EQUILIBRIUM, STABILITY, AND ORBITAL EVOLUTION OF CLOSE BINARY-SYSTEMS

We present a new analytic study of the equilibrium and stability prope rties of close binary systems containing polytropic components. Our me thod is based on the use of ellipsoidal trial functions in an energy v ariational principle. We consider both synchronized and nonsynchronize d systems, constructing the compressible generalizations of the classi cal Darwin and Darwin-Riemann configurations. Our method can be applie d to a wide variety of binary models where the stellar masses, radii, spins, entropies, and polytropic indices are all allowed to vary over wide ranges and independently for each component. We find that both se cular and dynamical instabilities can develop before a Roche limit or contact is reached along a sequence of models with decreasing binary s eparation. High incompressibility always makes a given binary system m ore susceptible to these instabilities, but the dependence on the mass ratio is more complicated. As simple applications, we construct model s of double degenerate systems and of low-mass main-sequence star bina ries. We also discuss the orbital evolution of close binary systems un der the combined influence of fluid viscosity and secular angular mome ntum losses from processes like gravitational radiation. We show that the existence of global fluid instabilities can have a profound effect on the terminal evolution of coalescing binaries. The validity of our analytic solutions is examined by means of detailed comparisons with the results of recent numerical fluid calculations in three dimensions .