The shapes of column density PDFs: The importance of the last closed contour

The probability distribution function of column density (PDF) has become the tool of choice for cloud structure analysis and star formation studies. Its simplicity is attractive, and the PDF could offer access to cloud physical parameters otherwise difficult to measure, but there has been some confusion in the literature on the definition of its completeness limit and shape at the low column density end. In this letter we use the natural definition of the completeness limit of a column density PDF, the last closed column density contour inside a surveyed region, and apply it to a set of large-scale maps of nearby molecular clouds. We conclude that there is no observational evidence for log-normal PDFs in these objects. We find that all studied molecular clouds have PDFs well described by power laws, including the diffuse cloud Polaris. Our results call for a new physical interpretation of the shape of the column density PDFs. We find that the slope of a cloud PDF is invariant to distance but not to the spatial arrangement of cloud material, and as such it is still a useful tool for investigating cloud structure.