# Gravitational Focusing and the Star Cluster Initial Mass Function

## TL;DR

This paper explores how gravitational focusing and accretion processes can naturally produce the observed power-law initial mass function of star clusters, supported by numerical simulations.

## Contribution

It demonstrates through N-body simulations that gravity-driven accretion alone can generate the cluster mass function without gas physics.

## Key findings

- N-body simulations produce a power-law mass distribution.
- Gravitational focusing can explain the cluster initial mass function.
- Conditions for cluster formation timescales are identified.

## Abstract

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.