Journal Article

Gauss's method for secular dynamics, softened

J. R. Touma, S. Tremaine and M. V. Kazandjian

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 394, issue 2, pages 1085-1108
Published in print April 2009 | ISSN: 0035-8711
Published online March 2009 | e-ISSN: 1365-2966 | DOI:
Gauss's method for secular dynamics, softened

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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.

Keywords: stellar dynamics; celestial mechanics; galaxies: kinematics and dynamics; galaxies: nuclei

Journal Article.  11595 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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