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We study the probability distribution function (PDF) of the mass density insimulations of supersonic turbulence with properties appropriate for molecularclouds. For this study we use Athena, a new higher-order Godunov code. We findthere are surprisingly similar relationships between the mean of thetime-averaged PDF and the turbulent Mach number for driven hydrodynamic andstrong-field MHD turbulence. There is, however, a large scatter about theserelations, indicating a high level of temporal and spatial variability in thePDF. Thus, the PDF of the mass density is unlikely to be a good measure ofmagnetic field strength. We also find the PDF of decaying MHD turbulencedeviates from the mean-Mach relation found in the driven case. This impliesthat the instantaneous Mach number alone is not enough to determine thestatistical properties of turbulence that is out of equilibrium. The scatterabout the mean-Mach relation for driven turbulence, along with the largedeparture of decaying turbulence PDFs from those of driven turbulence, mayilluminate one factor contributing to the large observed cloud-to-cloudvariation in the star formation rate per solar mass.

Density Probability Distribution Functions in Supersonic Hydrodynamic and MHD Turbulence