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

ABSTRACT A joint effect of the density-stratified turbulence (or inhomogeneous turbulence) and a large-scale shear for arbitrary Mach numbers results in the $\alpha$ 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 effect) does not affect the contributions to the $\alpha$ tensor caused by the joint effect of inhomogeneity of turbulence and a large-scale shear, but it influences the effective pumping velocity of the mean magnetic field. The isotropic part of the ${\boldsymbol \alpha }$ tensor is independent of the exponent of the turbulent kinetic energy spectrum, while its anisotropic part depends on this exponent. This anisotropic part of the ${\boldsymbol \alpha }$ tensor depends on the latitudinal profile of the large-scale shear velocity (differential rotation), which may be important for dynamo operation in the upper parts of the solar and stellar convection zones. 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, protogalactic and protostellar clouds are discussed.