Wednesday, June 6, 2012 - 4:15pm
"The density variance-Mach number relation in supersonic turbulence"
Abstract. It is widely accepted that supersonic, magnetized turbulence plays a fundamental role for star formation in molecular clouds. It produces the initial dense gas seeds out of which new stars can form. However, the exact relation between gas compression, turbulent Mach number, and magnetic field strength is still poorly understood. Here, we introduce and test an analytical prediction for the relation between the density variance and the root-mean-square Mach number in supersonic, magnetized turbulent flows. We approximate the density and velocity structure of the interstellar medium as a superposition of shock waves. We obtain the density contrast considering the momentum equation for a single magnetized shock and extrapolate this result to the entire cloud. Depending on the field geometry, we then make three different assumptions for the magnetic filed dependence on density based on observational and theoretical constraints. We test the analytically derived density variance--Mach number relation with numerical simulations, and find that our relation fits very well to simulated data with turbulent forcing parameter b=0.4, when the gas is super-Alfvénic. However, this result breaks down when the turbulence becomes trans-Alfvénic or sub-Alfvénic, because in this regime the turbulence becomes highly anisotropic.