Estimating effective higher order terms in the post-Newtonian binding energy and gravitational-wave flux: Non-spinning compact binary inspiral

TL;DR

This paper estimates higher order post-Newtonian terms to improve gravitational wave template accuracy for non-spinning compact binary inspirals, achieving better agreement with numerical relativity models.

Contribution

It introduces effective higher order PN terms that enhance the agreement of multiple approximants with numerical relativity waveforms for non-spinning binaries.

Findings

PN approximants with effective higher order terms show significantly improved agreement with EOBNR.

Most approximants achieve over 99% faithfulness with EOBNR and each other.

Enhanced PN models are effective for component masses between 1.4 and 15 solar masses.

Abstract

In the adiabatic post-Newtonian (PN) approximation, the phase evolution of gravitational waves (GWs) from inspiralling compact binaries in quasicircular orbits is computed by equating the change in binding energy with the GW flux. This energy balance equation can be solved in different ways, which result in multiple approximants of the PN waveforms. Due to the poor convergence of the PN expansion, these approximants tend to differ from each other during the late inspiral. Which of these approximants should be chosen as templates for detection and parameter estimation of GWs from inspiraling compact binaries is not obvious. In this paper, we present estimates of the effective higher order (beyond the currently available 4PN and 3.5PN) non-spinning terms in the PN expansion of the binding energy and the GW flux that minimize the difference of multiple PN approximants (TaylorT1, TaylorT2, TaylorT4, TaylorF2) with effective one body waveforms calibrated to numerical relativity (EOBNR). We show that PN approximants constructed using the effective higher order terms show significantly better agreement (as compared to 3.5PN) with the inspiral part of the EOBNR. For non-spinning binaries with component masses $m_{1,2} \in [1.4 M_\odot, 15 M_\odot]$, most of the approximants have a match (faithfulness) of better than 99% with both EOBNR and each other.