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Observations of spiral galaxies show a strong linear correlation between theratio of molecular to atomic hydrogen surface density R_mol and midplanepressure. To explain this, we simulate three-dimensional, magnetizedturbulence, including simplified treatments of non-equilibrium chemistry andthe propagation of dissociating radiation, to follow the formation of H_2 fromcold atomic gas. The formation time scale for H_2 is sufficiently long thatequilibrium is not reached within the 20-30 Myr lifetimes of molecular clouds.The equilibrium balance between radiative dissociation and H_2 formation ondust grains fails to predict the time-dependent molecular fractions we find. Asimple, time-dependent model of H_2 formation can reproduce the gross behavior,although turbulent density perturbations increase molecular fractions by afactor of few above it. In contradiction to equilibrium models, radiativedissociation of molecules plays little role in our model for diffuse radiationfields with strengths less than ten times that of the solar neighborhood,because of the effective self-shielding of H_2. The observed correlation ofR_mol with pressure corresponds to a correlation with local gas density if theeffective temperature in the cold neutral medium of galactic disks is roughlyconstant. We indeed find such a correlation of R_mol with density. If weexamine the value of R_mol in our local models after a free-fall time at theiraverage density, as expected for models of molecular cloud formation bylarge-scale gravitational instability, our models reproduce the observedcorrelation over more than an order of magnitude range in density.

The Abundance of Molecular Hydrogen and its Correlation with Midplane Pressure in Galaxies: Non-Equilibrium, Turbulent, Chemical Models