Suitability of post-Newtonian/numerical-relativity hybrid waveforms for gravitational wave detectors

TL;DR

This study assesses the accuracy requirements for hybrid gravitational waveforms combining post-Newtonian and numerical relativity methods, crucial for precise parameter estimation in advanced detectors, highlighting the need for high alignment accuracy.

Contribution

It provides a detailed error analysis for hybrid waveforms, establishing stringent accuracy criteria for phase alignment and waveform modeling in gravitational wave data analysis.

Findings

Phase alignment must be accurate to 1/100 of a cycle.

Numerical relativity phase errors should be less than 0.1 rad.

Inaccuracies in post-Newtonian approximants dominate errors.

Abstract

This article presents a study of the sufficient accuracy of post-Newtonian and numerical relativity waveforms for the most demanding usage case: parameter estimation of strong sources in advanced gravitational wave detectors. For black hole binaries, these detectors require accurate waveform models which can be constructed by fusing an analytical post-Newtonian inspiral waveform with a numerical relativity merger-ringdown waveform. We perform a comprehensive analysis of errors that enter such "hybrid waveforms". We find that the post-Newtonian waveform must be aligned with the numerical relativity waveform to exquisite accuracy, about 1/100 of a gravitational wave cycle. Phase errors in the inspiral phase of the numerical relativity simulation must be controlled to less than about 0.1rad. (These numbers apply to moderately optimistic estimates about the number of GW sources; exceptionally strong signals require even smaller errors.) The dominant source of error arises from the inaccuracy of the investigated post-Newtonian Taylor-approximants. Using our error criterium, even at 3.5-th post-Newtonian order, hybridization has to be performed significantly before the start of the longest currently available numerical waveforms which cover 30 gravitational wave cycles. The current investigation is limited to the equal-mass, zero-spin case and does not take into account calibration errors of the gravitational wave detectors.