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

TL;DR

This paper introduces a new method based on bPLFIT to accurately extract and analyze the power-law tail of density probability density functions in star-forming clouds, applicable to both simulations and observational data.

Contribution

It adapts the bPLFIT method to assess the power-law part of density PDFs without assumptions, providing robust slope and deviation point estimates.

Findings

The method successfully extracts power-law tails from simulation data.

It reveals consistent evolution of PDFs with theoretical predictions.

Applied to Herschel data, it identifies pronounced power-law tails in star-forming regions.

Abstract

We present a new approach to extract the power-law part of a density/column-density probability density function (rho-pdf/N-pdf) in star-forming clouds. It is based on the mathematical method bPLFIT of Virkar & Clauset (2014) and assesses the power-law part of an arbitrary distribution, without any assumptions about the other part 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 displays rho-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.