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

Abstract

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 ∝ M Γ , 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 predictedṀ ∝ M 2 behavior. 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 M 2 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.

Gravitational Focusing and the Star Cluster Initial Mass Function

“…Perhaps a schematic way of understanding the results is that the initial random velocity fluctuations average out so that overdensities can accrete matter at a rate ∝ M 2 . Whatever the interpretation, the common results of both the SPH simulations in Ballesteros-Paredes et al (2015) and the N-body calculations in this paper provide strong evidence for gravitational accretion producing power law distributions with Γ ∼ −1.…”

“…But the molecular clouds within which stars and clusters form exhibit density and velocity fields that are far from uniform; in addition, the cloud itself is self-gravitating. Nevertheless, using isothermal SPH simulations with decaying turbulence, Ballesteros-Paredes et al (2015) (BP15) demonstrated the development of power-law sink mass functions with Γ = −1. These results suggest that gravitational focusing -which is at the heart of the BHL accretion process -is able to operate despite the complex, time-variable environment.…”

The big problems in star formation: The star formation rate, stellar clustering, and the initial mass function

“…Simulations that begin with initial turbulent structure show much shorter delays in the onset of star formation (e.g., Padoan et al 2012). Observations strongly rule out the possibility that real molecular clouds experience a long quiescent phase before the onset of star formation (Hartmann et al 2001;Ballesteros-Paredes & Hartmann 2007;Tamburro et al 2008), suggesting that a more sensible procedure would be to ignore the initial transient when the star formation rate is low, and instead measure ff from the onset of star formation rather than from the start of the simulation; doing so yields ff ≈ 0.3 for Bonnell et al's simulation. Measuring ff only after star formation has begun is also the standard procedure in all other published measurements of ff from simulations.…”

Slingshot mechanism in Orion: Kinematic evidence for ejection of protostars by filaments

“…Hartmann et al (2001) and Ballesteros-Paredes & Hartmann (2007) argue that lifetimes of nearby low mass molecular clouds are ∼1 to 3 Myr. These lifetime estimates hinge on two facts.…”