Analytic HI-to-H2 Photodissociation Transition Profiles
Abstract
We present a simple analytic procedure for generating atomic-to-molecular (HI-to-H2) density profiles for optically thick clouds illuminated by far-ultraviolet radiation. Our procedure is based on the analytic theory for the structure of one-dimensional HI/H2 photon-dominated regions, presented by Sternberg et al. (2014). Depth-dependent HI and H2 density fractions may be computed for arbitrary gas density, far-ultraviolet field intensity, and the metallicity dependent H2 formation rate coefficient, and dust absorption cross section. We use our procedure to generate a set of HI-to-H2 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 HI and H2 density profiles depend primarily on the Sternberg "α G parameter" (dimensionless) that determines the dust optical depth associated with the total photodissociated HI column. We derive a universal analytic formula for the HI-to-H2 transition points as a function of just α G. Our formula will be useful for interpreting emission-line observations of HI/H2 interfaces, for estimating star-formation thresholds, and for sub-grid components in hydrodynamics simulations.
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