What is the physics behind the Larson mass-size relation?

TL;DR

This paper investigates the physical reasons behind the Larson mass-size relation in molecular clouds, suggesting that line-of-sight superposition and observational effects influence the observed power-law index.

Contribution

It demonstrates that line-of-sight contamination can explain the observed mass-size relation index greater than 2, challenging the assumption of virial equilibrium for individual clouds.

Findings

Line-of-sight superposition can produce mass-size indices around 2.2-2.3.

Superposition effects are likely present even within single clouds or galaxies.

Defining fractal dimension via mass-size relation is inadequate.

Abstract

Different studies have reported a power-law mass-size relation $M \propto R^q$ for ensembles of molecular clouds. In the case of nearby clouds, the index of the power-law $q$ is close to 2. However, for clouds spread all over the Galaxy, indexes larger than 2 are reported. We show that indexes larger than 2 could be the result of line-of-sight superposition of emission that does not belong to the cloud itself. We found that a random factor of gas contamination, between 0.001\%\ and 10\%\ of the line-of-sight, allows to reproduce the mass-size relation with $q \sim 2.2-2.3$ observed in Galactic CO surveys. Furthermore, for dense cores within a single cloud, or molecular clouds within a single galaxy, we argue that, even in these cases, there is observational and theoretical evidence that some degree of superposition may be occurring. However, additional effects may be present in each case, and are briefly discussed. We also argue that defining the fractal dimension of clouds via the mass-size relation is not adequate, since the mass is not {necessarily} a proxy to the area, and the size reported in $M-R$ relations is typically obtained from the square root of the area, rather than from an estimation of the size independent from the area. Finally, we argue that the statistical analysis of finding clouds satisfying the Larson's relations does not mean that each individual cloud is in virial equilibrium.