Vorticity and magnetic dynamo from subsonic expansion waves II: Dependence on magnetic Prandtl number, forcing scale, cooling time

The amplification of astrophysical magnetic fields takes place via dynamo instability in turbulent environments. The presence of vorticity is crucial for the dynamo to happen. However, the role of vorticity is not yet fully understood. This work is an extension of previous research on the effect of an irrotational subsonic forcing on a magnetized medium in the presence of rotation or a differential velocity profile, aimed at exploring a wider parameter space in terms of Reynolds numbers, magnetic Prandtl number, forcing scale, cooling timescale in a Newtonian cooling. We study the effect of imposing either the acceleration or the velocity forcing function to be curl-free and evaluate the terms responsible for the evolution vorticity. We use Direct Numerical Simulations (DNS) to solve the fully compressible, resistive magnetohydrodynamical (MHD) equations with the Pencil Code. We study both isothermal and non-isothermal regimes and address the relative importance of different vorticity source terms.We report no small-scale dynamo for the models that do not include shear. We find a hydro instability, followed by a magnetic one, when a shearing velocity profile is applied. The vorticity production is found to be numerical in the purely irrotational case. Non-isothermality, rotation, shear or forcing in the form of a velocity curl-free, when included, contribute to increasing vorticity. Consistently with our previous study, we find that turbulence driven by subsonic expansion waves can amplify vorticity and magnetic field only in the presence of a background shearing profile. The presence of a cooling function make the instability happens on a shorter timescale. We estimate critical Reynolds and Magnetic Reynolds Numbes of 40 and 20, respectively.