SCYON Abstract

Received on March 04 2011

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

Authors	Genevieve Parmentier (¹)
Affiliation	(¹) Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, D-53121 Bonn, Germany
To appear in	Monthly Notices of the Royal Astronomical Society
Contact	gparm@astro.uni-bonn.de
URL	http://xxx.lanl.gov/abs/1101.0813
Links

Abstract

The mass function dN ∝ m^-β₀dm of molecular clouds and clumps is shallower than the mass function dN ∝ m^-β(star)dm of young star clusters, gas-embedded and gas-free alike, as their respective mass function indices are β₀ ≅ 1.7 and β(star) ≅ 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 volume density in the central regions of molecular clouds of constant mean 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 ≅ 10^4-5cm^-3. Adopting power-law volume density profiles of index p for spherically symmetric molecular clouds (clumps), we define two zones within each cloud (clump): a central cluster-forming region, actively forming stars by virtue of a local number density higher than n_th, and an outer envelope inert in terms of star formation. We map how much the slope of the cluster-forming region mass function differs from that of their host-clouds (clumps) as a function of their respective mass-radius relations and of the cloud (clump) density index. We find that for constant surface density clouds with density index p ≅ 1.9, a cloud mass function of index β₀ = 1.7 gives rise to a cluster-forming region mass function of index β ≅ 2. Our model equates with defining two distinct SFEs: a global mass-varying SFE averaged over the whole cloud (clump), and a local mass-independent SFE measured over the central cluster-forming region. While the global SFE relates the mass function of clouds to that of embedded-clusters, the local SFE rules cluster evolution after residual star-forming gas expulsion. That the cluster mass function slope does not change through early cluster evolution implies a mass-independent local SFE and, thus, the same mass function index for cluster-forming regions and embedded-clusters, that is, β = β(star). Our model can therefore reproduce the observed cluster mass function index β(star) ≅ 2. For the same model parameters, the radius distribution also steepens from clouds (clumps) to embedded-clusters, which contributes to explaining observed cluster radius distributions.