Instability of synchronized binary neutron stars in the first post-Newtonian approximation of general relativity

We investigate the stability property of binary neutron stars (BNSs) just before the merging in the first post-Newtonian(PN) approximation. Stability analysis is performed making use of equilibrium configurations for synchronized BNSs which are obtained by the numerical scheme developed in a previous paper. NSs are modeled by means of the polytropic equation of state with the polytropic exponent Gamma = 2 and 3. From numerical calculations, we find that as in the Newtonian case, in the PN approximation, the secular instability will occur for synchronized BNSs at a critical angular velocity Omega(crit) before the surfaces of the two stars come into contact. The PN correction changes not only the gravitational attraction force between two NSs, but also the configuration of each NS of a binary system. As a result, Omega(crit) in the PN approximation is similar to 10-15% larger than that in the Newtonian case for a NS of mass M(ADM)similar to 1.4 M(.) and radius gamma(A) similar to 10-15 km. The implication of this property to the orbital evolution of BNSs just before merging is discussed.