Large-Eccentricity Asymptotics and Fast Analytic Approximation for Fourier modes of Post-Newtonian Eccentric Waveforms

TL;DR

This paper introduces analytic asymptotic methods and a fast approximation for Fourier modes of gravitational waves from highly eccentric binary systems, improving computational efficiency and accuracy.

Contribution

It develops new asymptotic techniques and an endpoint-constrained approximation for Fourier modes in high eccentricity regimes, enhancing modeling of gravitational waves.

Findings

Achieved an approximation error within 10^{-3} for modes with p ≤ 200.

Provided analytic tools for frequency-domain gravitational wave modeling.

Accelerated computation of Fourier modes at large eccentricity.

Abstract

In this work, we developed analytic asymptotic methods for computing the Fourier modes of gravitational waves from post-Newtonian binary systems in the quasi-Keplerian parametrization in the high eccentricity regime. We have also derived the large-eccentricity asymptotic expansion of the eccentricity enhancement function appearing in the tail contributions to the radiation. Furthermore, based on these results, we constructed an endpoint-constrained analytic approximation that significantly accelerate the computation of the Fourier modes at large eccentricity.The overall error of this analytic approximation is controlled within $10^{-3}$, and it remains valid for Fourier modes with $p\le200$. This approach provides an analytic building blocks for modeling frequency-domain gravitational wave from highly eccentric binaries.