Integrability of motion around galactic razor-thin disks

Abstract

We consider the three-dimensional bounded motion of a test particle around razor-thin disk configurations, by focusing on the adiabatic invariance of the vertical action associated with disk-crossing orbits. We find that it leads to an approximate third integral of motion predicting envelopes of the form $Z(R)\propto [\Sigma (R){]}^{-1/3}$, where $R$ is the radial galactocentric coordinate, $Z$ is the z-amplitude (vertical amplitude) of the orbit and $\Sigma$ represents the surface mass density of the thin disk. This third integral, which was previously formulated for the case of flattened 3D configurations, is tested for a variety of trajectories in different thin-disk models.

Version accepted for publication at Celestial Mechanics and Dynamical Astronomy. Replaces arxiv version arxiv:1206.6501. The final publication is available at Springer via http://dx.doi.org/10.1007/s10569-016-9705-0

References in corpus (8)

• Free motion around black holes with discs or rings: between integrability and chaos - II
• Free motion around black holes with discs or rings: between integrability and chaos - I
• Quasi integral of motion for axisymmetric potentials
• An Infinite Family of Generalized Kalnajs Disks
• An Infinite Family of Self-consistent Models for Axisymmetric Flat Galaxies
• Chaotic and regular motion around generalized Kalnajs discs
• Charged Annular Disks and Reissner-Nordström Type Black Holes from Extremal Dust
• On the stability of circular orbits in galactic dynamics: Newtonian thin disks

Cited by in corpus (9)

• Free motion around black holes with discs or rings: between integrability and chaos -- V
• Vertical stability of circular orbits in relativistic razor-thin disks
• Curvature dependence of relativistic epicyclic frequencies in static, axially symmetric spacetimes
• Self-gravitating razor-thin disks around black holes via multi-hole seeds
• Envelopes and vertical amplitudes of disk-crossing orbits
• Envelopes for orbits around axially symmetric sources with spheroidal shape
• Chaotic dynamics of pulsating spheres orbiting black holes
• Chaotic orbital dynamics of pulsating stars around black holes surrounded by dark matter halos
• Post-Newtonian Hamiltonian dynamics: applications to stationary spacetimes and statistical mechanics