The Anatomy of the Column Density Probability Distribution Function
  (N-PDF)
  The column density probability distribution function (N-PDF) of GMCs has been
used as a diagnostic of star formation. Simulations and analytic predictions
have suggested the N-PDF is composed of a low density lognormal component and a
high density power-law component, tracing turbulence and gravitational
collapse, respectively. In this paper, we study how various properties of the
true 2D column density distribution create the shape, or "anatomy" of the PDF.
We test our ideas and analytic approaches using both a real, observed, PDF
based on Herschel observations of dust emission as well as a simulation that
uses the ENZO code. Using a dendrogram analysis, we examine the three main
components of the N-PDF: the lognormal component, the power-law component, and
the transition point between these two components. We find that the power-law
component of an N-PDF is the summation of N-PDFs of power-law substructures
identified by the dendrogram algorithm. We also find that the analytic solution
to the transition point between lognormal and power-law components proposed by
Burkhart, Stalpes & Collins (2017) is applicable when tested on observations
and simulations, within the uncertainties. We reconfirm and extend the results
of Lombardi, Alves & Lada (2015), which stated that the lognormal component of
the N-PDF is difficult to constrain due to the artificial choice of the map
area. Based on the resulting anatomy of the N-PDF, we suggest avoiding
analyzing the column density structures of a star forming region based solely
on fits to the lognormal component of an N-PDF. We also suggest applying the
N-PDF analysis in combination with the dendrogram algorithm, to obtain a more
complete picture of the global and local environments and their effects on the
density structures.
