ANALYTIC H i-to-H{sub 2} PHOTODISSOCIATION TRANSITION PROFILES
We present a simple analytic procedure for generating atomic (H i) to molecular (H{sub 2}) density profiles for optically thick hydrogen gas clouds illuminated by far-ultraviolet radiation fields. Our procedure is based on the analytic theory for the structure of one-dimensional H i/H{sub 2} photon-dominated regions, presented by Sternberg et al. Depth-dependent atomic and molecular density fractions may be computed for arbitrary gas density, far-ultraviolet field intensity, and the metallicity-dependent H{sub 2} formation rate coefficient, and dust absorption cross section in the Lyman–Werner photodissociation band. We use our procedure to generate a set of H I-to-H{sub 2} transition profiles for a wide range of conditions, from the weak- to strong-field limits, and from super-solar down to low metallicities. We show that if presented as functions of dust optical depth, the H I and H{sub 2} density profiles depend primarily on the Sternberg “αG parameter” (dimensionless) that determines the dust optical depth associated with the total photodissociated H I column. We derive a universal analytic formula for the H I-to-H{sub 2} transition points as a function of just αG. Our formula will be useful for interpreting emission-line observations of H i/H{sub 2} interfaces, for estimating star formation thresholds, and for sub-grid components in hydrodynamics simulations.