Orbital and escape dynamics in barred galaxies - II. The 3D system: Exploring the role of the normally hyperbolic invariant manifolds

Abstract

A three degrees of freedom (3-dof) barred galaxy model composed of a spherically symmetric nucleus, a bar, a flat disc and a spherically symmetric dark matter halo is used for investigating the dynamics of the system. We use colour-coded plots to demonstrate how the value of the semi-major axis of the bar influences the regular or chaotic dynamics of the 3-dof system. For distinguishing between ordered and chaotic motion we use the Smaller ALingment Index (SALI) method, a fast yet very accurate tool. Undoubtedly, the most important elements of the dynamics are the normally hyperbolic invariant manifolds (NHIMs) located in the vicinity of the index 1 Lagrange points $L_2$ and $L_3$. These manifolds direct the flow of stars over the saddle points, while they also trigger the formation of rings and spirals. The dynamics in the neighbourhood of the saddle points is visualized by bifurcation diagrams of the Lyapunov orbits as well as by the restriction of the Poincaré map to the NHIMs. In addition, we reveal how the semi-major axis of the bar influences the structure of these manifolds which determine the final stellar structure (rings or spirals). Our numerical simulations suggest that in galaxies with weak bars the formation of $R_1$ rings or $R_1^{\prime }$ pseudo-rings is favoured. In the case of galaxies with intermediate and strong bars the invariant manifolds seem to give rise to $R_1{R}_2$ rings and twin spiral formations, respectively. We also compare our numerical outcomes with earlier related work and with observational data.

arXiv commentPublished in Monthly Notices of the Royal Astronomical Society (MNRAS) journal

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• Orbit classification and networks of periodic orbits in the planar circular restricted five-body problem
• Geometry of escape and transition dynamics in the presence of dissipative and gyroscopic forces in two degree of freedom systems
• Galactic resonance rings. Modelling of motions in the wide solar neighborhood
• Unraveling the escape dynamics and the nature of the normally hyperbolic invariant manifolds in tidally limited star clusters
• Orbital and escape dynamics in barred galaxies - III. The 3D system: Correlations between the basins of escape and the NHIMs
• Correlating the escape dynamics and the role of the normally hyperbolic invariant manifolds in a binary system of dwarf spheroidal galaxies
• Orbit classification in the Hill problem: I. The classical case
• Orbital and escape dynamics in barred galaxies -- IV. Heteroclinic connections