The Column Density Probability Density Function of Cygnus-X

TL;DR

This study analyzes the column density probability density functions (N-PDFs) of Cygnus-X, revealing how turbulence and gravity shape molecular cloud structures and identifying a stable star formation threshold.

Contribution

It demonstrates that N-PDFs of Cygnus-X follow a log-normal plus power-law shape and introduces the concept of a unique, stable star formation threshold for molecular clouds.

Findings

N-PDFs exhibit log-normal + power-law shapes.

The power-law segment flattens over time.

A stable star formation threshold is identified.

Abstract

The density distribution within molecular clouds offers critical insights into their underlying physical processes, which are essential for understanding star formation. As a statistical measure of column density on the cloud scale, the shape and evolution of the column density probability density function (N-PDF) serve as important tools for understanding the dynamics between turbulence and gravity. Here we investigate the N-PDFs of Cygnus-X using the column density map obtained from Herschel, supplemented by HI and Young Stellar Objects (YSO) data. We find that the N-PDFs of Cygnus-X and four sub-regions display log-normal + power-law shapes, indicating the combined effects of turbulence and gravity in sculpting the density structure. We find evidence that the power-law segment of the N-PDFs flattens over time, and the transitional column density can be seen as a unique and stable star formation threshold specific to each molecular cloud. These results not only clarify the physical state of Cygnus-X but also emphasize the utility of the N-PDF as a statistical diagnostic tool, as it is an accessible indicator of evolutionary stages and star formation thresholds in molecular clouds.