HYDRODYNAMIC INSTABILITY AND COALESCENCE OF CLOSE BINARY-SYSTEMS

Close binary systems in hydrostatic equilibrium can become unstable. The stability limit for circular orbits occurs at the orbital separation that simultaneously minimizes the total equilibrium energy and angular momentum in the system. The occurrence of such a minimum is a purely Newtonian hydrodynamic effect resulting from tidal interactions. Its existence is independent of the degree of synchronization, assuming alignment of spin and orbital angular momentum. The development of an instability can drastically affect the terminal evolution of coalescing binary systems. In particular, it can cause a rapid acceleration of the coalescence, such that the final merging takes place on a time scale much shorter than the energy dissipation time scale. For orbital decay by gravitational wave emission of a system containing two identical stars of mass m and radius R, the radial infall velocity at contact is given by v(r)/(Gm/R)1/2 approximately 10(-2)-10(-1) for 0 < Gm/(Rc2) < 0.1. Expressed as a fraction of the Keplerian orbital velocity at the stellar surface, the radial velocity approaches a finite limiting value as Gm/(RC2) --> 0.