Gravitational waves from inspiralling compact binaries: Energy flux to third post-Newtonian order

TL;DR

This paper computes the third post-Newtonian order energy flux for gravitational waves from inspiralling compact binaries, including multipole moments and tail effects, with some parameters still undetermined due to regularization issues.

Contribution

It provides the first detailed 3PN order calculation of the energy flux, including multipole moments and tail effects, using the multipolar-post-Minkowskian approach.

Findings

Agreement with black hole perturbation results in the test-mass limit

Computed mass quadrupole to 3PN order, current quadrupole and mass octupole to 2PN order

Energy flux depends on one unknown physical parameter due to regularization limitations

Abstract

The multipolar-post-Minkowskian approach to gravitational radiation is applied to the problem of the generation of waves by the compact binary inspiral. We investigate specifically the third post-Newtonian (3PN) approximation in the total energy flux. The new results are the computation of the mass quadrupole moment of the binary to the 3PN order, and the current quadrupole and mass octupole to the 2PN order. Wave tails and tails of tails in the far zone are included up to the 3.5PN order. The recently derived 3PN equations of binary motion are used to compute the time-derivatives of the moments. We find perfect agreement to the 3.5PN order with perturbation calculations of black holes in the test-mass limit for one body. Technical inputs in our computation include a model of point particles for describing the compact objects, and the Hadamard self-field regularization. Because of a physical incompleteness of the Hadamard regularization at the 3PN order, the energy flux depends on one unknown physical parameter, which is a combination of a parameter \lambda in the equations of motion, and a new parameter \theta coming from the quadrupole moment.