Analytic HI-to-H2 Photodissociation Transition Profiles

TL;DR

This paper introduces a simple analytic method to generate atomic-to-molecular hydrogen density profiles in clouds exposed to ultraviolet radiation, aiding interpretation of observations and simulations.

Contribution

It provides a universal analytic formula for HI-to-H2 transition points based on the $\alpha G$ parameter, applicable across various conditions and metallicities.

Findings

Density profiles depend mainly on the $\alpha G$ parameter.

Derived a universal formula for HI-to-H2 transition points.

Profiles applicable for different metallicities and radiation fields.

Abstract

We present a simple analytic procedure for generating atomic-to-molecular (HI-to-H$_2$) 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/H$_2$ photon-dominated regions, presented by Sternberg et al. (2014). Depth-dependent HI and H$_2$ density fractions may be computed for arbitrary gas density, far-ultraviolet field intensity, and the metallicity dependent H$_2$ formation rate coefficient, and dust absorption cross section. We use our procedure to generate a set of HI-to-H$_2$ 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 HI and H$_2$ density profiles depend primarily on the Sternberg "$\alpha G$ 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-H$_2$ transition points as a function of just $\alpha G$. Our formula will be useful for interpreting emission-line observations of HI/H$_2$ interfaces, for estimating star-formation thresholds, and for sub-grid components in hydrodynamics simulations.