Gauss's method for secular dynamics, softened |
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Authors: | J. R. Touma S. Tremaine M. V. Kazandjian |
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Affiliation: | Department of Physics, American University of Beirut, PO Box 11-0236, Riad El-Solh, Beirut 11097 2020, Lebanon;School of Natural Sciences, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA |
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Abstract: | We show that the algorithm proposed by Gauss to compute the secular evolution of gravitationally interacting Keplerian rings extends naturally to softened gravitational interactions. The resulting tool is ideal for the study of the secular dynamical evolution of nearly Keplerian systems such as stellar clusters surrounding black holes in galactic nuclei, cometary clouds or planetesimal discs. We illustrate its accuracy, efficiency and versatility on a variety of configurations. In particular, we examine a secularly unstable system of counterrotating discs, and follow the unfolding and saturation of the instability into a global, uniformly precessing, lopsided ( m = 1) mode. |
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Keywords: | stellar dynamics celestial mechanics galaxies: kinematics and dynamics galaxies: nuclei |
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