Evolution of star clusters on eccentric orbits

TL;DR

This study uses direct N-body simulations to analyze how star cluster evolution depends on orbital eccentricity, finding that cluster lifetime and structural evolution are approximately independent of eccentricity when scaled appropriately, providing benchmarks for theoretical models.

Contribution

It provides the first detailed empirical analysis of star cluster evolution on eccentric orbits, establishing approximate independence of lifetime from eccentricity and offering benchmarks for theoretical models.

Findings

Cluster lifetime is approximately independent of eccentricity when scaled to apogalactic radius.

Cluster structural evolution (bound particles, half-mass radius) is roughly independent of eccentricity.

Results serve as benchmarks for theoretical and semi-analytic models of cluster evolution.

Abstract

We study the evolution of star clusters on circular and eccentric orbits using direct $N$-body simulations. We model clusters with initially $N=8{\rm k}$ and $N=16{\rm k}$ single stars of the same mass, orbiting around a point-mass galaxy. For each orbital eccentricity that we consider, we find the apogalactic radius at which the cluster has the same lifetime as the cluster with the same $N$ on a circular orbit. We show that then, the evolution of bound particle number and half-mass radius is approximately independent of eccentricity. Secondly, when we scale our results to orbits with the same semi-major axis, we find that the lifetimes are, to first order, independent of eccentricity. When the results of Baumgardt and Makino for a singular isothermal halo are scaled in the same way, the lifetime is again independent of eccentricity to first order, suggesting that this result is independent of the Galactic mass profile. From both sets of simulations we empirically derive the higher order dependence of the lifetime on eccentricity. Our results serve as benchmark for theoretical studies of the escape rate from clusters on eccentric orbits. Finally, our results can be useful for generative models for cold streams and cluster evolution models that are confined to spherical symmetry and/or time-independent tides, such as Fokker-Planck models, Monte Carlo models, and (fast) semi-analytic models.