Evolution of column density distributions within Orion~A
  We compare the structure of star-forming molecular clouds in different
regions of Orion A to determine how the column density probability distribution
function (N-PDF) varies with environmental conditions such as the fraction of
young protostars. A correlation between the N-PDF slope and Class 0 protostar
fraction has been previously observed in a low-mass star-formation region
(Perseus) by Sadavoy; here we test if a similar correlation is observed in a
high-mass star-forming region. We use Herschel data to derive a column density
map of Orion A. We use the Herschel Orion Protostar Survey catalog for accurate
identification and classification of the Orion A young stellar object (YSO)
content, including the short-lived Class 0 protostars (with a $\sim$ 0.14 Myr
lifetime). We divide Orion A into eight independent 13.5 pc$^2$ regions; in
each region we fit the N-PDF distribution with a power-law, and we measure the
fraction of Class 0 protostars. We use a maximum likelihood method to measure
the N-PDF power-law index without binning. We find that the Class 0 fraction is
higher in regions with flatter column density distributions. We test the
effects of incompleteness, YSO misclassification, resolution, and pixel-scale.
We show that these effects cannot account for the observed trend. Our
observations demonstrate an association between the slope of the power-law
N-PDF and the Class 0 fractions within Orion A. Various interpretations are
discussed including timescales based on the Class 0 protostar fraction assuming
a constant star-formation rate. The observed relation suggests that the N-PDF
can be related to an "evolutionary state" of the gas. If universal, such a
relation permits an evaluation of the evolutionary state from the N-PDF
power-law index at much greater distances than those accesible with protostar
counts. (abridged)
