Evolving Molecular Cloud Structure and the Column Density Probability
  Distribution Function
  The structure of molecular clouds can be characterized with the probability
distribution function (PDF) of the mass surface density. In particular, the
properties of the distribution can reveal the nature of the turbulence and star
formation present inside the molecular cloud. In this paper, we explore how
these structural characteristics evolve with time and also how they relate to
various cloud properties as measured from a sample of synthetic column density
maps of molecular clouds. We find that, as a cloud evolves, the peak of its
column density PDF will shift to surface densities below the observational
threshold for detection, resulting in an underlying lognormal distribution
which has been effectively lost at late times. Our results explain why certain
observations of actively star-forming, dynamically older clouds, such as the
Orion molecular cloud, do not appear to have any evidence of a lognormal
distribution in their column density PDFs. We also study the evolution of the
slope and deviation point of the power-law tails for our sample of simulated
clouds and show that both properties trend towards constant values, thus
linking the column density structure of the molecular cloud to the surface
density threshold for star formation.
