Magnetic field amplification during gravitational collapse - influence of turbulence, rotation and gravitational compression

We study the influence of initial conditions on the magnetic field amplification during the collapse of a magnetized 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 magnetized cloud. In order to follow the evolution of the magnetic field in both the kinematic and the non-linear regime, we choose an initial field strength of with the magnetic to kinetic energy ratio, E_m/E_k~ 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/ρ^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_rms/c_s~ 0.2 to 0.4 and then starts decreasing from v_rms/c_s~ 1.0. We obtain saturation values of E_m/E_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_m/E_k~ 0.2-0.4 of the equipartition value. The overall saturation level of the magnetic energy, obtained by varying the initial conditions, is in agreement with previous analytical and numerical studies of small-scale dynamo action where turbulence is driven by an external forcing instead of gravitational collapse.