Gravitational-wave tails of tails

TL;DR

This paper investigates the nonlinear gravitational wave effects called tails of tails, which arise from curvature scattering of wave tails, and computes their contribution to gravitational wave signals up to 3.5PN order for binary inspirals.

Contribution

It provides the first detailed calculation of tails of tails at the 3PN order and their impact on gravitational wave energy flux for inspiraling binaries.

Findings

Tails of tails appear at 3PN order in gravitational wave signals.

The study quantifies the contribution of tails and tails of tails up to 3.5PN order.

Results improve the accuracy of gravitational wave templates for data analysis.

Abstract

The tails of gravitational waves are caused by scattering of linear waves onto the space-time curvature generated by the total mass-energy of the source. Quite naturally, the tails of tails are caused by curvature scattering of the tails of waves themselves. The tails of tails are associated with the cubic non-linear interaction between two mass monopole moments and, dominantly, the mass quadrupole of the source. In this paper we determine the radiation field at large distances from the source for this particular monopole-monopole-quadrupole interaction. We find that the tails of tails appear at the third post-Newtonian (3PN) order beyond the usual quadrupole radiation. Motivated by the need of accurate templates to be used in the data analysis of future detectors of gravitational waves, we compute the contribution of tails, and of tails of tails, up to the 3.5PN order in the energy flux generated by inspiraling compact binaries.