Alpha effect and dynamo in density-stratified turbulence with large-scale shear: applications to protoplanetary discs and astrophysical clouds

TL;DR

This work derives the $\alpha$-effect and pumping velocity arising from the joint action of density-stratified (or inhomogeneous) turbulence and large-scale shear, valid for arbitrary Mach numbers via the spectral $\tau$-approximation. It shows that the isotropic part of the $\alpha$-tensor is independent of the turbulent energy spectrum exponent and that a density-stratification–divergence coupling generates an additional pumping term, while the $\alpha$-tensor itself is insensitive to cloud collapse. The results are applied to protoplanetary discs and merging astrophysical clouds, yielding quantitative estimates of $\alpha$ and $V^{\rm eff}$ that imply significant large-scale magnetic-field amplification in these systems. Overall, the study extends mean-field dynamo theory to compressible, density-stratified, and inhomogeneous turbulent backgrounds with large-scale shear, providing a framework for magnetic-field generation in diverse astrophysical contexts.

Abstract

A joint effect of the density-stratified turbulence (or inhomogeneous turbulence) and a large-scale shear for arbitrary Mach numbers results in the $α$ effect and mean-field dynamo action. These effects also produce the effective pumping velocity of a large-scale magnetic field. Compressibility of the turbulent velocity field (i.e., finite Mach number effects) does not affect the contributions to the $α$ tensor caused by the joint effect of inhomogeneity of turbulence and a large-scale shear. The isotropic part of the $α$ tensor is independent of the exponent of the turbulent kinetic energy spectrum. There is also an additional contribution to the effective pumping velocity of the mean magnetic field that is proportional to the product of the fluid density gradient and the divergence of the mean fluid velocity caused, e.g., by collapsing (or expanding) astrophysical clouds. Applications of these effects to protoplanetary discs, proto-galactic and proto-stellar clouds are discussed.