Search

We discuss selected aspects regarding the magnetic field evolution of solar-type stars. Most of the stars with activity cycles are in the range where the normalized chromospheric Calcium emission increases linearly with the inverse Rossby number. For Rossby numbers below about a quarter of the solar value, the activity saturates and no cycles have been found. For Rossby numbers above the solar value, again no activity cycles have been found, but now the activity goes up again for a major fraction of the stars. Rapidly rotating stars show nonaxisymmetric large-scale magnetic fields, but there is disagreement between models and observations regarding the actual value of the Rossby number where this happens. We also discuss the prospects of detecting the sign of magnetic helicity using various linear polarization techniques both at the stellar surface using the parity-odd contribution to linear polarization and above the surface using Faraday rotation., Comment: 13 pages, 3 figures, 3 tables, proceedings of IAU symposium 354, Solar and Stellar Magnetic Fields: Origins and Manifestations

The large-scale magnetic field of the Milky Way is thought to be created by an alpha-Omega dynamo, which implies that it should have opposite handedness North and South of the Galactic midplane. Here we attempt to detect a variation in handedness using polarization data from the Wilkinson Microwave Anisotropy Probe. Previous analyzes of the parity-even and parity-odd parts of linear polarization of the global dust and synchrotron emission have focused on quadratic correlations in spectral space of, and between, these two components. Here, by contrast, we analyze the parity-odd polarization itself and show that it has, on average, opposite signs in Northern and Southern Galactic hemispheres. Comparison with a Galactic mean-field dynamo model shows broad qualitative agreement and reveals that the sign of the observed hemispheric dependence of the azimuthally averaged parity-odd polarization is not determined by the sign of alpha, but by the sense of differential rotation., Comment: 7 pages, 4 figures, 1 table, submitted to ApJL

We study the prospects of detecting magnetic helicity in galaxies by observing the dust polarization of the edge-on galaxy NGC 891. Our numerical results of mean-field dynamo calculations show that there should be a large-scale component of the rotationally invariant parity-odd B polarization that we predict to be negative in the first and third quadrants, and positive in the second and fourth quadrants. The large-scale parity-even E polarization is predicted to be negative near the axis and positive further away in the outskirts. These properties are shown to be mostly a consequence of the magnetic field being azimuthal and the polarized intensity being maximum at the center of the galaxy and are not a signature of magnetic helicity., Comment: 12 pages, 11 figures, 2 tables, MNRAS, in press

The temporal growth in the number of deaths in the COVID-19 epidemic is subexponential. Here we show that a piecewise quadratic law provides an excellent fit during the thirty days after the first three fatalities on January 20 and later since the end of March 2020. There is also a brief intermediate period of exponential growth. During the second quadratic growth phase, the characteristic time of the growth is about eight times shorter than in the beginning, which can be understood as the occurrence of separate hotspots. Quadratic behavior can be motivated by peripheral growth when further spreading occurs only on the outskirts of an infected region. We also study numerical solutions of a simple epidemic model, where the spatial extend of the system is taken into account. To model the delayed onset outside China together with the early one in China within a single model with minimal assumptions, we adopt an initial condition of several hotspots, of which one reaches saturation much earlier than the others. At each site, quadratic growth commences when the local number of infections has reached a certain saturation level. The total number of deaths does then indeed follow a piecewise quadratic behavior., Comment: 9 pages, 14 figures, 2 tables, published in Infectious Disease Modelling

We perform fully kinetic simulations of flows known to produce dynamo in magnetohydrodynamics (MHD), considering scenarios with low Reynolds number and high magnetic Prandtl number, relevant for galaxy cluster scale fluctuation dynamos. We find that Landau damping on the electrons leads to a rapid decay of magnetic perturbations, impeding the dynamo. This collisionless damping process operates on spatial scales where electrons are nonmagnetized, reducing the range of scales where the magnetic field grows in high magnetic Prandtl number fluctuation dynamos. When electrons are not magnetized down to the resistive scale, the magnetic energy spectrum is expected to be limited by the scale corresponding to magnetic Landau damping or, if smaller, the electron gyroradius scale, instead of the resistive scale. In simulations we thus observe decaying magnetic fields where resistive MHD would predict a dynamo., Comment: Simulation data available at Zenodo https://doi.org/10.5281/zenodo.3886562

For velocity and magnetic fields, the turbulent pressure and, more generally, the squared fields such as the components of the turbulent stress tensor, play important roles in astrophysics. For both one and three dimensions, we derive the equations relating the energy spectra of the fields to the spectra of their squares. We solve the resulting integrals numerically and show that for turbulent energy spectra of Kolmogorov type, the spectral slope of the stress spectrum is also of Kolmogorov type. For shallower turbulence spectra, the slope of the stress spectrum quickly approaches that of white noise, regardless of how blue the spectrum of the field is. For fully helical fields, the stress spectrum is elevated by about a factor of two in the subinertial range, while that in the inertial range remains unchanged. We discuss possible implications for understanding the spectrum of primordial gravitational waves from causally generated magnetic fields during cosmological phase transitions in the early universe. We also discuss potential diagnostic applications to the interstellar medium, where polarization and scintillation measurements characterize the square of the magnetic field., Comment: 7 pages, 9 figures, ApJ, in press

In recent years, several optimal dynamos have been discovered. They minimize the magnetic energy dissipation or, equivalently, maximize the growth rate at a fixed magnetic Reynolds number. In the optimal dynamo of Willis (2012, Phys. Rev. Lett. 109, 251101), we find mean-field dynamo action for planar averages. One component of the magnetic field grows exponentially while the other decays in an oscillatory fashion near onset. This behavior is different from that of an alpha^2 dynamo, where the two non-vanishing components of the planar averages are coupled and have the same growth rate. For the Willis dynamo, we find that the mean field is excited by a negative turbulent magnetic diffusivity, which has a non-uniform spatial profile near onset. The temporal oscillations in the decaying component are caused by the corresponding component of the diffusivity tensor being complex when the mean field is decaying and, in this way, time-dependent. The growing mean field can be modeled by a negative magnetic diffusivity combined with a positive magnetic hyperdiffusivity. In two other classes of optimal dynamos of Chen et al. (2015, J. Fluid Mech. 783, 23), we find, to some extent, similar mean-field dynamo actions. When the magnetic boundary conditions are mixed, the two components of the planar averaged field grow at different rates when the dynamo is 15% supercritical. When the mean magnetic field satisfies homogeneous boundary conditions (where the magnetic field is tangential to the boundary), mean-field dynamo action is found for one-dimensional averages, but not for planar averages. Despite having different spatial profiles, both dynamos show negative turbulent magnetic diffusivities. Our finding suggests negative turbulent magnetic diffusivities may support a broader class of dynamos than previously thought, including these three optimal dynamos., Comment: 23 pages, 15 figures, 2 tables, submitted to J. Plasma Phys

We study a turbulent helical dynamo in a periodic domain by solving the ideal magnetohydrodynamic (MHD) equations with the FLASH code using the divergence-cleaning eight-wave method and compare our results with direct numerical simulations (DNS) using the Pencil Code. At low resolution, FLASH reproduces the DNS results qualitatively by developing the large-scale magnetic field expected from DNS, but at higher resolution, no large-scale magnetic field is obtained. In all those cases in which a large-scale magnetic field is generated, the ideal MHD results yield too little power at small scales. As a consequence, the small-scale current helicity is too small compared with that of the DNS. The resulting net current helicity has then always the wrong sign, and its statistical average also does not approach zero at late times, as expected from the DNS. Our results have implications for astrophysical dynamo simulations of stellar and galactic magnetism using ideal MHD codes., Comment: 9 pages, 14 figures, 2 tables, ApJ 889, 55 (2020)

If the alpha effect plays a role in the generation of the Sun's magnetic field, the field should show evidence of magnetic helicity of opposite signs at large and small length scales. Measuring this faces two challenges: (i) in weak-field regions, horizontal field measurements are unreliable because of the pi ambiguity, and (ii) one needs a truly global approach to computing helicity spectra in the case where one expects a sign reversal across the equator at all wavenumbers. Here we develop such a method using spin-2 spherical harmonics to decompose the linear polarization in terms of the parity-even and parity-odd E and B polarizations, respectively. Using simple one- and two-dimensional models, we show that the product of the spectral decompositions of E and B, taken at spherical harmonic degrees that are shifted by one, can act as a proxy of the global magnetic helicity with a sign that represents that in the northern hemisphere. We then apply this method to the analysis of solar synoptic vector magnetograms, from which we extract a pseudo-polarization corresponding to a "pi-ambiguated" magnetic field, i.e., a magnetic field vector that has no arrow. We find a negative sign of the global EB helicity proxy at spherical harmonic degrees of around 6. This could indicate a positive magnetic helicity at large length scales, but the spectrum fails to capture clear evidence of the well-known negative magnetic helicity at smaller scales. This method might also be applicable to stellar and Galactic polarization data., Comment: 11 pages, 7 figures, 5 tables, ApJ, in press

Large-scale magnetic fields in stars and galaxies are thought to arise by mean-field dynamo action due to the combined influence of both helical turbulence and shear. Those systems are also highly conducting and the turbulence therein leads to a fluctuation (or small-scale) dynamo which more rapidly amplifies magnetic field fluctuations on the eddy scales and smaller. Will this then interfere with and suppress the mean (or large-scale) field growth? Using direct numerical simulations of helical turbulence (with and without shear), we identify a novel quasi-kinematic large-scale dynamo which operates as the small-scale dynamo saturates. Thus both dynamos operate efficiently, one after the other, and lead to the generation of significant large-scale fields., Comment: 8 pages, 11 figures. Comments/feedback/discussions are welcome

We show that at large magnetic Prandtl numbers, the Lorentz force does work on the flow at small scales and drives fluid motions, whose energy is dissipated viscously. This situation is opposite to that in a normal dynamo, where the flow does work against the Lorentz force. We compute the spectral conversion rates between kinetic and magnetic energies for several magnetic Prandtl numbers and show that normal (forward) dynamo action occurs on large scales over a progressively narrower range of wavenumbers as the magnetic Prandtl number is increased. At higher wavenumbers, reversed dynamo action occurs, i.e., magnetic energy is converted back into kinetic energy at small scales. We demonstrate this in both direct numerical simulations forced by volume stirring and in large eddy simulations of solar convectively driven small-scale dynamos. Low density plasmas such as stellar coronae tend to have large magnetic Prandtl numbers, i.e., the viscosity is large compared with the magnetic diffusivity. The regime in which viscous dissipation dominates over resistive dissipation for large magnetic Prandtl numbers was also previously found in large eddy simulations of the solar corona, i.e., our findings are a more fundamental property of MHD that is not just restricted to dynamos. Viscous energy dissipation is a consequence of positive Lorentz force work, which may partly correspond to particle acceleration in close-to-collisionless plasmas. This is, however, not modeled in the MHD approximation employed. By contrast, resistive energy dissipation on current sheets is expected to be unimportant in stellar coronae., Comment: 9 pages, 6 figures, 2 tables, Astrophys. J., in press

We study the effects of ambipolar diffusion (AD) on hydromagnetic turbulence. In most of the cases, we use the single fluid approximation where the drift velocity between charged and neutral particles is proportional to the Lorentz force. In two cases we also compare with the corresponding two-fluid model, where ionization and recombination are included in the continuity and momentum equations for the neutral and charged species. We consider the regime of large magnetic Prandtl number, relevant to the interstellar medium. The magnetic field properties are found to be well represented by the single fluid approximation. We quantify the effects of AD on total and spectral kinetic and magnetic energies, the Ohmic and AD dissipation rates, the statistics of the magnetic field, the current density, and the linear polarization as measured by the rotationally invariant E and B mode polarizations. We show that the kurtosis of the magnetic field decreases with increasing AD. The E mode polarization changes its skewness from positive values for small AD to negative ones for large AD. Even when AD is weak, changes in AD have a marked effect on the skewness and kurtosis of E, and only a weak effect on those of B. These results open the possibility of employing E and B mode polarizations as diagnostic tools for characterizing turbulent properties of the interstellar medium., Comment: 13 pages, 13 figures, 1 table, MNRAS, in press

We perform direct numerical simulations of magnetohydrodynamic turbulence in the early universe and numerically compute the resulting stochastic background of gravitational waves and relic magnetic fields. These simulations do not make the simplifying assumptions of earlier analytic work. If the turbulence is assumed to have an energy-carrying scale that is about a hundredth of the Hubble radius at the time of generation, as expected in a first-order phase transition, the peak of gravitational wave power will be in the mHz frequency range for a signal produced at the electroweak scale. The efficiency of gravitational wave (GW) production varies significantly with how the turbulence is driven. Detectability of turbulence at the electroweak scale by the planned Laser Interferometer Space Antenna (LISA) requires anywhere from 0.1% to 10% of the thermal plasma energy density to be in plasma motions or magnetic fields, depending on the model of the driving process. Our results predict a new universal form below the spectral peak frequency that is shallower than previously thought. This implies larger values of the GW energy spectra in the low-frequency range. This extends the range where turbulence is detectable with LISA to lower frequencies, corresponding to higher energy scales than the assumed energy-carrying scale., Comment: 11 pages, 1 appendix, 7 + 1 (appendix) figures, 2 tables, published in PRD, updated figures and corrected normalization error

To understand the effects of fluctuations on achieving homochirality, we employ a Monte-Carlo method where autocatalysis and enantiomeric cross-inhibition, as well as racemization and deracemization reactions are included. The results of earlier work either without autocatalysis or without cross-inhibition are reproduced. Bifurcation diagrams and the dependencies of the number of reaction steps on parameters are studied. In systems with 30,000 molecules, for example, up to a billion reaction steps may be needed to achieve homochirality without autocatalysis., Comment: 14 pages, 5 figures, 2 tables, Orig. Life Evol. Biosph., in press

We compute magnetic helicity and energy spectra from about 2485 patches of about 100 megameters (Mm) side length on the solar surface using data from Hinode during 2006--2017. An extensive database is assembled where we list magnetic energy and helicity, large- and small-scale magnetic helicity, mean current helicity density, fractional magnetic helicity, and correlation length along with the Hinode map identification number (MapID), as well as Carrington latitude and longitude for each MapID. While there are departures from the hemispheric sign rule for magnetic and current helicities, the weak trend reported here is in agreement with the previous results. This is argued to be a physical effect associated with the dominance of individual active regions that contribute more strongly in the better resolved Hinode maps. In comparison with earlier work, the typical correlation length is found to be 6-8 Mm, while the length scale relating magnetic and current helicity to each other is found to be around 1.4 Mm., Comment: 10 pages, 7 figures, 3 tables, submitted to ApJ; see http://www.nordita.org/~brandenb/project/Hinode for online data

We present a high-resolution convergence study of detonation initiated by a temperature gradient in a stoichiometric hydrogen-oxygen mixture using the Pencil Code and compare with a code that employs a fifth order weighted essentially non-oscillating (WENO) scheme. With Mach numbers reaching 10-30, a certain amount of shock viscosity is needed in the Pencil Code to remove or reduce numerical pressure oscillations on the grid scale at the position of the shock. Detonation is found to occur for intermediate values of the shock viscosity parameter. At fixed values of this parameter, the numerical error associated with those small wiggles in the pressure profile is found to decrease with decreasing mesh width $\delta x$ like $\delta x^{-1.4}$ down to $\delta x=0.2\mu$m. With the WENO scheme, solutions are smooth at $\delta x=10\mu$m, but no detonation is obtained for $\delta x=5\mu$m. This is argued to be an artifact of a decoupling between pressure and reaction fronts., Comment: 18 pages, 10 figures, 1 table, Geophys. Astrophys. Fluid Dynam., in press, special issue "Physics and Algorithms of the Pencil Code"

Explicit radiation hydrodynamic simulations of the atmospheres of massive stars and of convection in accretion discs around white dwarfs suffer from prohibitively short time steps due to radiation. This constraint is related to the cooling time rather than the radiative pressure, which also becomes important in hot stars and discs. We show that the radiative time step constraint is governed by the minimum of the sum of the optically thick and thin contributions rather than the smaller one of the two. In simulations with the Pencil Code, their weighting fractions are found empirically. In three-dimensional convective accretion disc simulations, the Deardorff term is found to be the main contributor to the enthalpy flux rather than the superadiabatic gradient. We conclude with a discussion of how the radiative time step problem could be mitigated in certain types of investigations., Comment: 30 pages, 11 figures, 5 tables, Geophys. Astrophys. Fluid Dynam., in press, special issue "Physics and Algorithms of the Pencil Code"

We study the evolution of kinetic and magnetic energy spectra in magnetohydrodynamic flows in the presence of strong cross helicity. For forced turbulence, we find weak inverse transfer of kinetic energy toward the smallest wavenumber. This is plausibly explained by the finiteness of scale separation between the injection wavenumber and the smallest wavenumber of the domain, which here is a factor of 15. In the decaying case, there is a slight increase at the smallest wavenumber, which is probably explained by the dominance of kinetic energy over magnetic energy at the smallest wavenumbers. Within a range of wavenumbers covering almost an order of magnitude the decay is purely exponential, which is argued to be a consequence of a suppression of nonlinearity due to the presence of strong cross helicity., Comment: 6 pages, 6 figures, Astron. Nachr

(abridged) Context: Turbulent diffusion of large-scale flows and magnetic fields play major roles in many astrophysical systems. Aims: Our goal is to compute turbulent viscosity and magnetic diffusivity, relevant for diffusing large-scale flows and magnetic fields, respectively, and their ratio, the turbulent magnetic Prandtl number, ${\rm Pm}_{\rm t}$, for isotropically forced homogeneous turbulence. Methods: We use simulations of forced turbulence in fully periodic cubes composed of isothermal gas with an imposed large-scale sinusoidal shear flow. Turbulent viscosity is computed either from the resulting Reynolds stress or from the decay rate of the large-scale flow. Turbulent magnetic diffusivity is computed using the test-field method. The scale dependence of the coefficients is studied by varying the wavenumber of the imposed sinusoidal shear and test fields. Results: We find that turbulent viscosity and magnetic diffusivity are in general of the same order of magnitude. Furthermore, the turbulent viscosity depends on the fluid Reynolds number (${\rm Re}$) and scale separation ratio of turbulence. The scale dependence of the turbulent viscosity is found to be well approximated by a Lorentzian. The results for the turbulent transport coefficients appear to converge at sufficiently high values of ${\rm Re}$ and the scale separation ratio. However, a weak decreasing trend is found even at the largest values of ${\rm Re}$. The turbulent magnetic Prandtl number converges to a value that is slightly below unity for large ${\rm Re}$ whereas for small ${\rm Re}$, we find values between 0.5 and 0.6. Conclusions: The turbulent magnetic diffusivity is in general consistently higher than the turbulent viscosity. The actual value of ${\rm Pm}_{\rm t}$ found from the simulations ($\approx0.9\ldots0.95$) at large ${\rm Re}$ and scale separation ratio is higher than any of the analytic predictions., Comment: 13 pages, 12 figures, accepted in Astron. Astrophys

Blazar observations point toward the possible presence of magnetic fields over intergalactic scales of the order of up to $\sim1\,$Mpc, with strengths of at least $\sim10^{-16}\,$G. Understanding the origin of these large-scale magnetic fields is a challenge for modern astrophysics. Here we discuss the cosmological scenario, focussing on the following questions: (i) How and when was this magnetic field generated? (ii) How does it evolve during the expansion of the universe? (iii) Are the amplitude and statistical properties of this field such that they can explain the strengths and correlation lengths of observed magnetic fields? We also discuss the possibility of observing primordial turbulence through direct detection of stochastic gravitational waves in the mHz range accessible to LISA., Comment: Invited talk given at FM8 "New Insights in Extragalactic Magnetic Fields", XXX IAU GA, Vienna, Austria, August 29, 2018; 4 pages; 2 figures; accepted for publication

It was previously shown that the superdroplet algorithm for modeling the collision-coalescence process can faithfully represent mean droplet growth in turbulent clouds. But an open question is how accurately the superdroplet algorithm accounts for fluctuations in the collisional aggregation process. Such fluctuations are particularly important in dilute suspensions. Even in the absence of turbulence, Poisson fluctuations of collision times in dilute suspensions may result in substantial variations in the growth process, resulting in a broad distribution of growth times to reach a certain droplet size. We quantify the accuracy of the superdroplet algorithm in describing the fluctuating growth history of a larger droplet that settles under the effect of gravity in a quiescent fluid and collides with a dilute suspension of smaller droplets that were initially randomly distributed in space ('lucky droplet model'). We assess the effect of fluctuations upon the growth history of the lucky droplet and compute the distribution of cumulative collision times. The latter is shown to be sensitive enough to detect the subtle increase of fluctuations associated with collisions between multiple lucky droplets. The superdroplet algorithm incorporates fluctuations in two distinct ways: through the random spatial distribution of superdroplets and through the Monte Carlo collision algorithm involved. Using specifically designed numerical experiments, we show that both on their own give an accurate representation of fluctuations. We conclude that the superdroplet algorithm can faithfully represent fluctuations in the coagulation of droplets driven by gravity.

Recent numerical work in helioseismology has shown that a periodically varying subsurface magnetic field leads to a fanning of the $f$-mode, which emerges from the density jump at the surface. In an attempt to model a more realistic situation, we now modulate this periodic variation with an envelope, giving thus more emphasis on localized bipolar magnetic structures in the middle of the domain. Some notable findings are: (i) compared to the purely hydrodynamic case, the strength of the $f$-mode is significantly larger at high horizontal wavenumbers $k$, but the fanning is weaker for the localized subsurface magnetic field concentrations investigated here than the periodic ones studied earlier; (ii) when the strength of the magnetic field is enhanced at a fixed depth below the surface, the fanning of the $f$-mode in the $k\omega$ diagram increases proportionally in such a way that the normalized $f$-mode strengths remain nearly the same in different such cases; (iii) the unstable Bloch modes reported previously in case of harmonically varying magnetic fields are now completely absent when more realistic localized magnetic field concentrations are imposed beneath the surface, thus suggesting that the Bloch modes are unlikely to be supported during most phases of the solar cycle; (iv) the $f$-mode strength appears to depend also on the depth of magnetic field concentrations such that it shows a relative decrement when the maximum of the magnetic field is moved to a deeper layer. We argue that detections of $f$-mode perturbations such as those being explored here could be effective tracers of solar magnetic fields below the photosphere before these are directly detectable as visible manifestations in terms of active regions or sunspots., Comment: 15 pages, 7 figures, revised version submitted to GAFD special issue on "Physics and Algorithms of the Pencil Code"

The chiral magnetic effect (CME) is a quantum relativistic effect that describes the appearance of an additional electric current along a magnetic field. It is caused by an asymmetry between the number densities of left- and right-handed fermions, which can be maintained at high energies when the chirality flipping rate can be neglected, for example in the early Universe. The inclusion of the CME in the Maxwell equations leads to a modified set of MHD equations. We discuss how the CME is implemented in the PENCIL CODE. The CME plays a key role in the evolution of magnetic fields since it results in a dynamo effect associated with an additional term in the induction equation. This term is formally similar to the $\alpha$ effect in classical mean-field MHD. However, the chiral dynamo can operate without turbulence and is associated with small spatial scales that can be, in the case of the early Universe, orders of magnitude below the Hubble radius. A chiral $\alpha_\mu$ effect has also been identified in mean-field theory. It occurs in the presence of turbulence but is not related to kinetic helicity. Depending on the plasma parameters, chiral dynamo instabilities can amplify magnetic fields over many orders of magnitude. These instabilities can affect the propagation of MHD waves, which is demonstrated by our DNS. We also study the coupling between the evolution of the chiral chemical potential and the ordinary chemical potential, which is proportional to the sum of the number densities of left- and right-handed fermions. An important consequence of this coupling is the emergence of chiral magnetic waves (CMWs). We confirm numerically that linear CMWs and MHD waves are not interacting. Our simulations suggest that the chemical potential has only a minor effect on the non-linear evolution of the chiral dynamo., Comment: 22 pages, 10 figures, in press at the GAFD special issue "Physics and Algorithms of the Pencil Code"

We investigate the effect of turbulence on the combined condensational and collisional growth of cloud droplets by means of high resolution direct numerical simulations of turbulence and a superparticle approximation for droplet dynamics and collisions. The droplets are subject to turbulence as well as gravity, and their collision and coalescence efficiencies are taken to be unity. We solve the thermodynamic equations governing temperature, water-vapor mixing ratio, and the resulting supersaturation fields together with the Navier-Stokes equation. We find that the droplet-size distribution broadens with increasing Reynolds number and/or mean energy dissipation rate. Turbulence affects the condensational growth directly through supersaturation fluctuations, and it influences collisional growth indirectly through condensation. Our simulations show for the first time that, in the absence of the mean updraft cooling, supersaturation fluctuation-induced broadening of droplet-size distributions enhances the collisional growth. This is contrary to classical (non-turbulent) condensational growth, which leads to a growing mean droplet size, but a narrower droplet-size distribution. Our findings, instead, show that condensational growth facilitates collisional growth by broadening the size distribution in the tails at an early stage of rain formation. With increasing Reynolds numbers, evaporation becomes stronger. This counteracts the broadening effect due to condensation at late stages of rain formation. Our conclusions are consistent with results of laboratory experiments and field observations, and show that supersaturation fluctuations are important for precipitation., Comment: revised version, 17 pages, 1 table, 13 figures

Gradient- and curl-type or E- and B-type polarizations have been routinely analyzed to study the physics contributing to the cosmic microwave background polarization and galactic foregrounds. They characterize the parity-even and parity-odd properties of the underlying physical mechanisms, for example hydromagnetic turbulence in the case of dust polarization. Here we study spectral correlation functions characterizing the parity-even and parity-odd parts of linear polarization for homogeneous and inhomogeneous turbulence to show that only the inhomogeneous helical case can give rise to a parity-odd polarization signal. We also study nonhelical turbulence and suggest that a strong nonvanishing (here negative) skewness of the E polarization is responsible for an enhanced ratio of the EE to the BB (quadratic) correlation in both helical and nonhelical cases. This could explain the enhanced EE/BB ratio observed recently for dust polarization. We close with a preliminary assessment of using linear polarization of the Sun to characterize its helical turbulence without being subjected to the pi ambiguity that magnetic inversion techniques have to address., Comment: 11 pages, 13 figures, 4 tables, ApJ, in press

The full-sky Planck polarization data at 850um revealed unexpected properties of the E and B mode power spectra of dust emission in the interstellar medium (ISM). The positive cross-correlation between the total dust intensity, T, with the B modes has raised new questions about the physical mechanisms that affect dust polarization, such as the Galactic magnetic-field structure. This is key both to better understanding ISM dynamics and to accurately describing Galactic foregrounds to the polarization of the Cosmic Microwave Background (CMB). In this theoretical paper we investigate the possibility that the observed cross-correlations in the dust polarization power spectra, and specifically between T and B, can be related to a parity-odd quantity in the ISM such as the magnetic helicity. We produce synthetic dust polarization data, derived from 3D analytical toy models of density structures and helical magnetic fields, to compare with the E and B modes of observations. Focusing on the observed T-B correlation, we propose a new line of interpretation of the Planck observations based on a large-scale helical component of the Galactic magnetic field in the solar neighborhood. Our analysis shows that: I) the sign of magnetic helicity does not affect E and B modes for isotropic magnetic-field configurations; II) helical magnetic fields threading interstellar filaments cannot reproduce the Planck results; III) a weak helical left-handed magnetic field structure in the solar neighborhood may explain the T-B correlation seen in the Planck data. This work suggests a new perspective for the interpretation of the dust polarization power spectra, which strongly supports the imprint of a large-scale structure of the Galactic magnetic field in the solar neighborhood., Comment: Accepted by Astronomy & Astrophysics on November 24, 2018

We test the sensitivity of hydrodynamic and magnetohydrodynamic turbulent convection simulations with respect to Mach number, thermal and magnetic boundary conditions, and the centrifugal force. We find that varying the luminosity, which also controls the Mach number, has only a minor effect on the large-scale dynamics. A similar conclusion can also be drawn from the comparison of two formulations of the lower magnetic boundary condition with either vanishing electric field or current density. The centrifugal force has an effect on the solutions, but only if its magnitude with respect to acceleration due to gravity is by two orders of magnitude greater than in the Sun. Finally, we find that the parameterisation of the photospheric physics, either by an explicit cooling term or enhanced radiative diffusion, is more important than the thermal boundary condition. In particular, runs with cooling tend to lead to more anisotropic convection and stronger deviations from the Taylor-Proudman state. In summary, the fully compressible approach taken here with the Pencil Code is found to be valid, while still allowing the disparate timescales to be taken into account., Comment: 26 pages, 14 figures, accepted to GAFD Special issue on 'Physics and Algorithms of the Pencil Code'

Condensational growth of cloud droplets due to supersaturation fluctuations is investigated by solving the hydrodynamic and thermodynamic equations using direct numerical simulations with droplets being modeled as Lagrangian particles. The supersaturation field is calculated directly by simulating the temperature and water vapor fields instead of being treated as a passive scalar. Thermodynamic feedbacks to the fields due to condensation are also included for completeness. We find that the width of droplet size distributions increases with time, which is contrary to the classical theory without supersaturation fluctuations, where condensational growth leads to progressively narrower size distributions. Nevertheless, in agreement with earlier Lagrangian stochastic models of the condensational growth, the standard deviation of the surface area of droplets increases as $t^{1/2}$. Also, for the first time, we explicitly demonstrate that the time evolution of the size distribution is sensitive to the Reynolds number, but insensitive to the mean energy dissipation rate. This is shown to be due to the fact that temperature fluctuations and water vapor mixing ratio fluctuations increases with increasing Reynolds number, therefore the resulting supersaturation fluctuations are enhanced with increasing Reynolds number. Our simulations may explain the broadening of the size distribution in stratiform clouds qualitatively, where the mean updraft velocity is almost zero., Comment: 17 pages, 2 tables, 4 figures, submitted to Atmosph. Chem. Phys

We develop a formalism that treats the calculation of solar kinetic energy and cross helicity spectra in an equal manner to that of magnetic energy and helicity spectra. The magnetic helicity spectrum is shown to be equal to the vertical part of the current helicity spectrum divided by the square of the wavenumber. For the cross helicity, we apply the recently developed two-scale approach globally over an entire active region to account for the sign change between the two polarities. Using vector magnetograms and Dopplergrams of NOAA 11158 and 12266, we show that kinetic and magnetic energy spectra have similar slopes at intermediate wavenumbers, where the contribution from the granulation velocity has been removed. At wavenumbers around 0.3 Mm$^{-1}$, the magnetic helicity is found to be close to its maximal value. The cross helicity spectra are found to be within about 10% of the maximum possible value. Using the two-scale method for NOAA 12266, the global cross helicity spectrum is found to be particularly steep, similarly to what has previously been found in theoretical models of spot generation. In the quiet Sun, by comparison, the cross helicity spectrum is found to be small., Comment: 6 pages, 4 figures, ApJL,2018

Using a recently developed two-scale formalism to determine the magnetic helicity spectrum (Brandenburg et al. 2017), we analyze synoptic vector magnetograms built with data from the Vector Spectromagnetograph (VSM) instrument on the \emph{Synoptic Optical Long-term Investigations of the Sun} (SOLIS) telescope during January 2010-July 2016. In contrast to an earlier study using only three Carrington rotations, our analysis includes 74 synoptic Carrington rotation maps. We recover here bihelical spectra at different phases of solar cycle~24, where the net magnetic helicity in the majority of the data is consistent with a large-scale dynamo with helical turbulence operating in the Sun. More than $20\%$ of the analyzed maps, however, show violations of the expected sign rule., Comment: 10 pages, 10 figures, submitted to the Astrophysical Journal

The emergence of dipolar magnetic features on the solar surface is an idealization. Most of the magnetic flux emergence occurs in complex multipolar regions. Here, we show that the surface pattern of magnetic structures alone can reveal the sign of the underlying magnetic helicity in the nearly force-free coronal regions above. The sign of the magnetic helicity can be predicted to good accuracy by considering the three-dimensional position vectors of three spots on the sphere ordered by their relative strengths at the surface and compute from them the skew product. This product, which is a pseudoscalar, is shown to be a good proxy for the sign of the coronal magnetic helicity., Comment: 7 pages, 3 figures, 2 tables, published

Solar and stellar dynamos shed small-scale and large-scale magnetic helicity of opposite signs. However, solar wind observations and simulations have shown that some distance above the dynamo both the small-scale and large-scale magnetic helicities have reversed signs. With realistic simulations of the solar corona above an active region now being available, we have access to the magnetic field and current density along coronal loops. We show that a sign reversal in the horizontal averages of the magnetic helicity occurs when the local maximum of the plasma beta drops below unity and the field becomes nearly fully force free. Hence, this reversal is expected to occur well within the solar corona and would not directly be accessible to in-situ measurements with the Parker Solar Probe or SolarOrbiter. We also show that the reversal is associated with subtle changes in the relative dominance of structures with positive and negative magnetic helicity., Comment: 9 pages, 8 figures, published

We investigate the statistical properties of isotropic, stochastic, Gaussian distributed, helical magnetic fields characterized by different shapes of the energy spectra at large length scales and study the associated realizability condition. We discuss smoothed magnetic fields that are commonly used when the primordial magnetic field is constrained by observational data. We are particularly interested in scale-invariant magnetic fields that can be generated during the inflationary stage by quantum fluctuations. We determine the correlation length of such magnetic fields and relate it to the infrared cutoff of perturbations produced during inflation. We show that this scale determines the observational signatures of the inflationary magnetic fields on the cosmic microwave background. At smaller scales, the scale-invariant spectrum changes with time. It becomes a steeper weak-turbulence spectrum at progressively larger scales. We show numerically that the critical length scale where this happens is the turbulent-diffusive scale, which increases with the square root of time., Comment: 24 pages, 9 figures. Discussion expanded, references added, results unchanged. Accepted for publication in JCAP

An asymmetry in the number density of left- and right-handed fermions is known to give rise to a new term in the induction equation that can result in a dynamo instability. At high temperatures, when a chiral asymmetry can survive for long enough, this chiral dynamo instability can amplify magnetic fields efficiently, which in turn drive turbulence via the Lorentz force. While it has been demonstrated in numerical simulations that this chiral magnetically driven turbulence exists and strongly affects the dynamics of the magnetic field, the details of this process remain unclear. The goal of this paper is to analyse the energetics of chiral magnetically driven turbulence and its effect on the generation and dynamics of the magnetic field using direct numerical simulations. We study these effects for different initial conditions, including a variation of the initial chiral chemical potential and the magnetic Prandtl number, Pm. In particular, we determine the ratio of kinetic to magnetic energy, Upsilon, in chiral magnetically driven turbulence. Within the parameter space explored in this study, Upsilon reaches a value of approximately 0.064-0.074 -independently of the initial chiral asymmetry and for Pm=1. Our simulations suggest, that Upsilon decreases as a power law when increasing Pm by decreasing the viscosity. While the exact scaling depends on the details of the fitting criteria and the Reynolds number regime, an approximate result of Upsilon(Pm)=0.1 Pm^{-0.4} is reported. Using the findings from our numerical simulations, we analyse the energetics of chiral magnetically driven turbulence in the early Universe., Comment: 22 pages, 11 figures, in press at the GAFD special issue "Recent Developments in Natural Dynamos"

We consider the effect of a subadiabatic layer at the base of the convection zone on convection itself and the associated large-scale dynamos in spherical wedge geometry. We use a heat conduction prescription based on the Kramers opacity law which allows the depth of the convection zone to dynamically adapt to changes in the physical characteristics such as rotation rate and magnetic fields. We find that the convective heat transport is strongly concentrated toward the equatorial and polar regions in the cases without a substantial radiative layer below the convection zone. The presence of a stable layer below the convection zone significantly reduces the anisotropy of radial enthalpy transport. Furthermore, the dynamo solutions are sensitive to subtle changes in the convection zone structure. We find that the kinetic helicity changes sign in the deeper parts of the convection zone at high latitudes in all runs. This region expands progressively toward the equator in runs with a thicker stably stratified layer., Comment: 32 pages, 18 figures, accepted to GAFD Special issue on 'Recent Developments in Natural Dynamos'

Small-scale dynamo action is often held responsible for the generation of quiet-Sun magnetic fields. We aim to determine the excitation conditions and saturation level of small-scale dynamos in non-rotating turbulent convection at low magnetic Prandtl numbers. We use high resolution direct numerical simulations of weakly stratified turbulent convection. We find that the critical magnetic Reynolds number for dynamo excitation increases as the magnetic Prandtl number is decreased, which might suggest that small-scale dynamo action is not automatically evident in bodies with small magnetic Prandtl numbers as the Sun. As a function of the magnetic Reynolds number (${\rm Rm}$), the growth rate of the dynamo is consistent with an ${\rm Rm}^{1/2}$ scaling. No evidence for a logarithmic increase of the growth rate with ${\rm Rm}$ is found., Comment: 6 pages, 5 figures, submitted to Astron. Nachr

High precision photometry of solar-like members of the open cluster M67 with Kepler/K2 data has recently revealed enhanced activity for stars with a large Rossby number, which is the ratio of rotation period to the convective turnover time. Contrary to the well established behavior for shorter rotation periods and smaller Rossby numbers, the chromospheric activity of the more slowly rotating stars of M67 was found to increase with increasing Rossby number. Such behavior has never been reported before, although it was theoretically predicted to emerge as a consequence of antisolar differential rotation (DR) for stars with Rossby numbers larger than that of the Sun, because in those models the absolute value of the DR was found to exceed that for solar-like DR. Using gyrochronological relations and an approximate age of 4 Gyr for the members of M67, we compare with computed rotation rates using just the B-V color. The resulting rotation--activity relation is found to be compatible with that obtained by employing the measured rotation rate. This provides additional support for the unconventional enhancement of activity at comparatively low rotation rates and the possible presence of antisolar differential rotation., Comment: 6 pages, 3 figures, ApJL (accepted)

Recent advances in mean-field theory are reviewed and applications to the Sun, late-type stars, accretion disks, galaxies, and the early Universe are discussed. We focus particularly on aspects of spatio-temporal nonlocality, which is one of the main insights that emerged from applying the test-field method to magnetic fields of different length and timescales. We also review the status of nonlinear quenching and the relation to magnetic helicity, which is an important observational diagnostic of modern solar dynamo theory. Both solar and some stellar dynamos seem to operate in an intermediate regime that has not yet been possible to model successfully. This regime is bracketed by antisolar-like differential rotation on one end and stellar activity cycles belonging to the superactive stars on the other. The difficulty in modeling this regime may be related to shortcomings in modelling solar/stellar convection. On galactic and extragalactic length scales, the observational constraints are still less stringent and uncertain, but recent advances both in theory and in observations suggest that more conclusive comparisons may soon be possible. The possibility of inversely cascading magnetic helicity throughout all of the early Universe is particularly exciting in explaining the lower limits of magnetic fields on cosmological length scales and the possibility of parity breaking and finite helicity of such a field., Comment: 65 pages, 11 figures, J. Plasma Phys, accepted

Using direct numerical simulations (DNS), we study laminar and turbulent dynamos in chiral magnetohydrodynamics (MHD) with an extended set of equations that accounts for an additional contribution to the electric current due to the chiral magnetic effect (CME). This quantum phenomenon originates from an asymmetry between left- and right-handed relativistic fermions in the presence of a magnetic field and gives rise to a chiral dynamo. We show that the magnetic field evolution proceeds in three stages: (1) a small-scale chiral dynamo instability; (2) production of chiral magnetically driven turbulence and excitation of a large-scale dynamo instability due to a new chiral effect (alpha_mu effect); and (3) saturation of magnetic helicity and magnetic field growth controlled by a conservation law for the total chirality. The $\alpha_\mu$ effect becomes dominant at large fluid and magnetic Reynolds numbers and is not related to kinetic helicity. The growth rate of the large-scale magnetic field and its characteristic scale measured in the numerical simulations agree well with theoretical predictions based on mean-field theory. The previously discussed two-stage chiral magnetic scenario did not include stage (2) during which the characteristic scale of magnetic field variations can increase by many orders of magnitude. Based on the findings from numerical simulations, the relevance of the CME and the chiral effects revealed in the relativistic plasma of the early universe and of proto-neutron stars are discussed., Comment: 24 pages, 21 figures

We present new simulations of decaying hydromagnetic turbulence for a relativistic equation of state relevant to the early universe. We compare helical and nonhelical cases either with kinetically or magnetically dominated initial fields. Both kinetic and magnetic initial helicities lead to maximally helical magnetic fields after some time, but with different temporal decay laws. Both are relevant to the early universe, although no mechanisms have yet been identified that produce magnetic helicity with strengths comparable to the big bang nucleosynthesis limit at scales comparable to the Hubble horizon at the electroweak phase transition. Nonhelical magnetically dominated fields could still produce picoGauss magnetic fields under most optimistic conditions. Only helical magnetic fields can potentially have nanoGauss strengths at scales up to 30 kpc today., Comment: 17 pages, 13 figures; submitted to PRD

We seek to understand the transition from nearly axisymmetric configurations at solar rotation rates to nonaxisymmetric configurations for rapid rotation using 3D numerical simulations of turbulent convection and considering rotation rates between 1 and 30 times the solar value. We find a transition from axi- to nonaxisymmetric solutions at around 1.8 times the solar rotation rate. This transition coincides with a change in the rotation profile from antisolar- to solar-like differential rotation with a faster equator and slow poles. In the solar-like rotation regime, the field configuration consists of an axisymmetric oscillatory field accompanied by an m=1 azimuthal mode (two active longitudes), which also shows temporal variability. At slow (rapid) rotation, the axisymmetric (nonaxisymmetric) mode dominates. The axisymmetric mode produces latitudinal dynamo waves with polarity reversals, while the nonaxisymmetric mode often exhibits a drift in the rotating reference frame and the strength of the active longitudes changes cyclically over time between the different hemispheres. Most of the obtained dynamo solutions exhibit cyclic variability either caused by latitudinal or azimuthal dynamo waves. In an activity-period diagram, the cycle lengths normalized by the rotation period form two different populations as a function of rotation rate or magnetic activity level. The slowly rotating axisymmetric population lies close to what is called the inactive branch in observations, while the rapidly rotating models are close to the superactive branch with a declining cycle to rotation frequency ratio with increasing rotation rate. We can successfully reproduce the transition from axi- to nonaxisymmetric dynamo solutions for high rotation rates, but high-resolution simulations are required to limit the effect of rotational quenching of convection at rotation rates above 20 times the solar value., Comment: 19 pages, 17 figures, accepted for publication in A&A

We show that in decaying hydromagnetic turbulence with initial kinetic helicity, a weak magnetic field eventually becomes fully helical. The sign of magnetic helicity is opposite to that of the kinetic helicity - regardless of whether or not the initial magnetic field was helical. The magnetic field undergoes inverse cascading with the magnetic energy decaying approximately like t^{-1/2}. This is even slower than in the fully helical case, where it decays like t^{-2/3}. In this parameter range, the product of magnetic energy and correlation length raised to a certain power slightly larger than unity, is approximately constant. This scaling of magnetic energy persists over long time scales. At very late times and for domain sizes large enough to accommodate the growing spatial scales, we expect a cross-over to the t^{-2/3} decay law that is commonly observed for fully helical magnetic fields. Regardless of the presence or absence of initial kinetic helicity, the magnetic field experiences exponential growth during the first few turnover times, which is suggestive of small-scale dynamo action. Our results have applications to a wide range of experimental dynamos and astrophysical time-dependent plasmas, including primordial turbulence in the early universe., Comment: 15 pages, 14 figures, submitted to Phys. Rev. Fluids

The presence of asymmetry between fermions of opposite handedness in plasmas of relativistic particles can lead to exponential growth of a helical magnetic field via a small-scale chiral dynamo instability known as the chiral magnetic effect. Here, we show, using dimensional arguments and numerical simulations, that this process produces through the Lorentz force chiral magnetically driven turbulence. A k^{-2} magnetic energy spectrum emerges via inverse transfer over a certain range of wavenumbers k. The total chirality (magnetic helicity plus normalized chiral chemical potential) is conserved in this system. Therefore, as the helical magnetic field grows, most of the total chirality gets transferred into magnetic helicity until the chiral magnetic effect terminates. Quantitative results for height, slope, and extent of the spectrum are obtained. Consequences of this effect for cosmic magnetic fields are discussed., Comment: 7 pages, 4 figures, 1 table, published in ApJL

A turbulent dynamo in spherical geometry with an outer corona is simulated to study the sign of magnetic helicity in the outer parts. In agreement with earlier studies, the sign in the outer corona is found to be opposite to that inside the dynamo. Line-of-sight observations of polarized emission are synthesized to explore the feasibility of using the local reduction of Faraday depolarization to infer the sign of helicity of magnetic fields in the solar corona. This approach was previously identified as an observational diagnostic in the context of galactic magnetic fields. Based on our simulations, we show that this method can be successful in the solar context if sufficient statistics is gathered by using averages over ring segments in the corona separately for the regions north and south of the solar equator., Comment: 5 pages, 3 figures, published in ApJL

The magnetic activity of the Sun becomes stronger and weaker over roughly an 11 year cycle, modulating the radiation and charged particle environment experienced by the Earth as "space weather". Decades of observations from the Mount Wilson Observatory have revealed that other stars also show regular activity cycles in their Ca II H+K line emission, and identified two different relationships between the length of the cycle and the rotation rate of the star. Recent observations at higher cadence have allowed the discovery of shorter cycles with periods between 1-3 yr. Some of these shorter cycles coexist with longer cycle periods, suggesting that two underlying dynamos can operate simultaneously. We combine these new observations with previous data, and we show that the longer and shorter cycle periods agree remarkably well with those expected from an earlier analysis based on the mean activity level and the rotation period. The relative turbulent length scales associated with the two branches of cyclic behavior suggest that a near-surface dynamo may be the dominant mechanism that drives cycles in more active stars, whereas a dynamo operating in deeper layers may dominate in less active stars. However, several examples of equally prominent long and short cycles have been found at all levels of activity of stars younger than 2.3 Gyr. Deviations from the expected cycle periods show no dependence on the depth of the convection zone or on the metallicity. For some stars that exhibit longer cycles, we compute the periods of shorter cycles that might be detected with future high-cadence observations., Comment: 14 pages, 11 figures, 4 tables, published in ApJ

Sunspots are of basic interest in the study of the Sun. Their relevance ranges from them being an activity indicator of magnetic fields to being the place where coronal mass ejections and flares erupt. They are therefore also an important ingredient of space weather. Their formation, however, is still an unresolved problem in solar physics. Observations utilize just 2D surface information near the spot, but it is debatable how to infer deep structures and properties from local helioseismology. For a long time, it was believed that flux tubes rising from the bottom of the convection zone are the origin of the bipolar sunspot structure seen on the solar surface. However, this theory has been challenged, in particular recently by new surface observation, helioseismic inversions, and numerical models of convective dynamos. In this article we discuss another theoretical approach to the formation of sunspots: the negative effective magnetic pressure instability. This is a large-scale instability, in which the total (kinetic plus magnetic) turbulent pressure can be suppressed in the presence of a weak large-scale magnetic field, leading to a converging downflow, which eventually concentrates the magnetic field within it. Numerical simulations of forced stratified turbulence have been able to produce strong super-equipartition flux concentrations, similar to sunspots at the solar surface. In this framework, sunspots would only form close to the surface due to the instability constraints on stratification and rotation. Additionally, we present some ideas from local helioseismology, where we plan to use the Hankel analysis to study the pre-emergence phase of a sunspot and to constrain its deep structure and formation mechanism., Comment: 14 pages, 5 figures, accepted for publication in the IAU proceeding series IAUS327

We present numerical simulations of hydrodynamic overshooting convection in local Cartesian domains. We find that a substantial fraction of the lower part of the convection zone (CZ) is stably stratified according to the Schwarzschild criterion while the enthalpy flux is outward directed. This occurs when the heat conduction profile at the bottom of the CZ is smoothly varying, based either on a Kramers-like opacity prescription as a function of temperature and density or a static profile of a similar shape. We show that the subadiabatic layer arises due to nonlocal energy transport by buoyantly driven downflows in the upper parts of the CZ. Analysis of the force balance of the upflows and downflows confirms that convection is driven by cooling at the surface. We find that the commonly used prescription for the convective enthalpy flux being proportional to the negative entropy gradient does not hold in the stably stratified layers where the flux is positive. We demonstrate the existence of a non-gradient contribution to the enthalpy flux, which is estimated to be important throughout the convective layer. A quantitative analysis of downflows indicates a transition from a tree-like structure where smaller downdrafts merge into larger ones in the upper parts to a structure in the deeper parts where a height-independent number of strong downdrafts persist. This change of flow topology occurs when a substantial subadiabatic layer is present in the lower part of the CZ., Comment: 6 pages, 3 figures, published in ApJL

The formation of sunspots requires the concentration of magnetic flux near the surface. The negative magnetic pressure instability (NEMPI) might be a possible mechanism for accomplishing this, but it has mainly been studied in simple systems using an isothermal equation of state without a natural free surface. We study NEMPI in a stratified Cartesian mean-field model where turbulence effects are parameterized. We use an ideal equation of state and include radiation transport, which establishes selfconsistently a free surface. We use a Kramers-type opacity with adjustable exponents chosen such that the deeper layers are approximately isentropic. No convection is therefore possible in this model, allowing us to study NEMPI with radiation in isolation. We restrict ourselves to two-dimensional models. We use artificially enhanced mean-field coefficients to allow NEMPI to develop, making it therefore possible to study the reason why it is much harder to excite in the presence of radiation. NEMPI yields moderately strong magnetic flux concentrations a certain distance beneath the surface where optical depth is unity. The instability is oscillatory and in the form of upward travelling waves. This seems to be a new effect that has not been found in earlier models without radiative transport. The horizontal wavelength is about ten times smaller than what has been found previously in more idealized isothermal models. In our models, NEMPI saturates at field strengths too low to explain sunspots. Furthermore, the structures appear too narrow and too far beneath the surface to cause significant brightness variations at the radiative surface. We speculate that the failure to reproduce effects resembling sunspots may be related to the neglect of convection., Comment: 10 pages, 10 figures

Analytic solutions of the mean-field induction equation predict a nonoscillatory dynamo for homogeneous helical turbulence or constant alpha effect in unbounded or periodic domains. Oscillatory dynamos are generally thought impossible for constant alpha. We present an analytic solution for a one-dimensional bounded domain resulting in oscillatory solutions for constant alpha, but different (Dirichlet and von Neumann or perfect conductor and vacuum) boundary conditions on the two boundaries. We solve a second order complex equation and superimpose two independent solutions to obey both boundary conditions. The solution has time-independent energy density. On one end where the function value vanishes, the second derivative is finite, which would not be correctly reproduced with sine-like expansion functions where a node coincides with an inflection point. The field always migrates away from the perfect conductor boundary toward the vacuum boundary, independently of the sign of alpha. The obtained solution may serve as a benchmark for numerical dynamo experiments and as a pedagogical illustration that oscillatory migratory dynamos are possible with constant alpha., Comment: 7 pages, 4 figures, published in A&A