The Distribution of Pressures in a Supernova-Driven Interstellar Medium. I. Magnetized Medium

Observations have suggested substantial departures from pressure equilibrium in the interstellar medium (ISM) in the plane of the Galaxy, even on scales under 50 pc. Nevertheless, multi-phase models of the ISM assume at least locally isobaric gas. The pressure then determines the density reached by gas cooling to stable thermal equilibrium. We use numerical models of the magnetized ISM to examine the consequences of supernova driving for interstellar pressures. In this paper we examine a (200 pc)^3 periodic domain threaded by magnetic fields. Individual parcels of gas at different pressures reach widely varying points on the thermal equilibrium curve: no unique set of phases is found, but rather a dynamically-determined continuum of densities and temperatures. A substantial fraction of the gas remains entirely out of thermal equilibrium. Our results appear consistent with observations of interstellar pressures. They also suggest that the high pressures observed in molecular clouds may be due to ram pressures in addition to gravitational forces. Much of the gas in our model lies far from equipartition between thermal and magnetic pressures, with ratios ranging from 0.1 to $10^4$ and ratios of uniform to fluctuating magnetic field of 0.5--1. Our models show broad pressure probability distribution functions with log-normal functional forms produced by both shocks and rarefaction waves, rather than power-law distributions produced by isolated supernova remnants. The width of the distribution can be described quantitatively by a formula derived from the work of Padoan, Nordlund, & Jones (1997).