The Influence of Orbital Eccentricity on Tidal Radii of Star Clusters

TL;DR

This study uses N-body simulations to show that star cluster tidal radii are better represented by their instantaneous orbital position rather than just at perigalacticon, especially for eccentric orbits.

Contribution

It introduces a correction factor for theoretical tidal radii that accounts for orbital eccentricity and phase, challenging the traditional assumption.

Findings

Clusters can re-capture unbound stars after perigalactic pass.

Tidal shocks energize inner stars, affecting cluster size.

Tidal radius varies with orbital phase, not just perigalacticon.

Abstract

We have performed N-body simulations of star clusters orbiting in a spherically symmetric smooth galactic potential. The model clusters cover a range of initial half-mass radii and orbital eccentricities in order to test the historical assumption that the tidal radius of a cluster is imposed at perigalacticon. The traditional assumption for globular clusters is that since the internal relaxation time is larger than its orbital period, the cluster is tidally stripped at perigalacticon. Instead, our simulations show that a cluster with an eccentric orbit does not need to fully relax in order to expand. After a perigalactic pass, a cluster re-captures previously unbound stars, and the tidal shock at perigalacticon has the effect of energizing inner region stars to larger orbits. Therefore, instead of the limiting radius being imposed at perigalacticon, it more nearly traces the instantaneous tidal radius of the cluster at any point in the orbit. We present a numerical correction factor to theoretical tidal radii calculated at perigalacticon which takes into consideration both the orbital eccentricity and current orbital phase of the cluster.