Density and velocity correlations in isothermal supersonic turbulence

In star-forming clouds, high velocity flow gives rise to large fluctuations of density. In this work, we explore the correlation between velocity magnitude (speed) and density. We develop an analytic formula for the joint probability distribution function (PDF) of density and speed, and discuss its properties. In order to develop an accurate model for the joint PDF, we first develop impro v ed models of the marginalized distributions of density and speed. We confront our results with a suite of 12 supersonic isothermal simulations with resolution of 1024 3 cells in which the turbulence is driven by 3 different forcing modes (solenoidal, mix ed, and compressiv e) and 4 rms Mach numbers (1, 2, 4, 8). We show, that for transsonic turbulence, density and speed are correlated to a considerable degree and the simple assumption of independence fails to accurately describe their statistics. In the supersonic regime, the correlations tend to weaken with growing Mach number. Our new model of the joint and marginalized PDFs are a factor of 3 better than uncorrelated, and provides insight into this important process.