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The turbulent dynamo may explain the origin of cosmic magnetism. While theexponential amplification of magnetic fields has been studied forincompressible gases, little is known about dynamo action inhighly-compressible, supersonic plasmas, such as the interstellar medium ofgalaxies and the early Universe. Here we perform the first quantitativecomparison of theoretical models of the dynamo growth rate and saturation levelwith three-dimensional magnetohydrodynamical simulations of supersonicturbulence with grid resolutions of up to 1024^3 cells. We obtain numericalconvergence and find that dynamo action occurs for both low and high magneticPrandtl numbers Pm = nu/eta = 0.1-10 (the ratio of viscous to magneticdissipation), which had so far only been seen for Pm >= 1 in supersonicturbulence. We measure the critical magnetic Reynolds number, Rm_crit = 129(+43, -31), showing that the compressible dynamo is almost as efficient as inincompressible gas. Considering the physical conditions of the present andearly Universe, we conclude that magnetic fields need to be taken into accountduring structure formation from the early to the present cosmic ages, becausethey suppress gas fragmentation and drive powerful jets and outflows, bothgreatly affecting the initial mass function of stars.

The Turbulent Dynamo in Highly Compressible Supersonic Plasmas