Gravitational Focusing and the Star Cluster Initial Mass Function

We discuss the possibility that gravitational focusing is responsible for the power-law mass function of star clusters N(logM) alpha 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 alpha M-2. Although Bondi-Hoyle-Lyttleton accretion formally produces this dependence on mass in a uniform medium, realistic environments are much more complicated. However, numerical simulations in SPH that allow 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.