When does a star cluster become a multiple star system? I. Lifetimes of equal-mass small-N systems

TL;DR

This study investigates the lifetimes and stability of small-N star systems through numerical simulations, aiming to distinguish between star clusters and multiple star systems based on disruption times and system properties.

Contribution

It introduces a framework analyzing disruption time distributions to differentiate star clusters from unstable multiple systems, with new insights into how particle number and virial coefficient influence stability.

Findings

System half-life increases with particle number

Long-lived quasi-stable encounters become more common with higher N

Lower virial coefficient leads to longer system lifetimes

Abstract

What is the difference between a long-lived unstable (or quasi-stable) multiple star system and a bona fide star cluster? In this paper, we present a possible framework to address this question, by studying the distributions of disruption times for chaotic gravitational encounters as a function of the number of interacting particles. To this end, we perform a series of numerical scattering experiments with the \texttt{FEWBODY} code, to calculate the distributions of disruption times as a function of both the particle number N and the virial coefficient k. The subsequent distributions are fit with a physically-motivated function, consisting of an initial exponential decay followed by a very slowly decreasing tail at long encounter times due to long-lived quasi-stable encounters. We find three primary features characteristic of the calculated distributions of disruption times. These are: (1) the system half-life increases with increasing particle number, (2) the fraction of long-lived quasi-stable encounters increases with increasing particle number and (3) both the system half-life and the fraction of quasi-stable encounters increase with decreasing virial coefficient. We discuss the significance of our results for collisional dynamics, and consider the extrapolation of our results to larger-N systems. We suggest that this could potentially offer a clear and unambiguous distinction between star clusters and (unstable or quasi-stable) multiple star systems. Although we are limited by very small-number statistics, our results tentatively suggest that (for our assumptions) this transition occurs at a critical particle number of order 100.