Post-Newtonian SPH calculations of binary neutron star coalescence. III. Irrotational systems and gravitational wave spectra

Gravitational wave (GW) signals from coalescing binary neutron stars may soon become detectable by laser-interferometer detectors. Using our new post-Newtonian (PN) smoothed particle hydrodynamics (SPH) code, we have studied numerically the mergers of neutron star binaries with irrotational initial configurations. These are the most physically realistic initial conditions just prior to merger, since the neutron stars in these systems are expected to be spinning slowly at large separation, and the viscosity of neutron star matter is too small for tidal synchronization to be effective at small separation. However, the large shear that develops during the merger makes irrotational systems particularly difficult to study numerically in 3D. In addition, in PN gravity, accurate irrotational initial conditions are much more difficult to construct numerically than corotating initial conditions. Here we describe a new method for constructing numerically accurate initial conditions for irrotational binary systems with circular orbits in PN gravity. We then compute the 3D hydrodynamic evolution of these systems until the two stars have completely merged, and we determine the corresponding GW signals. We present results for systems with different binary mass ratios, and for neutron stars represented by polytropes with $\Gamma =2\mathrm{}$ or $\Gamma =3.\mathrm{}$ Compared to mergers of corotating binaries, we find that irrotational binary mergers produce similar peak GW luminosities, but they shed almost no mass at all to large distances. The dependence of the GW signal on numerical resolution for calculations performed with $N\gtrsim {10}^5$ SPH particles is extremely weak, and we find excellent agreement between runs utilizing ${N=10\mathrm{}}^5$ and ${N=10\mathrm{}}^6$ SPH particles (the largest SPH calculation ever performed to study such irrotational binary mergers). We also compute GW energy spectra based on all calculations reported here and in our previous works. We find that PN effects lead to clearly identifiable features in the GW energy spectrum of binary neutron star mergers, which may yield important information about the nuclear equation of state at extreme densities.