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Both observational and theoretical research over the past decade hasdemonstrated that the probability distribution function (PDF) of the gasdensity in turbulent molecular clouds is a key ingredient for understandingstar formation. It has recently been argued that the PDF of molecular clouds isa pure power-law distribution. It has been claimed that the log-normal part isruled out when using only the part of the PDF up/down to which it is complete,that is where the column density contours are still closed. By using theresults from high-resolution magnetohydrodynamical simulations of molecularcloud formation and evolution, we find that the column density PDF is indeedcomposed of a log-normal and, if including self-gravity, a power-law part. Weshow that insufficient sampling of a molecular cloud results in closed contoursthat cut off the log-normal part. In contrast, systematically increasing thefield of view and sampling the entire cloud yields a completeness limit at thelower column densities, which also recovers the log-normal part. Thisdemonstrates that the field of view must be sufficiently large for the PDF tobe complete down to its log-normal part, which has important implications forpredictions of star-formation activity based on the PDF.

On the shape and completeness of the column density probability distribution function of molecular clouds