Multipolar invariants and the eccentricity enhancement function parametrization of gravitational radiation

TL;DR

This paper advances the understanding of gravitational wave emission from hyperboliclike orbits by computing gauge-invariant multipolar invariants at 2.5PN order, incorporating tail effects, and introducing eccentricity enhancement functions.

Contribution

It introduces eccentricity enhancement functions for hyperboliclike motion and completes 2.5PN calculations of energy and angular momentum fluxes including tail effects.

Findings

Computed gauge-invariant multipolar invariants at 2.5PN order.

Expressed invariants in terms of eccentricity enhancement functions.

Analyzed adiabatic evolution of orbital elements under radiation reaction.

Abstract

Gravitational radiation can be decomposed as an infinite sum of radiative multipole moments, which parametrize the waveform at infinity. The multipolar-post-Minkowskian formalism provides a connection between these multipoles and the source multipole moments, known as explicit integrals over the matter source. The gravitational wave energy, angular momentum and linear momentum fluxes are then expressed as multipolar expansions containing certain combinations of the source moments. We compute several gauge-invariant quantities as "building blocks" entering the multipolar expansion of both radiated energy and angular momentum at the 2.5 post-Newtonian (PN) level of accuracy in the case of hyperboliclike motion, by completing previous studies through the calculation of tail effects up to the fractional 1PN order. We express such multipolar invariants in terms of certain eccentricity enhancement factor functions, which are the counterpart of the well known enhancement functions already introduced in the literature for ellipticlike motion. Finally, we use the complete 2.5PN-accurate averaged energy and angular momentum fluxes to study the associated adiabatic evolution of orbital elements under gravitational radiation reaction.