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arXiv · 0906.0919

Analytical Potential-Density Pairs for Flat Rings and Toroidal Structures

D. Vogt·P. S. Letelier
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Abstract

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.

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D. Vogt, P. S. Letelier. 2009-06-04. Analytical Potential-Density Pairs for Flat Rings and Toroidal Structures. https://doi.org/10.1111/j.1365-2966.2009.14803.x

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