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

TL;DR

This work derives the gravitational waveform and energy flux for inspiralling compact binaries at 2PN order for quasi-circular orbits using a 2PN generation formalism. It computes the complete 2PN mass quadrupole moment by including compact, nonlinear (Y), and cubically nonlinear (W) contributions, with tails accounted for in both waveform and luminosity. The tail integrals and the 2PN corrections to the phase are shown to be highly sensitive to the mass ratio, yielding up to a 52% increase in the 2PN phase relative to the test-mass limit, underscoring the importance of finite-mass-ratio effects for accurate LIGO/VIRGO templates. The results provide explicit, high-precision templates for the inspiral phase, enabling improved detection and parameter estimation of gravitational waves from compact binaries. These 2PN expressions form a foundational step toward robust, waveform-modeling pipelines for current and future gravitational-wave detectors.

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.