Abstract

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.