On the Probability Density Function of Galactic Gas. I. Numerical Simulations and the Significance of the Polytropic Index

We investigate the form of the one-point probability distribution function (pdf) for the density field of the interstellar medium using numerical simulations that successively reduce the number of physical processes included. Two-dimensional simulations of self-gravitating supersonic MHD and hydrodynamic turbulence, and of decaying Burgers turbulence, produce in all cases filamentary density structures and a power-law density pdf with logarithmic slope around -1.7. This suggests that the functional form of the pdf and the general filamentary morphology are the signature of the nonlinear advection operator. These results do not support previous claims that the pdf is lognormal. A series of 1D simulations of forced supersonic polytropic turbulence is used to resolve the discrepancy. They suggest that the pdf is lognormal only for effective polytropic indices $\gamma=1$ (or nearly lognormal for $\gamma\not=1$ if the Mach number is sufficiently small), while power laws develop at high densities if $\gamma