Instability of Synchronized Binary Neutron Stars in the First Post-Newtonian Approximation of General Relativity

Abstract

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 equilib­ rium 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 r=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 .!krlt 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, Jhlt in the PN approximation is ~10-15 % larger than that in the Newtonian case for a NS of mass MADM~ 1.4 M. and radius rA ~ 10-15 km. The implication of this property to the orbital evolution of BNSs just before merging is discussed.