Post-Newtonian diagnostic of quasiequilibrium binary configurations of compact objects

Abstract

Using equations of motion accurate to the third post-Newtonian (3PN) order $[{O(v/c)}^{6}$ beyond Newtonian gravity], we derive expressions for the total energy E and angular momentum J of the orbits of compact binary systems (black holes or neutron stars) for arbitrary orbital eccentricity. We also incorporate finite-size contributions such as spin-orbit and spin-spin coupling, and rotational and tidal distortions, calculated to the lowest order of approximation, but we exclude the effects of gravitational radiation damping. We describe how these formulas may be used as an accurate diagnostic of the physical content of quasiequilibrium configurations of compact binary systems of black holes and neutron stars generated using numerical relativity. As an example, we show that quasiequilibrium configurations of corotating neutron stars recently reported by Miller et al. can be fit by our diagnostic to better than one percent with a circular orbit and with physically reasonable tidal coefficients.