The HI-to-H2 Transition in a Turbulent Medium
  We study the effect of density fluctuations induced by turbulence on the
HI/H$_2$ structure in photodissociation regions (PDRs) both analytically and
numerically. We perform magnetohydrodynamic numerical simulations for both
subsonic and supersonic turbulent gas, and chemical HI/H$_2$ balance
calculations. We derive atomic-to-molecular density profiles and the HI column
density probability density function (PDF) assuming chemical equilibrium. We
find that while the HI/H$_2$ density profiles are strongly perturbed in
turbulent gas, the mean HI column density is well approximated by the
uniform-density analytic formula of Sternberg et al. (2014). The PDF width
depends on (a) the radiation intensity to mean density ratio, (b) the sonic
Mach number and (c) the turbulence decorrelation scale, or driving scale. We
derive an analytic model for the HI PDF and demonstrate how our model, combined
with 21 cm observations, can be used to constrain the Mach number and driving
scale of turbulent gas. As an example, we apply our model to observations of HI
in the Perseus molecular cloud. We show that a narrow observed HI PDF may imply
small scale decorrelation, pointing to the potential importance of
subcloud-scale turbulence driving.
