Uniformly Rotating Polytropic Rings in Newtonian Gravity

Abstract

An iterative method is presented for solving the problem of a uniformly rotating, self-gravitating ring without a central body in Newtonian gravity by expanding about the thin ring limit. Using this method, a simple formula relating mass to the integrated pressure is derived to the leading order for a general equation of state. For polytropes with the index n=1, analytic coefficients of the iterative approach are determined up to the third order. Analogous coefficients are computed numerically for other polytropes. Our solutions are compared with those generated by highly accurate numerical methods to test their accuracy.

10 pages, 8 figures, minor corrections, references added. This paper has be combined with arXiv:0802.0078 and published in MNRAS, see arXiv:0808.2612

References in corpus (6)

• Highly accurate calculation of rotating neutron stars: Detailed description of the numerical methods
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Cited by in corpus (7)

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• Pseudo-Newtonian Models for the Equilibrium Structures of Rotating Relativistic Stars
• Uniformly Rotating Homogeneous Rings in post-Newtonian Gravity
• The exterior gravitational potential of toroids
• A Roche Model for Uniformly Rotating Rings