Integrability of motion around galactic razor-thin disks |
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| Authors: | Email author" target="_blank">Ronaldo?S?S?VieiraEmail author Javier?Ramos-Caro |
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| Institution: | 1.Instituto de Astronomia, Geofísica e Ciências Atmosféricas,Universidade de S?o Paulo,S?o Paulo,Brazil;2.Departamento de Física,Universidade Federal de S?o Carlos,S?o Carlos,Brazil |
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| 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 \(Z(R)\propto \varSigma (R)]^{-1/3}\), where R is the radial galactocentric coordinate, Z is the z-amplitude (vertical amplitude) of the orbit and \(\varSigma \) 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. |
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