Comparing the escape dynamics in tidally limited star cluster models

TL;DR

This study compares the orbital dynamics and escape processes in different star cluster models using numerical analysis, focusing on how various potentials influence escape basins and times in tidally limited clusters.

Contribution

It introduces a comparative analysis of isochrone and Hernquist models against the Plummer model for star clusters, highlighting differences in escape dynamics and orbital properties.

Findings

Different potentials produce distinct escape basin structures.

Escape times vary significantly with the model used.

Chaotic and ordered orbit distributions depend on the potential.

Abstract

The aim of this work is to compare the orbital dynamics in three different models describing the properties of a star cluster rotating around its parent galaxy in a circular orbit. In particular, we use the isochrone and the Hernquist potentials to model the spherically symmetric star cluster and we compare our results with the corresponding ones of a previous work in which the Plummer model was applied for the same purpose. Our analysis takes place both in the configuration $(x,y)$ and in the phase $(x,\dot{x})$ space in order to elucidate the escape process as well as the overall orbital properties of the tidally limited star cluster. We restrict our investigation into two dimensions and we conduct a thorough numerical analysis distinguishing between ordered and chaotic orbits as well as between trapped and escaping orbits, considering only unbounded motion for several energy levels above the critical escape energy. It is of particular interest to determine the escape basins towards the two exit channels (near the Lagrangian points $L_1$ and $L_2$) and relate them with the corresponding escape times of the orbits.