Hydrodynamics of Binary Coalescence.I. 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 $\gam > 5/3$, 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 {\em axisymmetric} merged configuration is always produced when $\gam\lo2.3$. As a consequence, the emission of gravitational radiation shuts off abruptly right after the onset of dynamical instability. In contrast, {\em triaxial\/} merged configurations are obtained when $\gam\go2.3$, and the system continues to emit gravitational waves after the final coalescence. Systems with mass ratios $q\ne1$ 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 $h_{max}$ and peak luminosity $L_{max}$ of the gravitational waves emitted during the final coalescence are nearly independent of $\gam$, but depend very sensitively on the mass ratio $q$.