General Fourier expansion of post-Newtonian binary dynamics based on a quasi-Keplerian framework

TL;DR

This paper introduces a new Fourier expansion method for post-Newtonian binary dynamics, enabling precise gravitational-wave calculations and compact tail flux expressions, advancing frequency-domain waveform modeling.

Contribution

A novel systematic Fourier expansion approach for post-Newtonian binary dynamics, including derivation of 3PN quantities and open-source numerical code.

Findings

Derived full 3PN dynamical quantities and Fourier modes.

Resummed tail contributions into compact expressions.

Provided open-source code for practical calculations.

Abstract

We have introduced a new method for computing gravitational-wave emission from nonspinning binaries which systematically unifies the various integrals arising in the Fourier expansions of post-Newtonian dynamics, providing a simple, practical scheme for calculations at arbitrary precision. Using this approach, we derived the full set of 3PN dynamical quantities and gravitational-wave Fourier modes and have released the corresponding numerical code as open source. Furthermore, when radiation-reaction effects is not included, we found that the tail contribution to the energy and angular momentum fluxes can be resummed into an exceptionally compact expression with the help of the new method. These advances pave the way for more convenient and accurate frequency-domain waveform modeling in the future.