Molecular clouds have power-law probability distribution functions

TL;DR

This study reveals that molecular cloud column density PDFs are better described by power-law functions with exponents near two, challenging the traditional log-normal model, and highlights limitations in probing lower extinction levels.

Contribution

The paper demonstrates that molecular cloud PDFs are power laws rather than log-normal, providing new insights into their statistical structure and the limits of current observational data.

Findings

Molecular cloud PDFs are power laws with exponents close to two.

Breaks in the PDFs occur near the CO self-shielding limit.

Intrinsic PDF shape cannot be determined below certain extinction levels.

Abstract

In this Letter we investigate the shape of the probability distribution of column densities (PDF) in molecular clouds. Through the use of low-noise, extinction-calibrated \textit{Herschel}/\textit{Planck} emission data for eight molecular clouds, we demonstrate that, contrary to common belief, the PDFs of molecular clouds are not described well by log-normal functions, but are instead power laws with exponents close to two and with breaks between $A_K \simeq 0.1$ and $0.2\,\mathrm{mag}$, so close to the CO self-shielding limit and not far from the transition between molecular and atomic gas. Additionally, we argue that the intrinsic functional form of the PDF cannot be securely determined below $A_K \simeq 0.1\,\mathrm{mag}$, limiting our ability to investigate more complex models for the shape of the cloud PDF.