Escape from the vicinity of fractal basin boundaries of a star cluster

TL;DR

This paper explores the complex escape dynamics of star clusters using chaotic systems theory, revealing fractal basin boundaries, chaotic saddles, and the influence of Coriolis asymmetry on escape times.

Contribution

It introduces a novel analysis of star cluster dissolution through chaotic dynamics, including fractal basin boundaries and the chaotic saddle, within a simplified gravitational and tidal model.

Findings

Longest escape times near fractal basin boundaries

Identification of a fractal chaotic saddle in phase space

Coriolis asymmetry affects the system's dynamics

Abstract

The dissolution process of star clusters is rather intricate for theory. We investigate it in the context of chaotic dynamics. We use the simple Plummer model for the gravitational field of a star cluster and treat the tidal field of the Galaxy within the tidal approximation. That is, a linear approximation of tidal forces from the Galaxy based on epicyclic theory in a rotating reference frame. The Poincar\'e surfaces of section reveal the effect of a Coriolis asymmetry. The system is non-hyperbolic which has important consequences for the dynamics. We calculated the basins of escape with respect to the Lagrangian points $L_1$ and $L_2$. The longest escape times have been measured for initial conditions in the vicinity of the fractal basin boundaries. Furthermore, we computed the chaotic saddle for the system and its stable and unstable manifolds. The chaotic saddle is a fractal structure in phase space which has the form of a Cantor set and introduces chaos into the system.