Unraveling the escape dynamics and the nature of the normally hyperbolic invariant manifolds in tidally limited star clusters

Abstract

The escape mechanism of orbits in a star cluster rotating around its parent galaxy in a circular orbit is investigated. A three degrees of freedom model is used for describing the dynamical properties of the Hamiltonian system. The gravitational field of the star cluster is represented by a smooth and spherically symmetric Plummer potential. We distinguish between ordered and chaotic orbits as well as between trapped and escaping orbits, considering only unbounded motion for several energy levels. The Smaller Alignment Index (SALI) method is used for determining the regular or chaotic nature of the orbits. The basins of escape are located and they are also correlated with the corresponding escape time of the orbits. Areas of bounded regular or chaotic motion and basins of escape were found to coexist in the $(x,z)$ plane. The properties of the normally hyperbolic invariant manifolds (NHIMs), located in the vicinity of the index-1 Lagrange points $L_1$ and $L_2$, are also explored. These manifolds are of paramount importance as they control the flow of stars over the saddle points, while they also trigger the formation of tidal tails observed in star clusters. Bifurcation diagrams of the Lyapunov periodic orbits as well as restrictions of the Poincaré map to the NHIMs are deployed for elucidating the dynamics in the neighbourhood of the saddle points. The extended tidal tails, or tidal arms, formed by stars with low velocity which escape through the Lagrange points are monitored. The numerical results of this work are also compared with previous related work.

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

References in corpus (34)

• Embedded Clusters in Molecular Clouds
• Detection of massive tidal tails around the globular cluster Pal 5 with SDSS commissioning data
• On the fraction of star formation occurring in bound stellar clusters
• The Spatial Distribution of Star Formation in the Solar Neighbourhood: Do all stars form in clusters?
• Galactic Kinematics of Cepheids from Hipparcos Proper Motions
• Globular Clusters with Tidal Tails: Deep Two-Color Star Counts
• The Time Scale of Escape from Star Clusters
• Modeling the disruption of the globular cluster Pal5 by Galactic tides
• The Discovery of Tidal Tails Around NGC 5466
• Scaling of N-body calculations
• Measuring Mass Loss Rates from Galactic Satellites
• On the structure of tidal tails
• Peculiarities in Velocity Dispersion and Surface Density Profiles of Star Clusters
• Quantitative analysis of clumps in the tidal tails of star clusters
• Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry
• Tidal tails around globular clusters. Are they a good tracer of cluster orbits?
• Mass Segregation in the Globular Cluster Palomar 5 and its Tidal Tails
• Formation and evolution of clumpy tidal tails around globular clusters
• Ejection velocities of high Galactic latitude runaway stars
• The dynamics of tidal tails from massive satellites
• The Tidal Tails of NGC 5466
• Metal-poor hypervelocity star candidates from the Sloan Digital Sky Survey
• Wide field CCD photometry of the globular cluster M92
• Where are the Old-Population High Velocity Stars?
• Bifurcations of transition states: Morse bifurcations
• Orbit classification in the meridional plane of a disk galaxy model with a spherical nucleus
• Escape from the vicinity of fractal basin boundaries of a star cluster
• Chaotic Dynamics in Multidimensional Transition States
• Revealing the escape mechanism of three-dimensional orbits in a tidally limited star cluster
• Effects of External Tidal Field on the Evolution of Multi-mass Star Clusters
• Orbital and escape dynamics in barred galaxies - II. The 3D system: Exploring the role of the normally hyperbolic invariant manifolds
• Introducing a new 3D dynamical model for barred galaxies
• Bifurcations of Normally Hyperbolic Invariant Manifolds and Consequences for Reaction Dynamics
• Comparing the escape dynamics in tidally limited star cluster models

Cited by in corpus (4)

• Orbit classification and networks of periodic orbits in the planar circular restricted five-body problem
• 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
• Transient chaos under coordinate transformations in relativistic systems