Coalescing neutron stars as gamma ray bursters?

We investigate the dynamics and evolution of coalescing neutron stars. The three-dimensional Newtonian equations of hydrodynamics are integrated by the “Piecewise Parabolic Method” on an equidistant Cartesian grid. The code is purely Newtonian, but does include the emission of gravitational waves and their back-reaction. The properties of neutron star matter are described by the equation of state of Lattimer and Swesty (1991). Energy loss by all types of neutrinos and changes of the electron fraction due to the emission of electron neutrinos and antineutrinos are taken into account by an elaborate “neutrino leakage scheme”. We simulate the coalescence of two identical, cool neutron stars with a baryonic mass of ≈ 1.6M⊙ and a radius of ≈ 15 km and with an initial center-to-center distance of 42 km. The initial distributions of density and electron concentration are given from a model of a cold neutron star in hydrostatic equilibrium. We investigate three cases which differ by the initial velocity distribution in the neutron stars. The orbit decays due to gravitational-wave emission and after one revolution the stars are so close that dynamical instability sets in. Within 1 ms the neutron stars merge into a rapidly spinning (P ≈ 1 ms), high-density body (ρ ≈ 1014 g/cm3) with a surrounding thick disk of material with densitiesρ ≈ 1010 − 1012 g/cm3 and orbital velocities of 0.3-0.5 c. The peak emission of gravitational waves has a maximum luminosity of a few times 1055 erg/s and is reached for about 1 ms. The amplitudes of the gravitational waves are close to 3 ⋅ 10−23 at a distance of 1 Gpc and the typical frequency is near the dynamical value of the orbital motion of the merging neutron stars of 2 KHz. In a post-processing step, the rate of neutrino-antineutrino annihilation is calculated from the neutrino luminosities generated during the hydrodynamical simulations. We find the integral annihilation rate to be a few 1050 erg/s during the phase of strongest neutrino emission, which is too small to generate the observed bursts considering the fact that the merged object of about 3M⊙ will most likely collapse to a black hole within milliseconds.