Bondi–Hoyle–Littleton accretion and the upper-mass stellar initial mass function

We report on a series of numerical simulations of gas clouds with self-gravity forming sink particles, adopting an isothermal equation of state to isolate the effects of gravity from thermal physics on the resulting sink mass distributions. Simulations starting with supersonic velocity fluctuations develop sink mass functions with a high-mass power-law tail dN/d log M ∝ MΓ, Γ = −1 ± 0. 1, independent of the initial Mach number of the velocity field. Similar results but with weaker statistical significance hold for a simulation starting with initial density fluctuations. This mass function power-law dependence agrees with the asymptotic limit found by Zinnecker assuming Bondi–Hoyle–Littleton (BHL) accretion, even though the mass accretion rates of individual sinks show significant departures from the predicted ̇\ M² behaviour. While BHL accretion is not strictly applicable due to the complexity of the environment, we argue that the final mass functions are the result of a relative M2 dependence resulting from gravitationally focused accretion. Our simulations may show the power-law mass function particularly clearly compared with others because our adoption of an isothermal equation of state limits the effects of thermal physics in producing a broad initial fragmentation spectrum; Γ → −1 is an asymptotic limit found only when sink masses grow well beyond their initial values. While we have purposely eliminated many additional physical processes (radiative transfer, feedback) which can affect the stellar mass function, our results emphasize the importance of gravitational focusing for massive star formation.