Rapidly rotating spheroids of polytropic index N = 1

Details Rapidly rotating spheroids of polytropic index N = 1 Rapidly rotating spheroids of polytropic index N = 1

Jan 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977apj...211..568c&link_type=abstract

Astrophysical Journal, vol. 211, Jan. 15, 1977, pt. 1, p. 568-578.

Astronomy and Astrophysics

Astrophysics

1

Angular Velocity, Rotating Spheres, Spheroids, Stellar Rotation, Stellar Structure, Astrodynamics, Energy Dissipation, Indexes (Ratios), Kinetic Energy, Oblate Spheroids, Polytropic Processes, Stellar Envelopes, Stellar Gravitation

Scientific paper

The special case of a polytrope with an index of unity is considered on the assumption that the star's surface is precisely spheroidal. The system of linear equations giving the coefficients of gravitational and centrifugal potential expansions is derived in appropriate basis functions, and these coefficients alone are used to determine stellar structure. Exact analytical solutions are obtained for spherical stars, but only one solution is shown to be physically realistic. The system of equations is then solved for slowly rotating stars by a perturbation technique. The results indicate that spheroidal stars rotate nearly uniformly and that the amount of gravitational binding energy released when a rapidly rotating star slows down is comparable to the kinetic energy lost. The properties of highly oblate stars are determined numerically. In this case, it is found that differential rotation is minor, the release of binding energy can greatly exceed the kinetic-energy loss, the most highly oblate polytropes are not the most rapidly rotating ones, surfaces of constant density are approximately spheroidal, and the eccentricities of all such surfaces are nearly equal. The results also show that a highly oblate star is surrounded by a large diffuse envelope and has a greater central-to-mean density ratio than a nonrotating star.

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