Hydrodynamics of binary coalescence. 1: Polytropes with stiff equations of state

We have performed a series of three-dimensional hydrodynamic calculations of binary coalescence using the smoothed particle hydrodynamics (SPH) method. The initial conditions are exact polytropic equilibrium configurations with > 5/3, on the verge of dynamical instability. We calculate the emission of gravitational radiation in the quadrupole approximation. The fully nonlinear development of the instability is followed until a new equilibrium configuration is reached. We find that the properties of this final configuration depend sensitively on both the compressibility and mass ratio. An axisymmetric merged configuration is always produced when 2. 3. As a consequence, the emission of gravitational radiation shuts off abruptly right after the onset of dynamical instability. In contrast, triaxial\/ merged configurations are obtained when 2. 3, and the system continues to emit gravitational waves after the final coalescence. Systems with mass ratios q1 typically become dynamically unstable before the onset of mass transfer. Stable mass transfer from one neutron star to another in a close binary is therefore probably ruled out. The maximum amplitude h₌₀ₗ and peak luminosity L₌₀ₗ of the gravitational waves emitted during the final coalescence are nearly independent of, but depend very sensitively on the mass ratio q.