A Post-Newtonian diagnostic of quasi-equilibrium binary configurations of compact objects

TL;DR

This paper develops third post-Newtonian order expressions for energy and angular momentum of compact binary systems, including finite-size effects, to diagnose quasi-equilibrium configurations in numerical relativity.

Contribution

It provides a new diagnostic framework using 3PN equations to analyze quasi-equilibrium binary configurations, incorporating finite-size effects and excluding gravitational radiation damping.

Findings

Accurately fits neutron star configurations with less than 1% error

Includes finite-size effects like spin and tidal distortions at lowest order

Offers a practical tool for analyzing numerical relativity data

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 formulae may be used as an accurate diagnostic of the physical content of quasi-equilibrium configurations of compact binary systems of black holes and neutron stars generated using numerical relativity. As an example, we show that quasi-equilibrium configurations of corotating neutron stars recently reported by Miller et al. can be fit by our diagnostic to better than one per cent with a circular orbit and with physically reasonable tidal coefficients.