Envelopes and vertical amplitudes of disk-crossing orbits

Abstract

We recently found that regular orbits in axially symmetric galactic disks have their envelopes $Z(R)$ accurately described by the relation $Z(R)\propto [{\Sigma }_I(R){]}^{-1/3}$, if their amplitudes are comparable to the disk thickness, where ${\Sigma }_I$ is the surface density of the disk (integrated over its whole vertical range). Moreover, the usual adiabatic approximation gives a good description of the orbits' envelopes for low vertical amplitudes. However, these two approaches are apparently disconnected, since their expressions differ qualitatively. Our purpose in this paper is to fill this gap by extending these previous formulae to regular orbits with arbitrary vertical amplitudes inside the disk. We compare existing $Z(R)$ estimates: the razor-thin disk case, the adiabatic approximation (low-amplitude orbits in three-dimensional disks), and the integrated surface-density estimate (high-amplitude orbits in three-dimensional disks) in order to establish a connection between them. The formula presented here links the aforementioned results in an elegant and continuous way, being valid for vertical amplitudes throughout the whole vertical extension of the disk and with an expression which has the same form for all regimes. The advantage of the present formalism is the dependence of $Z(R)$ only on observable quantities, namely the disk's vertically integrated surface density, without the need to obtain the gravitational potential for the system.

arXiv comment7 pages, 3 figures. Accepted for publication in MNRAS

References in corpus (22)

• Gaia Data Release 2. Summary of the contents and survey properties
• Rotation Curves of Spiral Galaxies
• The Disruption of the Sagittarius Dwarf Galaxy.
• Actions for axisymmetric potentials
• Milky Way Mass Models for Orbit Calculations
• Distribution functions for the Milky Way
• Evidence for a Triaxial Milky Way Dark Matter Halo from the Sagittarius Stellar Tidal Stream
• Models of our Galaxy II
• Is the dark halo of our Galaxy spherical?
• Disassembling the Galaxy with angle-action coordinates
• More dynamical models of our Galaxy
• The Sagittarius Stream and Halo Triaxiality
• Angle-action estimation in a general axisymmetric potential
• Does the Sagittarius Stream constrain the Milky Way halo to be triaxial?
• Actions, angles and frequencies for numerically integrated orbits
• Galaxy rotation curves from General Relativity with Renormalization Group corrections
• Quasi integral of motion for axisymmetric potentials
• Models for the 3-D axisymmetric gravitational potential of the Milky Way Galaxy - A detailed modelling of the Galactic disk
• Chaotic and regular motion around generalized Kalnajs discs
• Approximate integrals of motion
• Integrability of motion around galactic razor-thin disks
• A simple formula for the third integral of motion of disk-crossing stars in the Galaxy

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