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

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 $n_{th}\simeq 10^{4-5}c{m}^{-3}$. 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]

15 pages, 12 figures, accepted to MNRAS

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• Can star cluster environment affect dust input from massive AGB stars?
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