From the molecular-cloud- to the embedded-cluster-mass function with a density threshold for star formation

TL;DR

This paper presents a model explaining the difference in mass functions between molecular clouds and star clusters, emphasizing the role of density thresholds and mass-radius relations in star formation.

Contribution

It introduces a density-threshold-based model that links molecular cloud properties to star cluster formation, explaining observed differences in their mass functions.

Findings

Mass function of clouds is shallower than that of star clusters.

Constant volume density formation steepens the cluster mass function.

Model aligns with observed surface density and density thresholds.

Abstract

The mass function of molecular clouds and clumps is shallower than the mass function of young star clusters, gas-embedded and gas-free alike, as their respective mass function indices are $\beta_0 \simeq 1.7$ and $\beta_\star \simeq 2$. We demonstrate that such a difference can arise from different mass-radius relations for the embedded-clusters and the molecular clouds (clumps) hosting them. In particular, the formation of star clusters with a constant mean {\it volume} density in the central regions of molecular clouds of constant mean {\it surface} density steepens the mass function from clouds to embedded-clusters. This model is observationally supported since the mean surface density of molecular clouds is approximately constant, while there is a growing body of evidence, in both Galactic and extragalactic environments, that efficient star-formation requires a hydrogen molecule number density threshold of $n_{th} \simeq 10^{4-5}\,cm^{-3}$. In the framework of the same model, the radius distribution steepens from clouds (clumps) to embedded-clusters, which contributes to explaining observed cluster radius distributions. [Abridged]