H I-TO-H₂ transitions and H i column densities in galaxy star-forming regions

We present new analytic theory and radiative transfer computations for the atomic-to-molecular (H I-to-H2) transitions and the buildup of atomic hydrogen (H I) gas columns in optically thick interstellar clouds irradiated by far-UV (FUV) photodissociating radiation fields. We derive analytic expressions for the total H I column densities for (one-dimensional (1D)) planar slabs, for beamed or isotropic radiation fields, from the weak- to strong-field limits, for gradual or sharp atomic-to-molecular transitions, and for arbitrary metallicity. Our expressions may be used to evaluate the H I column densities as functions of the radiation field intensity and the H2-dust-limited dissociation flux, the hydrogen gas density, and the metallicity-dependent H2 formation rate coefficient and FUV dust grain absorption cross section. We make the distinction between "H I-dust" and "H2-dust" opacity, and we present computations for the "universal H2-dust-limited effective dissociation bandwidth." We validate our analytic formulae with Meudon PDR code computations for the H I-to-H2 density profiles and total H I column densities. We show that our general 1D formulae predict H I columns and H2 mass fractions that are essentially identical to those found in more complicated (and approximate) spherical (shell-core) models. We apply our theory to compute H2 mass fractions and star-formation thresholds for individual clouds in self-regulated galaxy disks, for a wide range of metallicities. Our formulae for the H I columns and H2 mass fractions may be incorporated into hydrodynamics simulations for galaxy evolution.