The Atomic to Molecular Transition in Galaxies. II: HI and H_2 Column Densities

Gas in galactic disks is collected by gravitational instabilities into giant atomic-molecular complexes, but only the inner, molecular parts of these structures are able to collapse to form stars. Determining what controls the ratio of atomic to molecular hydrogen in complexes is therefore a significant problem in star formation and galactic evolution. In this paper we use the model of H_2 formation, dissociation, and shielding developed in the previous paper in this series to make theoretical predictions for atomic to molecular ratios as a function of galactic properties. We find that the molecular fraction in a galaxy is determined primarily by its column density and secondarily by its metallicity, and is to good approximation independent of the strength of the interstellar radiation field. We show that the column of atomic hydrogen required to shield a molecular region against dissociation is ~10 Msun pc^-2 at solar metallicity. We compare our model to data from recent surveys of the Milky Way and of nearby galaxies, and show that the both the primary dependence of molecular fraction on column density and the secondary dependence on metallicity that we predict are in good agreement with observed galaxy properties.