# Correlating the escape dynamics and the role of the normally hyperbolic invariant manifolds in a binary system of dwarf spheroidal galaxies

## TL;DR

This study investigates how stars escape from a binary dwarf galaxy system by analyzing the dynamics near invariant manifolds, providing insights into the flow of stars and the influence of saddle points on escape behavior.

## Contribution

It offers a detailed analysis of escape dynamics in a realistic binary dwarf galaxy model, emphasizing the role of normally hyperbolic invariant manifolds near saddle points.

## Key findings

- Identification of escape basins and times for different initial conditions.
- Characterization of the role of NHIMs in controlling star escape flow.
- Bifurcation analysis of Lyapunov orbits near saddle points.

## Abstract

We elucidate the escape properties of stars moving in the combined gravitational field of a binary system of two interacting dwarf spheroidal galaxies. A galaxy model of three degrees of freedom is adopted for describing the dynamical properties of the Hamiltonian system. All the numerical values of the involved parameters are chosen having in mind the real binary system of the dwarf spheroidal galaxies NGC 147 and NGC 185. We distinguish between bounded (regular, sticky or chaotic) and escaping motion by classifying initial conditions of orbits in several types of two dimensional planes, considering only unbounded motion for several energy levels. We analyze the orbital structure of all types of two dimensional planes of initial conditions by locating the basins of escape and also by measuring the corresponding escape time of the orbits. Furthermore, the properties of the normally hyperbolic invariant manifolds (NHIMs), located in the vicinity of the index-1 saddle points $L_1$, $L_2$, and $L_3$, are also investigated. These manifolds are of great importance, as they control the flow of stars (between the two galaxies and toward the exterior region) over the different saddle points. In addition, bifurcation diagrams of the Lyapunov periodic orbits as well as restrictions of the Poincar\'e map to the NHIMs are presented for revealing the dynamics in the neighbourhood of the saddle points. Comparison between the current outcomes and previous related results is also made.