Approximate third integrals for axisymmetric potentials using local Stäckel fits |
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Authors: | V De Bruyne F Leeuwin H Dejonghe |
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Institution: | Astronomical Observatory, Gent University, Krijgslaan 281 S9, B-9000 Gent, Belgium |
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Abstract: | 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. |
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Keywords: | methods: analytical methods: numerical galaxies: elliptical and lenticular cD galaxies: kinematics and dynamics galaxies: structure |
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