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Title: A simple formula for the third integral of motion of disk-crossing stars in the galaxy

We present a simple analytical formula for an approximated third integral of motion associated with nearly equatorial orbits in the Galaxy: I{sub 3}=ZΣ{sub I}{sup 1/3}, where Z(R) is the vertical amplitude of the orbit at galactocentric distance R and Σ {sub I}(R) is the integrated dynamical surface mass density of the disk, a quantity which has recently become measurable. We also suggest that this relation is valid for disk-crossing orbits in a wide variety of axially symmetric galactic models, which range from razor-thin disks to disks with non-negligible thickness, whether or not the system includes bulges and halos. We apply our formalism to a Miyamoto-Nagai model and to a realistic model for the Milky Way. In both cases, the results provide fits for the shape of nearly equatorial orbits which are better than the corresponding curves obtained by the usual adiabatic approximation when the orbits have vertical amplitudes comparable to the disk's scale height. We also discuss the role of this approximate third integral of motion in modified theories of gravity.
Authors:
 [1] ;  [2]
  1. Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, 13083-859 Campinas, SP (Brazil)
  2. Departamento de Física, Universidade Federal de São Carlos, 13565-905 São Carlos, SP (Brazil)
Publication Date:
OSTI Identifier:
22357021
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 786; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ADIABATIC APPROXIMATION; AMPLITUDES; AXIAL SYMMETRY; COMPARATIVE EVALUATIONS; DENSITY; DISTANCE; GALAXIES; GRAVITATION; MASS; MILKY WAY; ORBITS; SCALE HEIGHT; STARS; SURFACES; THICKNESS