The Role of Gravity in Producing Power-Law Mass Functions

TL;DR

This paper investigates how gravity influences the formation of power-law mass functions in star formation, demonstrating that considering the combined mass of sinks and their environment aligns accretion rates with theoretical models, emphasizing gravitational focusing.

Contribution

It shows that including environmental mass in accretion rate calculations explains the development of power-law mass functions via gravitational focusing in star formation.

Findings

Accretion rates better match M^2 dependence when environmental mass is included.

Power-law mass functions arise from gravitational focusing mechanisms.

Reconciles simulation results with analytic models of star formation.

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.