# Relaxation of spherical stellar systems

## TL;DR

This study uses extensive simulations to show that self-gravity significantly amplifies initial noise in stellar clusters, affecting star diffusion and challenging traditional local-scattering theories.

## Contribution

It demonstrates the importance of self-gravity in cluster evolution and advocates for using the Balescu-Lenard equation over local-scattering theory.

## Key findings

- Self-gravity amplifies Poisson noise over three crossing times.
- The fundamental dipole mode is strongly excited by Poisson noise.
- Local-scattering theory fails to predict diffusion accurately.

## Abstract

10,000 simulations of 1000-particle realisations of the same cluster are computed by direct force summation. Over three crossing times the original Poisson noise is amplified more than tenfold by self-gravity. The cluster's fundamental dipole mode is strongly excited by Poisson noise, and this mode makes a major contribution to driving diffusion of stars in energy. The diffusive flow through action space is computed for the simulations and compared with the predictions of both local-scattering theory and the Balescu-Lenard (BL) equation. The predictions of local-scattering theory are qualitatively wrong because the latter neglects self-gravity. These results imply that local-scattering theory is of little value. Future work on cluster evolution should employ either N-body simulation or the BL equation. However, significant code development will be required to make use of the BL equation practicable.