Pressure relations and vertical equilibrium in the turbulent, multiphase interstellar medium

We use numerical simulations of turbulent, multiphase, self-gravitating gas orbiting in the disks of model galaxies to study the relationships among pressure, the vertical distribution of gas, and the relative proportions of dense and diffuse gas. A common assumption is that the interstellar medium (ISM) is in vertical hydrostatic equilibrium. We show that the disk height and mean midplane pressure in our multiphase, turbulent simulations are indeed consistent with effective hydrostatic equilibrium, provided that the turbulent contribution to the vertical velocity dispersion and the gas self-gravity are included. Although vertical hydrostatic equilibrium gives a good estimate for the mean midplane pressure 〈P〉_midplane, this does not represent the pressure experienced by most of the ISM. Mass-weighted mean pressures 〈P〉_ρ are typically an order of magnitude higher than 〈P〉_midplane because self-gravity concentrates gas and increases the pressure in individual clouds without raising the ambient pressure. We also investigate the ratio R _mol=M_H2/ M _H1 for our hydrodynamic simulations. Blitz & Rosolowsky showed that R _mol is proportional to the estimated midplane pressure in a number of systems. We find that for model series in which the epicyclic frequency κ and gas surface density Σ vary together as κ Σ, we recover the empirical relation. For other model series in which κ and Σ are varied independently, the midplane pressure (or Σ) and R _mol are not well correlated. We conclude that the molecular fraction - and hence the star formation rate - of a galactic disk inherently depends on its rotational state, not just the local values of Σ and the stellar density ρ_*. The empirical result R _mol 〈P〉_midplane implies that the three "environmental parameters" κ, Σ, and ρ_* are interdependent in real galaxies, presumably as a consequence of evolution: real galaxies tend toward states with Toomre Q parameter near unity. Finally, we note that R _mol in static comparison models far exceeds both the values in our turbulent hydrodynamic simulations and observed values of R _mol, when Σ>10 M _⊙ pc^-2, indicating that incorporation of turbulence is crucial to obtaining a realistic molecular fraction in numerical models of the ISM.