2016/06/20 by Ronaldo S. S. Vieira, Javier Ramos-Caro
Physics and Astronomy · #astro-ph.GA #astro-ph.CO #nlin.CD
paper · pdf · doi:10.1007/s10569-016-9705-0
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
arxiv created 2016/06/20 · arxiv updated 2016/06/22
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)∝[Σ(R)]-1/3, where R is the radial galactocentric coordinate, Z is the z-amplitude (vertical amplitude) of the orbit and Σ 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.