Approximate third integrals for axisymmetric potentials using local Stackel fits

Details Approximate third integrals for axisymmetric potentials using local Stackel fits Approximate third integrals for axisymmetric potentials using local Stackel fits

1999-09-28

arxiv.org/abs/astro-ph/9909462v1

Astronomy and Astrophysics

Astrophysics

11 pages, 12 figures, accepted for publication in MNRAS

Scientific paper

10.1046/j.1365-8711.2000.03056.x

We use a set of Stackel potentials to obtain a local approximation for an effective third integral in axisymmetric systems. We present a study on the feasibility and effectiveness of this approach. We have applied it to three trial potentials of various flattenings, corresponding to nearly ellipsoidal, disky and boxy density isophotes. In all three cases, a good fit to the potential requires only a small set of Stackel potentials, and the associated Stackel third integral provides a very satisfactory, yet analytically simple, approximation to the trial potentials effective third integral.

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