Astronomy and Astrophysics – Astrophysics
Scientific paper
1994-04-15
Astronomy and Astrophysics
Astrophysics
43 pages, plain TeX file, figures available upon request from Best@sns.ias.edu. IAS number AST 94/12
Scientific paper
10.1086/175036
We develop a new formalism to study the dynamics of fluid polytropes in three dimensions. The stars are modeled as compressible ellipsoids and the hydrodynamic equations are reduced to a set of ordinary differential equations for the evolution of the principal axes and other global quantities. Both viscous dissipation and the gravitational radiation reaction are incorporated. We establish the validity of our approximations and demonstrate the simplicity and power of the method by rederiving a number of known results concerning the stability and dynamical oscillations of rapidly rotating polytropes. In particular, we present a generalization to compressible fluids of Chandrasekhar's classical results for the secular and dynamical instabilities of incompressible Maclaurin spheroids. We also present several applications of our method to astrophysical problems of great current interest such as the tidal disruption of a star by a massive black hole, the coalescence of compact binaries driven by the emission of gravitational waves, and the development of instabilities in close binary systems.
Lai Dong
Rasio Frederic A.
Shapiro Stuart L.
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