Small-N collisional dynamics II: Roaming the realm of not-so-small-N

TL;DR

This paper introduces a formalism for calculating probabilities of stellar collision outcomes in multi-body interactions, applicable to systems with up to six particles, aiding the study of dense stellar environments.

Contribution

The authors develop a binomial theorem-based method to estimate collision probabilities in stellar encounters, valid for various particle masses and radii, extending to larger N-body systems.

Findings

Method achieves accuracy within a few percent for diverse mass ratios.

Applicable to large stellar systems like globular clusters and galactic nuclei.

Can be adapted to predict ejections and exchange outcomes.

Abstract

We develop a formalism for calculating probabilities for the outcomes of stellar dynamical interactions, based on results from $N$-body scattering experiments. We focus here on encounters involving up to six particles and calculate probabilities for direct stellar collisions; however our method is in principle valid for larger particle numbers. Our method relies on the binomial theorem, and is applicable to encounters involving any combination of particle radii. We further demonstrate that our base model is valid to within a few percent for any combination of particle masses, provided the minimum mass ratio is within a factor of a few from unity. This method is particularly suitable for models of collisional systems involving large numbers of stars, such as globular clusters, old open clusters and galactic nuclei, where small subsets of stars may regularly have very close encounters, and the direct integration of all such encounters is computationally expensive. Variations of our method may also be used to treat other encounter outcomes, such as ejections and exchanges.