Gravitational waves from inspiralling compact binaries: Energy loss and waveform to second--post-Newtonian order

TL;DR

This paper calculates the gravitational waveforms and energy loss for inspiralling compact binaries at the second-post-Newtonian order, providing detailed models crucial for gravitational wave detection.

Contribution

It introduces a 2PN-accurate waveform and energy loss formalism, including the computation of the source quadrupole moment and tail effects, enhancing modeling precision for gravitational wave signals.

Findings

Finite mass ratio effects significantly increase the 2PN phase contribution.

The 2PN waveform and energy loss are explicitly computed, including tail effects.

Results are applicable for improving gravitational wave data analysis for LIGO/VIRGO.

Abstract

Gravitational waves generated by inspiralling compact binaries are investigated to the second--post-Newtonian (2PN) approximation of general relativity. Using a recently developed 2PN-accurate wave generation formalism, we compute the gravitational waveform and associated energy loss rate from a binary system of point-masses moving on a quasi-circular orbit. The crucial new input is our computation of the 2PN-accurate ``source'' quadrupole moment of the binary. Tails in both the waveform and energy loss rate at infinity are explicitly computed. Gravitational radiation reaction effects on the orbital frequency and phase of the binary are deduced from the energy loss. In the limiting case of a very small mass ratio between the two bodies we recover the results obtained by black hole perturbation methods. We find that finite mass ratio effects are very significant as they increase the 2PN contribution to the phase by up to 52\%. The results of this paper should be of use when deciphering the signals observed by the future LIGO/VIRGO network of gravitational-wave detectors.