Abstract
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). 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 important effect of supersonic density
fluctuations is to produce a wide HI column density PDF which 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. We test our model using observations of HI in the Perseus GMC.
We find that the narrow observed HI PDF may imply small scale decorrelation,
pointing to the potential importance of subcloud-scale turbulence driving in
Perseus.
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