On the Spatial Distribution of $^{13}$CO Structures within $^{12}$CO Molecular Clouds

TL;DR

This study analyzes the spatial distribution of $^{13}$CO structures within $^{12}$CO molecular clouds, revealing a universal angular separation and proposing a fundamental unit for cloud assembly and destruction.

Contribution

It introduces a statistical analysis of $^{13}$CO structures' distribution within $^{12}$CO clouds and suggests a universal separation scale relevant for cloud evolution.

Findings

Approximately 50% of angular separations are 3-7 arcmin.

Radial velocity separations mainly range from 0.3 to 2.5 km/s.

A scaling relation exists between cloud area and $^{13}$CO structure count.

Abstract

We look into the 2851 $^{12}$CO molecular clouds harboring $^{13}$CO structures to reveal the distribution of the projected angular separations and radial velocity separations between their internal $^{13}$CO structures. The projected angular separations are determined using the minimal spanning tree algorithm. We find that $\sim$ 50$\%$ of the angular separations fall in a narrow range of $\sim$ 3 - 7 arcmin with a median of $\sim$ 5 arcmin, and the corresponding radial velocity separations mainly range from $\sim$ 0.3 km s$^{-1}$ to 2.5 km s$^{-1}$. The mean and standard deviation of the angular separations of the internal $^{13}$CO structures within $^{12}$CO clouds appear to be universal, independent of the $^{12}$CO cloud angular areas and the counts of their internal $^{13}$CO structures. We also reveal a scaling relation between the $^{12}$CO cloud angular area and its harbored $^{13}$CO structure count. These results suggest there is a preferred angular separation between $^{13}$CO structures in these $^{12}$CO clouds, considering the distance effects. According to that, we propose an alternative picture for the assembly and destruction of molecular clouds: there is a fundamental separation for the internal structures of molecular clouds, the build-up and destruction of molecular clouds proceeds under this fundamental unit.