Journal Article

Uniformly rotating homogeneous and polytropic rings in Newtonian gravity

David Petroff and Stefan Horatschek

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 389, issue 1, pages 156-172
Published in print September 2008 | ISSN: 0035-8711
Published online August 2008 | e-ISSN: 1365-2966 | DOI:
Uniformly rotating homogeneous and polytropic rings in Newtonian gravity

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An analytical method is presented for treating the problem of a uniformly rotating, self-gravitating ring without a central body in Newtonian gravity. The method is based on an expansion about the thin ring limit, where the cross-section of the ring tends to a circle. The iterative scheme developed here is applied to homogeneous rings up to the 20th order and to polytropes with the index n= 1 up to the third order. For other polytropic indices no analytic solutions are obtainable, but one can apply the method numerically. However, it is possible to derive a simple formula relating mass to the integrated pressure to leading order without specifying the equation of state. Our results are compared with those generated by highly accurate numerical methods to test their accuracy.

Keywords: equation of state; gravitation; hydrodynamics; methods: analytical; stars: rotation

Journal Article.  6457 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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