Pressure Relations and Vertical Equilibrium in the Turbulent, Multiphase   ISM
  We use numerical simulations of turbulent, multiphase, self-gravitating gas orbiting in model disk galaxies to study the relationships among pressure, the vertical gas distribution, and the ratio of dense to diffuse gas. We show that the disk height and mean midplane pressure are consistent with effective hydrostatic equilibrium, provided that the turbulent vertical velocity dispersion and gas self-gravity are included. Mass-weighted pressures are an order of magnitude higher than the midplane pressure because self-gravity concentrates gas and increases the pressure in clouds. We also investigate the ratio Rmol=M(H2)/M(HI) for our simulations. Blitz and Rosolowsky (2006) showed that Rmol is proportional to the estimated midplane pressure. For model series in which the epicyclic frequency, kappa, and gas surface density, Sigma, are proportional, we recover the empirical relation. For other model series in which kappa and Sigma are independent, the midplane pressure and Rmol are not well correlated. We conclude that the molecular fraction -- and star formation rate -- of a galactic disk inherently depends on its rotational state, not just the local values of Sigma and the stellar density rho*. The empirical correlation between Rmol and midplane pressure implies that the "environmental parameters" kappa, Sigma, and rho* are interdependent in real galaxies, presumably as a consequence of evolution toward states with Toomre Q near unity. We note that Rmol in static models far exceeds both the values in our turbulent simulations and observed values, implying that turbulence is crucial to obtaining a realistic molecular fraction in the ISM. 
H. Koyama and E. C. Ostriker