Analytic HI-to-H2 Photodissociation Transition Profiles
  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.
