Abstract

The turbulent dynamo may explain the origin of cosmic magnetism. While the exponential amplification of magnetic fields has been studied for incompressible gases, little is known about dynamo action in highly compressible, supersonic plasmas, such as the interstellar medium of galaxies and the early universe. Here we perform the first quantitative comparison of theoretical models of the dynamo growth rate and saturation level with three-dimensional magnetohydrodynamical simulations of supersonic turbulence with grid resolutions of up to 1024$^{3}$ cells. We obtain numerical convergence and find that dynamo action occurs for both low and high magnetic Prandtl numbers Pm = {$\nu$}/{$\eta$} = 0.1-10 (the ratio of viscous to magnetic dissipation), which had so far only been seen for Pm $\gt$= 1 in supersonic turbulence. We measure the critical magnetic Reynolds number, $\{$Rm$\}$$_{crit}$=129$^{+43}$$_{-31}$, showing that the compressible dynamo is almost as efficient as in incompressible gas. Considering the physical conditions of the present and early universe, we conclude that magnetic fields need to be taken into account during structure formation from the early to the present cosmic ages, because they suppress gas fragmentation and drive powerful jets and outflows, both greatly affecting the initial mass function of stars.