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We aim at understanding the massive star formation (MSF) limit $m(r) = 870 M_{odot} (r/pc)^{1.33}$ in the mass-size space of molecular structures recently proposed by Kauffmann & Pillai (2010). As a first step, we build on the hypothesis of a volume density threshold for overall star formation and the model of Parmentier (2011) to establish the mass-radius relations of molecular clumps containing given masses of star-forming gas. Specifically, we relate the mass $m_{clump}$, radius $r_{clump}$ and density profile slope $-p$ of molecular clumps which contain a mass $m_{th}$ of gas denser than a volume density threshold $rho_{th}$. In a second step, we use the relation between the mass of embedded-clusters and the mass of their most-massive star to estimate the minimum mass of star-forming gas needed to form a $10,M_{odot}$ star. Assuming a star formation efficiency of $SFE simeq 0.30$, this gives $m_{th,crit} simeq 150 M_{odot}$. In a third step, we demonstrate that, for sensible choices of the clump density index ($p simeq 1.7$) and of the cluster formation density threshold ($n_{th} simeq 10^4,cm^{-3}$), the line of constant $m_{th,crit} simeq 150 M_{odot}$ in the mass-radius space of molecular structures equates with the MSF limit for spatial scales larger than 0.3,pc. Hence, the observationally inferred MSF limit of Kauffmann & Pillai is consistent with a threshold in star-forming gas mass beyond which the star-forming gas reservoir is large enough to allow the formation of massive stars. For radii smaller than 0.3,pc, the MSF limit is shown to be consistent with the formation of a $10,M_{odot}$ star out of its individual pre-stellar core of density threshold $n_{th} simeq 10^5,cm^{-3}$. The inferred density thresholds for the formation of star clusters and individual stars within star clusters match those previously suggested in the literature.
To make predictions for the existence of ``dark galaxies, it is necessary to understand what determines whether a gas cloud will form stars. Star formation thresholds are generally explained in terms of the Toomre criterion for gravitational instabil
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The Kennicutt-Schmidt (KS) relationship between the surface density of the star formation rate (SFR) and the gas surface density has three distinct power laws that may result from one model in which gas collapses at a fixed fraction of the dynamical
We study global star formation thresholds in the outer parts of galaxies by investigating the stability of disk galaxies embedded in dark halos. The disks are self-gravitating, contain metals and dust, and are exposed to UV radiation. We find that th