The Anatomy of the Column Density Probability Distribution Function (N-PDF)

Abstract

The column density probability distribution function (N-PDF) of Giant Molecular Clouds (GMCs) has been used as a diagnostic of star formation. Simulations and analytic predictions have suggested that 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 and 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 et al. is applicable when tested on observations and simulations, within the uncertainties. Based on the resulting anatomy of the N-PDF, we 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.