Application of three-body stability to globular clusters: I. The stability radius

TL;DR

This paper introduces a new analytical method based on the three-body problem to estimate the stability radius of globular clusters, revealing that orbital eccentricity significantly influences stellar stability boundaries.

Contribution

It presents a novel analytical formula for the stability radius of globular clusters, improving understanding of stellar escape mechanisms compared to traditional tidal radius estimates.

Findings

Stability radius is smaller than the tidal radius.

Orbital eccentricity greatly affects stability boundaries.

Stars can escape via a random walk process from the stability radius.

Abstract

The tidal radius is commonly determined analytically by equating the tidal field of the galaxy to the gravitational potential of the cluster. Stars crossing this radius can move from orbiting the cluster centre to independently orbiting the galaxy. In this paper, the stability radius of a globular cluster is estimated using a novel approach from the theoretical standpoint of the general three-body problem. This is achieved by an analytical formula for the transition radius between stable and unstable orbits in a globular cluster. A stability analysis, outlined by Mardling, is used here to predict the occurrence of unstable stellar orbits in the outermost region of a globular cluster in a distant orbit around a galaxy. It is found that the eccentricity of the cluster-galaxy orbit has a far more significant effect on the stability radius of globular clusters than previous theoretical results of the tidal radius have found. A simple analytical formula is given for determining the transition between stable and unstable orbits, which is analogous to the tidal radius for a globular cluster. The stability radius estimate is interior to tidal radius estimates and gives the innermost region from which stars can random walk to their eventual escape from the cluster. The time-scale for this random walk process is also estimated using numerical three-body scattering experiments.