Magnetic field amplification during gravitational collapse - Influence of initial conditions on dynamo evolution and saturation

TL;DR

This study investigates how initial conditions like turbulence strength, scale, and rotation influence magnetic field amplification and saturation during gravitational collapse, highlighting the role of the small-scale dynamo in this process.

Contribution

It provides new insights into the dependence of dynamo growth and saturation on initial turbulence and rotation conditions in collapsing gas clouds.

Findings

Dynamo amplification saturates at 20-30% of kinetic energy.

Saturation involves a shift in magnetic energy spectrum to larger scales.

Growth rate varies with Mach number, peaking at intermediate values.

Abstract

We study the influence of initial conditions on the magnetic field amplification during the collapse of a magnetised gas cloud. We focus on the dependence of the growth and saturation level of the dynamo generated field on the turbulent properties of the collapsing cloud. In particular, we explore the effect of varying the initial strength and injection scale of turbulence and the initial uniform rotation of the collapsing magnetised cloud. In order to follow the evolution of the magnetic field in both the kinematic and the nonlinear regime, we choose an initial field strength of $\simeq 1\,\mkG$ with the magnetic to kinetic energy ratio, $E_{\rm m}/E_{\rm k} \sim 10^{-4}$. Both gravitational compression and the small-scale dynamo initially amplify the magnetic field. Further into the evolution, the dynamo-generated magnetic field saturates but the total magnetic field continues to grow because of compression. The saturation of the small-scale dynamo is marked by a change in the slope of $B/\rho^{2/3}$ and by a shift in the peak of the magnetic energy spectrum from small scales to larger scales. For the range of initial Mach numbers explored in this study, the dynamo growth rate increases as the Mach number increases from $v_{\rm rms}/c_{\rm s}\sim 0.2$ to 0.4 and then starts decreasing from $v_{\rm rms}/c_{\rm s}\sim 1.0$. We obtain saturation values of $E_{\rm m}/E_{\rm k} = 0.2 - 0.3$ for these runs. Simulations with different initial injection scales of turbulence also show saturation at similar levels. For runs with different initial rotation of the cloud, the magnetic energy saturates at $E_{\rm m}/E_{\rm k}\sim 0.2 - 0.4$ of the equipartition value. (Abridged)