Gravitational waves from inspiraling compact binaries: The quadrupole-moment term

TL;DR

The paper analyzes how the quadrupole moments of spinning compact objects in inspiraling binaries affect orbital dynamics and gravitational-wave phasing. It derives the quadrupole-monopole interaction contribution to the phasing parameter sigma, providing an explicit expression and showing it enters at order v^4 (a 2PN-like term), with magnitude comparable to spin-spin effects for realistic neutron stars and black holes. The authors quantify the resulting Newtonian orbital corrections and precession, and compute the gravitational-wave energy loss and frequency evolution to demonstrate the quadrupole effect as a measurable modulation of the waveform phase. These results inform high-precision waveform modeling for matched filtering in kilometer-scale detectors like LIGO and VIRGO.

Abstract

A rotating star's oblateness creates a deformation in the gravitational field outside the star, which is measured by the quadrupole-moment tensor. We consider the effect of the quadrupole moment on the orbital motion and rate of inspiral of a compact binary system, composed of neutron stars and/or black holes. We find that in the case of circular orbits, the quadrupole-monopole interaction affects the relation between orbital radius and angular velocity, and also the rate of inspiral, by a quantity of order (v/c)^4, where v is the orbital velocity and c the speed of light.