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

TL;DR

This paper investigates how the quadrupole moment of rotating stars influences the orbital dynamics and inspiral rate of compact binary systems, with implications for gravitational wave signals.

Contribution

It introduces the effect of the quadrupole moment on binary inspiral dynamics, extending previous models to include stellar oblateness impacts.

Findings

Quadrupole-monopole interaction affects orbital radius and angular velocity relations.

The influence on inspiral rate is of order (v/c)^4.

Results are relevant for gravitational wave signal modeling.

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.