out based on the axis-distance-dependent law: one with a large-scale dynamo field only, one with an additional strong small-scale field and one with a weaker small-scale field. The surface differential rotation patterns obtained from the snapshots of all four dynamo calculations show variability over the activity cycle. Clear evolution and variation in the measured surface rotation patterns is seen, but in the models using only the large-scale dynamo field the measured rotation patterns are only at times similar to the input rotation law. This is because the spot motion is mainly determined by the geometric properties of the large-scale dynamo field. In the models with an additional small-scale magnetic field the surface differential rotation measured from the model follows the input rotation law well.Conclusions. Here, the surface differential rotation patterns are investigated in detail based on dynamo calculations for the first time. The results imply that the stellar spots caused by the large-scale dynamo field are not necessarily tracing the stellar differential rotation, whereas the spots formed from small-scale fields trace the surface flow patterns well. One may wonder whether the large spots observed in active stars could be caused by small-scale fields. Therefore, it is still unclear if the true stellar surface rotation can be recovered using measurements of large starspots, which are currently the only observable feature.

The current-driven instability of toroidal magnetic fields under the influence of both axial magnetic-field components and (differential) rotation is studied. The MHD equations are solved by means of a simplified model with cylindric geometry that assumes both the axial field and the axial current as uniform and the fluid as incompressible. If azimuthal and axial field components are nearly the same size, then the instability is (slightly) supported, and modes with m > 1 dominate. If the axial field dominates, then the most unstable modes again have m > 1, but the field is strongly stabilized. The modes are suppressed by a fast rigid rotation where the m = 1 mode maximally resists. Only this mode becomes best re-animated for Omega > Omega(A) (Omega(A) the Alfven frequency) if the rotation has a negative shear. The general finding of the linear theory is that the higher modes with m > 1 do not play an important role for the stability of rotating fluids.If applied to dynamo-generated galactic magnetic fields influenced by the typical rotation law with constant azimuthal velocity, the result is that galactic fields should only be marginally unstable against perturbations with m <= 1. Modes with higher m may not appear. The corresponding growth rates are close to the rotation period of the inner part of the galaxy.

Supernovae are known to be the dominant energy source for driving turbulence in the interstellar medium. Yet, their effect on magnetic field amplification in spiral galaxies is still poorly understood. Analytical models based on the uncorrelated-ensemble approach predicted that any created field will be expelled from the disk before a significant amplification can occur. By means of direct simulations of supernova-driven turbulence, we demonstrate that this is not the case. Accounting for vertical stratification and galactic differential rotation, we find an exponential amplification of the mean field on timescales of 100 Myr. We highlight the importance of rotation in the generation of helicity by showing that a similar mechanism based on Cartesian shear does not lead to a sustained amplification of the mean magnetic field.