Ellipsoidal Figures of Equilibrium: Compressible Models
Abstract
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 RiemannS ellipsoids) and to the stability of these single star configurations. The compressible generalizations of the Roche and RocheRiemann problems for a polytrope in orbit about a pointmass companion are solved, and the generalized Darwin problem for two identical polytropes in a binary is considered.
 Publication:

The Astrophysical Journal Supplement Series
 Pub Date:
 September 1993
 DOI:
 10.1086/191822
 Bibcode:
 1993ApJS...88..205L
 Keywords:

 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;
 Astrophysics;
 STARS: BINARIES: CLOSE;
 HYDRODYNAMICS;
 STARS: ROTATION