The Lognormal Probability Distribution Function of the Perseus Molecular Cloud: A Comparison of HI and Dust
The shape of the probability distribution function (PDF) of molecular clouds is an important ingredient for modern theories of star formation and turbulence. Recently, several studies have pointed out observational difficulties with constraining the low column density (i.e. Av <1) PDF using dust tracers. In order to constrain the shape and properties of the low column density probability distribution function, we investigate the PDF of multiphase atomic gas in the Perseus molecular cloud using opacity corrected GALFA HI data and compare the PDF shape and properties to the total gas PDF and the N(H2) PDF. We find that the shape of the PDF in the atomic medium of Perseus is well described by a lognormal distribution, and not by a power law or bimodal distribution. The peak of the atomic gas PDF in and around Perseus lies at the HI H2 transition column density for this cloud, past which the N(H2) PDF takes on a powerlaw form. We find that the PDF of the atomic gas is narrow and at column densities larger than the HI H2 transition the HI rapidly depletes, suggesting that the HI PDF may be used to find the HI H2 transition column density. We also calculate the sonic Mach number of the atomic gas by using HI absorption line data, which yields a median value of Ms=4.0 for the CNM, while the HI emission PDF, which traces both the WNM and CNM, has a width more consistent with transonic turbulence.