Post-Newtonian models of binary neutron stars

Using an energy variational method, we calculate quasiequilibrium configurations of binary neutron stars modeled as compressible triaxial ellipsoids obeying a polytropic equation of state. Our energy functional includes terms both for the internal hydrodynamics of the stars and for the external orbital motion. We add the leading post-Newtonian (PN) corrections to the internal and gravitational energies of the stars, and adopt hybrid orbital terms which are fully relativistic in the test-mass limit and always accurate to PN order. The total energy functional is varied to find quasiequilibrium sequences for both corotating and irrotational binaries in circular orbits. We examine how the orbital frequency at the innermost stable circular orbit depends on the polytropic index $n$ and the compactness parameter ${GM/Rc}^2$. We find that, for a given ${GM/Rc}^2$, the innermost stable circular orbit along an irrotational sequence is about 17% larger than the innermost secularly stable circular orbit along the corotating sequence when $n=0.5\mathrm{}$, and 20% larger when $n=1\mathrm{}$. We also examine the dependence of the maximum neutron star mass on the orbital frequency and find that, if PN tidal effects can be neglected, the maximum equilibrium mass increases as the orbital separation decreases.