Volume 581, September 2015
|Number of page(s)||9|
|Section||Galactic structure, stellar clusters and populations|
|Published online||21 September 2015|
Quasi integral of motion for axisymmetric potentials
Observatoire astronomique de Strasbourg, Université de Strasbourg, CNRS,
UMR 7550, 11 rue de l’Université,
2 Institut Utinam, CNRS UMR 6213, Université de Franche-Comté, OSU THETA Franche-Comté-Bourgogne, Observatoire de Besançon, BP 1615, 25010 Besançon Cedex, France
Received: 12 May 2015
Accepted: 20 July 2015
We present an estimate of the third integral of motion for axisymmetric three-dimensional potentials. This estimate is based on a Stäckel approximation and is explicitly written as a function of the potential. We tested this scheme for the Besançon Galactic model and two other disc-halo models and find that orbits of disc stars have an accurately conserved third quasi integral. The accuracy ranges from of 0.1% to 1% for heights varying from z = 0 kpc to z = 6 kpc and Galactocentric radii R from 5 to 15 kpc. We also tested the usefulness of this quasi integral in analytic distribution functions of disc stellar populations: we show that the distribution function remains approximately stationary and that it allows to recover the potential and forces by applying Jeans equations to its moments.
Key words: methods: numerical / Galaxy: kinematics and dynamics
© ESO, 2015
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