Numerical study of synchronized binary neutron stars in the post-Newtonian approximation of general relativity

In order to investigate general relativistic effects on the hydrodynamic evolution of coalescing binary neutron stars (BNS’s) just before merging, we numerically calculate equilibrium sequences of BNS’s in synchronized circular orbits using the first post-Newtonian (PN) approximation of general relativity. The numerical solutions are obtained by solving the integral form of the Euler equation in the PN approximation for a uniformly rotating fluid, which was derived by Chandrasekhar. NS’s are modeled by means of the polytropic equation of state with the polytropic exponent $\Gamma =2\mathrm{}$, and the stiffness is adjusted using the polytropic constant $K$. From numerical calculations, we find that by the PN effect, the critical orbital radius $r_{\mathrm{crit}},$ where the hydrodynamic instability pointed out by Lai, Rasio, and Shapiro occurs, becomes smaller than the Newtonian result and as a result the corresponding angular frequency at $r_{\mathrm{crit}}$ is larger than that of the Newtonian binary.