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 $N(\log M) \propto M^{-1}$. This
power law can be produced asymptotically when the mass accretion rate of an
object depends upon the mass of the accreting body as $\dot{M} \propto M^2$.
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.
