Higher-order tail contributions to the energy and angular momentum fluxes in a two-body scattering process

TL;DR

This paper calculates higher-order tail effects on energy and angular momentum fluxes in two-body scattering, enhancing gravitational wave models by including hereditary nonlinear contributions at the leading post-Newtonian order.

Contribution

It introduces the computation of tail-of-tail and tail-squared effects on fluxes for hyperbolic orbits within a multipolar-post-Minkowskian framework, advancing accuracy in gravitational wave templates.

Findings

Derived explicit formulas for tail contributions to fluxes.

Provided results in the Fourier domain for hyperbolic orbits.

Enhanced understanding of hereditary effects in gravitational wave emission.

Abstract

The need for more and more accurate gravitational wave templates requires taking into account all possible contributions to the emission of gravitational radiation from a binary system. Therefore, working within a multipolar-post-Minkowskian framework to describe the gravitational wave field in terms of the source multipole moments, the dominant instantaneous effects should be supplemented by hereditary contributions arising from nonlinear interactions between the multipoles. The latter effects are referred to as tails being described in terms of integrals depending on the past history of the source. We compute higher-order tail (i.e., tail-of-tail and tail-squared) contributions to both energy and angular momentum fluxes and their averaged values along hyperboliclike orbits at the leading post-Newtonian approximation, using harmonic coordinates and working in the Fourier domain. Due to the increasing level of accuracy recently achieved in the determination of the scattering angle in a two-body system by several complementary approaches, the knowledge of these terms will provide useful information to compare results from different formalisms.