Revisiting The Mass-Size Relation Of Structures In Molecular Clouds

TL;DR

This study revisits the mass-size relation in molecular clouds, showing how the relation depends on the column density threshold and the density distribution, with implications for understanding cloud structure.

Contribution

It demonstrates that the mass-size relation's slope is linked to the density profile and threshold choices, clarifying previous ambiguities in molecular cloud studies.

Findings

The $N(R)$ profiles are well fitted by broken power-laws.

The $M-R$ relation's slope depends on the column density threshold.

Constant thresholds lead to a slope near 2, varying with density distribution.

Abstract

We revisit the mass-size relation of molecular cloud structures based on the column density map of the Cygnus-X molecular cloud complex. We extract 135 column density peaks in Cygnus-X and analyze the column density distributions around these peaks. The averaged column density profiles, $N(R)$, around all the peaks can be well fitted with broken power-laws, which are described by an inner power-law index $n$, outer power-law index $m$, and the radius $R_{\rm TP}$ and column density $N_{\rm TP}$ at the transition point. We then explore the $M-R$ relation with different samples of cloud structures by varying the $N(R)$ parameters and the column density threshold, $N_0$, which determines the boundary of a cloud structure. We find that only when $N_0$ has a wide range of values, the $M - R$ relation may largely probe the density distribution, and the fitted power-law index of the $M-R$ relation is related to the power-law index of $N(R)$. On the contrary, with a constant $N_0$, the $M - R$ relation has no direct connection with the density distribution; in this case, the fitted power-law index of the $M - R$ relation is equal to 2 (when $N_0\ge N_{\rm TP}$ and $n$ has a narrow range of values), larger than 2 (when $N_0\ge N_{\rm TP}$ and $n$ has a wide range of values), or slightly less than 2 (when $N_0< N_{\rm TP}$).