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

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.

On the spatial collinear restricted four-body problem with non-spherical primaries

“…Zotos (2015c), the author has compared the orbital dynamics in three models which describe the various properties of a star cluster which rotates in a circular orbit around its parent galaxy. Moreover, Zotos and Jung (2018) have discussed the orbit and escape dynamics in barred galaxies and illustrated the basins of escape linked to the escape through the escape channels in the vicinity of the libration points L 2,3 which are symmetrical in nature and further established the relation with the corresponding distribution of the escape times of the orbits. In , the motion of the test particle in a non-spinning binary black hole system is investigated numerically when the masses are equal.…”