Post-Newtonian SPH calculations of binary neutron star coalescence: Methodand first results - art. no. 064012

We present the first results from our post-Newtonian (PN) smoothed particle hydrodynamics (SPH) code, which has been used to study the coalescence of binary neutron star (NS) systems. The Lagrangian particle-based code incorp orates consistently all lowest-order (1PN) relativistic effects, as well as gravitational radiation reaction; the lowest-order dissipative term in gen eral relativity. We test our code on sequences of single NS models of varyi ng compactness, and we discuss ways to make PN simulations more relevant to realistic NS models. We also present a PN SPH relaxation procedure for con structing equilibrium models of synchronized binaries, and we use these equ ilibrium models as initial conditions for our dynamical calculations of bin ary coalescence. Though unphysical, since tidal synchronization is not expe cted in NS binaries, these initial conditions allow us to compare our PN wo rk with previous Newtonian results. We compare calculations with and withou t 1PN effects, for NS with stiff equations of state, modeled as polytropes with Gamma = 3. We find that 1PN effects can play a major role in the coale scence, accelerating the final inspiral and causing a significant misalignm ent in the binary just prior to final merging. In addition, the character o f the gravitational wave signal is altered dramatically, showing strong mod ulation of the exponentially decaying wave form near the end of the merger. We also discuss briefly the implications of our results for models of gamm a-ray bursts at cosmological distances.