Gravitational Focusing and the Star Cluster Initial Mass Function

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We discuss the possibility that gravitational focusing, is responsible for the power-law mass function of star clusters N(M) ∝ M⁻¹. This power law can be produced asymptotically when the mass accretion rate of an object depends upon the mass of the accreting body as M ∝ M². While Bondi-Hoyle-Littleton accretion formally produces this dependence on mass in a uniform medium, realistic environments are much more complicated. However, numerical simulations in SPH allowing for sink formation yield such an asymptotic power-law mass function. We perform pure N-body simulations to isolate the effects of gravity from those of gas physics and to show that clusters naturally result with the power-law mass distribution. We also consider the physical conditions necessary to produce clusters on appropriate timescales. Our results help support the idea that gravitationally-dominated accretion is the most likely mechanism for producing the cluster mass function.