The HI Probability Distribution Function and the Atomic-to-Molecular Transition in Molecular Clouds

We characterize the column density probability distributions functions (PDFs) of the atomic hydrogen gas, HI, associated with seven Galactic molecular clouds (MCs). We use 21 cm observations from the Leiden/Argentine/Bonn Galactic HI Survey to derive column density maps and PDFs. We find that the peaks of the HI PDFs occur at column densities ranging from ~1-2$\times 10^{21}$ cm$^2$ (equivalently, ~0.5-1 mag). The PDFs are uniformly narrow, with a mean dispersion of $\sigma_{HI}\approx 10^{20}$ cm$^2$ (~0.1 mag). We also investigate the HI-to-H$_2$ transition towards the cloud complexes and estimate HI surface densities ranging from 7-16 $M_\odot$ pc$^{-2}$ at the transition. We propose that the HI PDF is a fitting tool for identifying the HI-to-H$_2$ transition column in Galactic MCs.