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Numerical simulations of star formation have found that a power-law mass function can develop at high masses. In a previous paper, we employed isothermal simulations which created large numbers of sinks over a large range in masses to show that the power law exponent of the mass function, $dN/dlog M propto M^{Gamma}$, asymptotically and accurately approaches $Gamma = -1.$ Simple analytic models show that such a power law can develop if the mass accretion rate $dot{M} propto M^2$, as in Bondi-Hoyle accretion; however, the sink mass accretion rates in the simulations show significant departures from this relation. In this paper we show that the expected accretion rate dependence is more closely realized provided the gravitating mass is taken to be the sum of the sink mass and the mass in the near environment. This reconciles the observed mass functions with the accretion rate dependencies, and demonstrates that power-law upper mass functions are essentially the result of gravitational focusing, a mechanism present in, for example, the competitive accretion model.
We introduce a new multi-power-law distribution for the Initial Mass Function (IMF) to explore its potential properties. It follows on prior work that introduced mechanisms accounting for mass accretion in star formation, developed within the framewo
We derive an analytical theory of the PDF of density fluctuations in supersonic turbulence in the presence of gravity in star-forming clouds. The theory is based on a rigorous derivation of a combination of the Navier-Stokes continuity equations for
We report the novel detection of complex high-column density tails in the probability distribution functions (PDFs) for three high-mass star-forming regions (CepOB3, MonR2, NGC6334), obtained from dust emission observed with Herschel. The low column
In the star formation process, the vital impact of environmental factors such as feedback from massive stars and stellar density on the form of the initial mass function (IMF) at low-mass end is yet to be understood. Hence a systematic, highly sensit
We study the star formation (SF) law in 12 Galactic molecular clouds with ongoing high-mass star formation (HMSF) activity, as traced by the presence of a bright IRAS source and other HMSF tracers. We define the molecular cloud (MC) associated to eac