Orbital and escape dynamics in barred galaxies - III. The 3D system: Correlations between the basins of escape and the NHIMs

TL;DR

This study investigates the complex escape dynamics of stars in a 3D barred galaxy model, revealing how invariant manifolds and system parameters influence escape routes, times, and resulting stellar structures like rings and spirals.

Contribution

It provides a detailed analysis of escape basins, the role of stable manifolds, and the impact of bar parameters on stellar structures in a realistic 3D galaxy model.

Findings

Basins of escape are identified and related to escape times.

Stable manifolds define fractal basin boundaries.

Bar parameters significantly influence stellar structures.

Abstract

The escape dynamics of the stars in a barred galaxy composed of a spherically symmetric central nucleus, a bar, a flat thin disk and a dark matter halo component is investigated by using a realistic three degrees of freedom (3-dof) dynamical model. Modern colour-coded diagrams are used for distinguishing between bounded and escaping motion. In addition, the smaller alignment index (SALI) method is deployed for determining the regular, sticky or chaotic nature of bounded orbits. We reveal the basins of escape corresponding to the escape through the two symmetrical escape channels around the Lagrange points $L_2$ and $L_3$ and also we relate them with the corresponding distribution of the escape times of the orbits. Furthermore, we demonstrate how the stable manifolds, around the index-1 saddle points, accurately define the fractal basin boundaries observed in the colour-coded diagrams. The development scenario of the fundamental vertical Lyapunov periodic orbit is thoroughly explored for obtaining a more complete view of the unfolding of the singular behaviour of the dynamics at the cusp values of the parameters. Finally, we examine how the combination of the most important parameters of the bar (such as the semi-major axis and the angular velocity) influences the observed stellar structures (rings and spirals) which are formed by escaping stars guided by the invariant manifolds near the saddle points.