Open AccessApproximate third integrals for axisymmetric potentials using local Stäckel fits
Author(s) -
De Bruyne V.,
Leeuwin F.,
Dejonghe H.
Publication year - 2000
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.2000.03056.x
Subject(s) - physics , rotational symmetry , ellipsoid , simple (philosophy) , set (abstract data type) , classical mechanics , mathematical analysis , mechanics , mathematics , philosophy , epistemology , astronomy , computer science , programming language
We use a set of Stäckel 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 apply it to three trial potentials of various flattenings, corresponding to nearly ellipsoidal, discy and boxy density isophotes. In all three cases, a good fit to the potential requires only a small set of Stäckel potentials, and the associated Stäckel third integral provides a very satisfactory, yet analytically simple, approximation to the trial potentials effective third integral.