New Avenue for Accurate Analytical Waveforms and Fluxes for Eccentric Compact Binaries

TL;DR

This paper presents a new method for constructing highly accurate analytical waveforms for eccentric compact binaries by combining Post-Newtonian techniques with effective-one-body resummation, validated against exact Kerr black hole solutions.

Contribution

It introduces a novel approach that retains implicit phase derivatives and uses EOB resummation, improving flux accuracy and convergence for eccentric binary waveforms.

Findings

40% improvement in angular momentum flux agreement using exact equations of motion

Achieves 4.5% fractional difference at high eccentricity and spin

Demonstrates convergence between Newtonian, 1PN, and 2PN results

Abstract

We introduce a new paradigm for constructing accurate analytic waveforms (and fluxes) for eccentric compact binaries. Our recipe builds on the standard Post-Newtonian (PN) approach but (i) retains implicit time-derivatives of the phase space variables in the instantaneous part of the noncircular waveform, and then (ii) suitably factorizes and resums this partly PN-implicit waveform using effective-one-body (EOB) procedures. We test our prescription against the exact results obtained by solving the Teukolsky equation with a test-mass source orbiting a Kerr black hole, and compare the use of the exact vs PN equations of motion for the time derivatives computation. Focusing only on the quadrupole contribution, we find that the use of the exact equations of motion yields an analytical/numerical agreement of the (averaged) angular momentum fluxes that is improved by $40\%$ with respect to previous work, with $4.5\%$ fractional difference for eccentricity $e=0.9$ and black hole dimensionless spin $-0.9\leq \hat{a}\leq +0.9$. We also find a remarkable convergence trend between Newtonian, 1PN and 2PN results. Our approach carries over to the comparable mass case using the resummed EOB equations of motion and paves the way to faithful EOB-based waveform model for long-inspiral eccentric binaries for current and future gravitational wave detectors.