Tail effects in the third post-Newtonian gravitational wave energy flux of compact binaries in quasi-elliptical orbits

TL;DR

This paper develops a semi-analytical frequency domain method to compute hereditary tail contributions to the 3PN gravitational wave energy flux from compact binaries in quasi-elliptical orbits, aiding gravitational wave detection.

Contribution

It introduces a novel semi-analytical approach to calculate tail effects at 3PN order for quasi-elliptical orbits, enhancing waveform modeling for gravitational wave detectors.

Findings

Method successfully computes tail contributions up to 3PN order.

Averages fluxes over orbital motion using quasi-Keplerian representation.

Provides essential inputs for gravitational wave template construction.

Abstract

The far-zone flux of energy contains hereditary (tail) contributions that depend on the entire past history of the source. Using the multipolar post-Minkowskian wave generation formalism, we propose and implement a semi-analytical method in the frequency domain to compute these contributions from the inspiral phase of a binary system of compact objects moving in quasi-elliptical orbits up to 3PN order. The method explicitly uses the quasi-Keplerian representation of elliptical orbits at 1PN order and exploits the doubly periodic nature of the motion to average the 3PN fluxes over the binary's orbit. Together with the instantaneous (non-tail) contributions evaluated in a companion paper, it provides crucial inputs for the construction of ready-to-use templates for compact binaries moving on quasi-elliptic orbits, an interesting class of sources for the ground based gravitational wave detectors such as LIGO and Virgo as well as space based detectors like LISA.