On the extraction of the power-law parts of probability density functions in star-forming clouds

Abstract

We present a new approach to extract the power-law part of a density/column-density probability density function (ρ-pdf/N-pdf) in star-forming clouds. This approach is based on the mathematical method BPLFIT of Virkar & Clauset (2014, Annals of Applied Statistics, 8, 89) and it assesses the power-law part of an arbitrary distribution, without any assumptions about the other parts of this distribution. The slope and deviation point are derived as averaged values as the number of bins is varied. Neither parameter is sensitive to spikes and other local features of the tail. This adapted BPLFIT method is applied to two different sets of data from numerical simulations of star-forming clouds at scales 0.5 and 500 pc, and it displays ρ-pdf and N-pdf evolution in agreement with a number of numerical and theoretical studies. Applied to Herschel data on the regions Aquila and Rosette, the method extracts pronounced power-law tails, consistent with those seen in simulations of evolved clouds.