On the shape and completeness of the column density probability
  distribution function of molecular clouds
  Both observational and theoretical research over the past decade has
demonstrated that the probability distribution function (PDF) of the gas
density in turbulent molecular clouds is a key ingredient for understanding
star formation. It has recently been argued that the PDF of molecular clouds is
a pure power-law distribution. It has been claimed that the log-normal part is
ruled 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 the
results from high-resolution magnetohydrodynamical simulations of molecular
cloud formation and evolution, we find that the column density PDF is indeed
composed of a log-normal and, if including self-gravity, a power-law part. We
show that insufficient sampling of a molecular cloud results in closed contours
that cut off the log-normal part. In contrast, systematically increasing the
field of view and sampling the entire cloud yields a completeness limit at the
lower column densities, which also recovers the log-normal part. This
demonstrates that the field of view must be sufficiently large for the PDF to
be complete down to its log-normal part, which has important implications for
predictions of star-formation activity based on the PDF.
