Ellipsoidal figures of equilibrium - Compressible models

Details Ellipsoidal figures of equilibrium - Compressible models Ellipsoidal figures of equilibrium - Compressible models

Sep 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993apjs...88..205l&link_type=abstract

Astrophysical Journal Supplement Series (ISSN 0067-0049), vol. 88, no. 1, p. 205-252.

Astronomy and Astrophysics

Astrophysics

165

Binary Stars, Compressible Fluids, Computerized Simulation, Dynamic Stability, Ellipsoids, Newtonian Fluids, Stellar Models, Stellar Rotation, Calculus Of Variations, Ejection, Hydrodynamics, Roche Limit, Rotating Fluids, Virial Coefficients

Scientific paper

The results of Chandrasekhar (1969) are generalized to polytropes, using a formalism based on ellipsoidal energy variational principle to construct approximate stellar equilibrium solutions and study their stability. After reviewing the energy variational method and describing the approach, several equivalent stability conditions are established and secular vs. dynamical instabilities are discussed. Then, the equilibrium structure equations are derived for isolated, rotating polytropes, and axisymmetric configurations (compressible Maclaurin spheroids) are considered. Particular attention is given to triaxial configurations, either in a state of uniform rotation (generalizing the classical Jacobi ellipsoids) or with internal fluid motions of uniform vorticity (the compressible analogues of Riemann-S ellipsoids) and to the stability of these single star configurations. The compressible generalizations of the Roche and Roche-Riemann problems for a polytrope in orbit about a point-mass companion are solved, and the generalized Darwin problem for two identical polytropes in a binary is considered.

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