Small-N Collisional Dynamics: Pushing Into the Realm of Not-So-Small-N

TL;DR

This study investigates small-N gravitational interactions involving up to six objects, revealing that collision probability scales approximately with N^2, bridging the understanding between small-N and large-N dynamical regimes.

Contribution

The paper extends numerical scattering experiments to include encounters with triple stars and explores collision probabilities for N up to six, advancing small-N dynamical understanding.

Findings

Collision probability increases roughly as N^2.

The N^2 scaling aligns with mean free path predictions for large N.

First step towards understanding larger-N collisional dynamics.

Abstract

In this paper, we study small-N gravitational dynamics involving up to six objects. We perform a large suite of numerical scattering experiments involving single, binary, and triple stars. This is done using the FEWBODY numerical scattering code, which we have upgraded to treat encounters involving triple stars. We focus on outcomes that result in direct physical collisions between stars, within the low angular momentum and high absolute orbital energy regime. The dependence of the collision probability on the number of objects involved in the interaction, N, is found for fixed total energy and angular momentum. Our results are consistent with a collision probability that increases approximately as N^2. Interestingly, this is also what is expected from the mean free path approximation in the limit of very large N. A more thorough exploration of parameter space will be required in future studies to fully explore this potentially intriguing connection. This study is meant as a first step in an on-going effort to extend our understanding of small-N collisional dynamics beyond the three- and four-body problems and into the realm of larger-N.