Journal Article

Analytical potential–density pairs for flat rings and toroidal structures

D. Vogt and P. S. Letelier

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 396, issue 3, pages 1487-1498
Published in print July 2009 | ISSN: 0035-8711
Published online June 2009 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2009.14803.x
Analytical potential–density pairs for flat rings and toroidal structures

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The Kuzmin–Toomre family of discs is used to construct potential–density pairs that represent flat ring structures in terms of elementary functions. Systems composed of two concentric flat rings, a central disc surrounded by one ring and a ring with a centre of attraction are also presented. The circular velocity of test particles and the epicyclic frequency of small oscillations about circular orbits are calculated for these structures. A few examples of three–dimensional potential–density pairs of ‘inflated’ flat rings (toroidal mass distributions) are presented.

Keywords: planets: rings; galaxies: kinematics and dynamics

Journal Article.  3726 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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