Coalescing binary systems of compact objects to (post)$^{5/2}-Newtonian order. V. Spin Effects

TL;DR

This paper investigates how spin-orbit and spin-spin interactions influence the gravitational waveforms from coalescing binary systems of compact objects, highlighting effects on orbital decay, waveform modulation, and amplitude.

Contribution

It introduces a detailed calculation of spin effects on gravitational waveforms using a formalism that includes spin contributions to multipole moments and orbital evolution.

Findings

Spins affect the orbital decay and phase of gravitational waves.

Spin-induced precession modulates the waveform shape.

Spin contributions alter the waveform amplitude.

Abstract

We examine the effects of spin-orbit and spin-spin coupling on the inspiral of a coalescing binary system of spinning compact objects and on the gravitational radiation emitted therefrom. Using a formalism developed by Blanchet, Damour, and Iyer, we calculate the contributions due to the spins of the bodies to the symmetric trace-free radiative multipole moments which are used to calculate the waveform, energy loss, and angular momentum loss from the inspiralling binary. Using equations of motion which include terms due to spin-orbit and spin-spin coupling, we evolve the orbit of a coalescing binary and use the orbit to calculate the emitted gravitational waveform. We find the spins of the bodies affect the waveform in several ways: 1) The spin terms contribute to the orbital decay of the binary, and thus to the accumulated phase of the gravitational waveform. 2) The spins cause the orbital plane to precess, which changes the orientation of the orbital plane with respect to an observer, thus causing the shape of the waveform to be modulated. 3) The spins contribute directly to the amplitude of the waveform. We discuss the size and importance of spin effects for the case of two coalescing neutron stars, and for the case of a neutron star orbiting a rapidly rotating $10M_\odot$ black hole.