HYDRODYNAMIC INSTABILITY AND COALESCENCE OF BINARY NEUTRON-STARS

We study the importance of hydrodynamic effects on the evolution of co alescing binary neutron stars. Using an approximate energy functional constructed from equilibrium solutions for polytropic binary configura tions, we incorporate hydrodynamic effects into the calculation of the orbital decay driven by gravitational wave emission. In particular, w e follow the transition between the quasi-static, secular decay of the orbit at large separation and the rapid dynamical evolution of config urations approaching contact. We show that a purely Newtonian hydrodyn amic instability can significantly accelerate the coalescence at small separation. Such an instability occurs in all close binary configurat ions containing sufficiently incompressible stars. Calculations are pe rformed for various neutron star masses, radii, and spins. The influen ce of the stiffness of the equation of state is also explored by varyi ng the effective polytropic index. Typically, we fmd that the radial i nfall velocity just prior to contact is about 10% of the tangential or bital velocity. Once the stability limit is reached, the final evoluti on only takes another orbit. Post-Newtonian effects can move the stabi lity limit to a larger binary separation, and may induce an even large r radial velocity. We also consider the possibility of mass transfer f rom one neutron star to the other. We show that stable mass transfer i s unlikely except when the mass of one of the components is very small (M less than or similar to 0.4 M.) and the viscosity is high enough t o maintain corotation. Otherwise, either the two stars come into conta ct or the dynamical instability sets in before a Roche limit can be re ached.