Analytical Potential-Density Pairs for Flat Rings and Toroidal Structures

Details Analytical Potential-Density Pairs for Flat Rings and Toroidal Structures Analytical Potential-Density Pairs for Flat Rings and Toroidal Structures

2009-06-04

arxiv.org/abs/0906.0919v1

MNRAS, 396, 1487 (2009)

Astronomy and Astrophysics

Astrophysics

Galaxy Astrophysics

25 pages, 11 figures, accepted for publication in MNRAS

Scientific paper

10.1111/j.1365-2966.2009.14803.x

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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