The Role of Gravity in Producing Power-Law Mass Functions

Abstract

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, $dN/d\log M\propto M^{\Gamma }$, 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.

arXiv comment11 pages, 10 figures, accepted by ApJ

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• The dynamics and outcome of star formation with jets, radiation, winds, and supernovae in concert
• The Physics of Star Cluster Formation and Evolution
• From the CMF to the IMF: Beyond the Core-Collapse Model
• The Origin of the Stellar Mass Distribution and Multiplicity
• The Origins of Protostellar Core Angular Momenta
• Angular Momenta, Magnetization, and Accretion of Protostellar Cores
• On the emergent System Mass Function: the contest between accretion and fragmentation
• Cloud properties across spatial scales in simulations of the interstellar medium
• Feedback in Forming Star Clusters: The Mass-Radius Relation and Mass Function of Molecular Clumps in the Large Magellanic Cloud