Accuracy limitations of existing numerical relativity waveforms on the data analysis of current and future ground-based detectors

TL;DR

As gravitational wave detectors improve, the paper assesses how finite grid resolution errors in numerical relativity waveforms affect parameter estimation, finding current models are adequate for some binaries but insufficient for high mass ratio cases in future detectors.

Contribution

The paper isolates the impact of finite grid resolution errors on waveform accuracy and introduces a measure to predict necessary resolution for unbiased parameter estimation.

Findings

Current waveforms are accurate for equal and moderately unequal mass binaries.

High mass ratio binaries require higher resolution for unbiased parameter estimation.

Existing waveforms may be inadequate for future detectors with high signal-to-noise ratios.

Abstract

As gravitational wave detectors improve in sensitivity, signal-to-noise ratios of compact binary coalescences will dramatically increase, reaching values in the hundreds and potentially thousands. Such strong signals offer both exciting scientific opportunities and pose formidable challenges to the template waveforms used for interpretation. Current waveform models are informed by calibrating or fitting to numerical relativity waveforms and such strong signals may unveil computational errors in generating these waveforms. In this paper, we isolate a single source of computational error, that of the finite grid resolution, and investigate its impact on parameter estimation for aLIGO and Cosmic Explorer. We demonstrate that increasing the inclination angle or decreasing the mass ratio $q$ ($q \leq 1 $) raises the resolution required for unbiased parameter estimation. We quantify the error associated with the highest-resolution waveform utilized in our study using an extrapolation procedure on the median of recovered posteriors and confirm the accuracy of current waveforms for the synthetic sources. We introduce a measure to predict the necessary numerical resolution for unbiased parameter estimation and use it to predict that current waveforms are suitable for equal and moderately unequal mass binaries for both detectors. However, current waveforms fail to meet accuracy requirements for high signal-to-noise ratio signals from highly unequal mass ratio binaries $(q \lesssim 1/6)$, for all inclinations in Cosmic Explorer, and for high inclinations in future updates to LIGO. Given that the resolution requirement becomes more stringent with more unequal mass ratios, current waveforms may lack the necessary accuracy, even at median signal-to-noise ratios for future detectors.