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.

We study the effects of ambipolar diffusion (AD) on hydromagnetic turbulence. We consider the regime of large magnetic Prandtl number, relevant to the interstellar medium. 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. 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.

Condensational growth of cloud droplets due to supersaturation fluctuations is investigated by solving the hydrodynamic and thermodynamic equations using direct numerical simulations (DNS) 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 increase 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.

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 like down to . With the WENO scheme, solutions are smooth at , but no detonation is obtained for . This is argued to be an artifact of a decoupling between pressure and reaction fronts.

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 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 timescales. At very late times and for domain sizes large enough to accommodate the growing spatial scales, we expect a crossover 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.

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, such as, 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 non-vanishing (here negative) skewness of the E polarization is responsible for an enhanced ratio of the EE to the BB (quadratic) correlation in both the 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 the linear polarization of the Sun to characterize its helical turbulence without being subjected to the pi ambiguity that magnetic inversion techniques have to address.

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 towards 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 towards the equator in runs with a thicker stably stratified layer.

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, . In particular, we determine the ratio of kinetic to magnetic energy, , in chiral magnetically driven turbulence. Within the parameter space explored in this study, reaches a value of approximately 0.064-0.074-independently of the initial chiral asymmetry and for . Our simulations suggest, that decreases as a power law when increasing 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 is reported. Using the findings from our numerical simulations, we analyse the energetics of chiral magnetically driven turbulence in the early Universe.

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 a 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 localised 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 localised 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 diagram increases proportionally in such a way that the normalised 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 localised 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.

Context. The analysis of the full-sky Planck polarization data at 850 mu m revealed unexpected properties of the E- and B-mode power spectra of dust emission in the interstellar medium (ISM). The positive cross-correlations over a wide range of angular scales between the total dust intensity, T, and both E and (most of all) 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 particular, in the quest to find primordial B modes of the CMB, the observed positive cross-correlation between T and B for interstellar dust requires further investigation towards parity-violating processes in the ISM. Aims. In this theoretical paper we investigate the possibility that the observed cross-correlations in the dust polarization power spectra, and specifically the one between T and B, can be related to a parity-odd quantity in the ISM such as the magnetic helicity. Methods. 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. We present several models. The first is an ideal fully helical isotropic case, such as the Arnold-Beltrami-Childress field. Second, following the nowadays favored interpretation of the T-E signal in terms of the observed alignment between the magnetic field morphology and the filamentary density structure of the diffuse ISM, we design models for helical magnetic fields wrapped around cylindrical interstellar filaments. Lastly, focusing on the observed T-B correlation, we propose a new line of interpretation of the Planck observations advocating the presence of a large-scale helical component of the Galactic magnetic field in the solar neighborhood. Results. 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; and III) a weak helical left-handed magnetic field structure in the solar neighborhood may explain the T-B correlation seen in the Planck data. Such a magnetic-field configuration would also account for the observed large-scale T-E correlation. Conclusions. This work suggests a new perspective for the interpretation of the dust polarization power spectra that supports the imprint of a large-scale structure of the Galactic magnetic field in the solar neighborhood.