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Cosmic structure formation is characterized by the complex interplay betweengravity, turbulence, and magnetic fields. The processes by which gravitationalenergy is converted into turbulent and magnetic energies, however, remainpoorly understood. Here, we show with high-resolution, adaptive-meshsimulations that MHD turbulence is efficiently driven by extracting energy fromthe gravitational potential during the collapse of a dense gas cloud.Compressible motions generated during the contraction are converted intosolenoidal, turbulent motions, leading to a natural energy ratio of E_sol/E_totof approximately 2/3. We find that the energy injection scale of gravity-driventurbulence is close to the local Jeans scale. If small seeds of the magneticfield are present, they are amplified exponentially fast via the small-scaledynamo process. The magnetic field grows most efficiently on the smallestscales, for which the stretching, twisting, and folding of field lines, and theturbulent vortices are sufficiently resolved. We find that this scalecorresponds to about 30 grid cells in the simulations. We thus suggest a newminimum resolution criterion of 30 cells per Jeans length in(magneto)hydrodynamical simulations of self-gravitating gas, in order toresolve turbulence on the Jeans scale, and to capture minimum dynamoamplification of the magnetic field. Due to numerical diffusion, however, anyexisting simulation today can at best provide lower limits on the physicalgrowth rates. We conclude that a small, initial magnetic field can grow todynamically important strength on time scales significantly shorter than thefree-fall time of the cloud.

astrophysical journal/the astrophysical journal

A new Jeans resolution criterion for (M)HD simulations of  self-gravitating gas: Application to magnetic field amplification by  gravity-driven turbulence