Regular and chaotic orbits in axisymmetric stellar systems
Abstract
The gravitational potentials of realistic galaxy models are in general nonintegrable, in the sense that they admit orbits that do not have three independent isolating integrals of motion and are therefore chaotic. However, if chaotic orbits are a small minority in a stellar system, it is expected that they have negligible impact on the main dynamical properties of the system. In this paper, we address the question of quantifying the importance of chaotic orbits in a stellar system, focusing, for simplicity, on axisymmetric systems. Chaotic orbits have been found in essentially all (nonStäckel) axisymmetric gravitational potentials in which they have been looked for. Based on the analysis of the surfaces of section, we add new examples to those in the literature, finding chaotic orbits, as well as resonantly trapped orbits among regular orbits, in MiyamotoNagai, flattened logarithmic and shifted Plummer axisymmetric potentials. We define the fractional contributions in mass of chaotic (ξ_{c}) and resonantly trapped (ξ_{t}) orbits to a stellar system of given distribution function (DF), which are very useful quantities, for instance in the study of the dispersal of stellar streams of galaxy satellites. As a case study, we measure ξ_{c} and ξ_{t} in two axisymmetric stellar systems obtained by populating flattened logarithmic potentials with the Evans ergodic DF, finding ξ_{c} ~ 10^{4}  10^{3} and ξ_{t} ~ 10^{2}  10^{1}.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 January 2022
 DOI:
 10.1093/mnras/stab2693
 arXiv:
 arXiv:2109.07501
 Bibcode:
 2022MNRAS.509.1465P
 Keywords:

 chaos;
 methods: numerical;
 methods: statistical;
 celestial mechanics;
 galaxies: kinematics and dynamics;
 Astrophysics  Astrophysics of Galaxies
 EPrint:
 Accepted for publication in MNRAS. 15 pages, 11 figures