Self-similar cluster structures in massive star-forming regions: Isolated evolution from clumps to embedded clusters

TL;DR

This study investigates the hierarchical and self-similar structures of star clusters and their relation to gas clumps in massive star-forming regions, revealing isolated local evolution and a consistent star formation efficiency.

Contribution

It introduces a hierarchical analysis of star cluster structures using dendrograms and demonstrates their self-similar power-law relations, highlighting isolated local evolution from clumps to clusters.

Findings

Star clusters exhibit self-similar, power-law mass-size relations.

Cluster and clump separations are comparable, indicating local, isolated evolution.

Star formation efficiency in ATLASGAL clumps is approximately 0.33.

Abstract

We used the dendrogram algorithm to decompose the surface density distributions of stars into hierarchical structures. These structures were tied to the multiscale structures of star clusters. A similar power-law for the mass-size relation of star clusters measured at different scales suggests a self-similar structure of star clusters. We used the minimum spanning tree method to measure the separations between clusters and gas clumps in each massive star-forming region. The separations between clusters, between clumps, and between clusters and clumps were comparable, which indicates that the evolution from clump to embedded cluster proceeds in isolation and locally, and does not affect the surrounding objects significantly. By comparing the mass functions of the ATLASGAL clumps and the identified embedded clusters, we confirm that a constant star formation efficiency of $\approx$ 0.33 can be a typical value for the ATLASGAL clumps.