Reliability of complete gravitational waveform models for compact binary coalescences

TL;DR

This paper develops a new method to estimate the accuracy of hybrid gravitational waveforms for binary coalescences without needing existing numerical relativity data, showing that about 10 NR orbits suffice for most cases.

Contribution

It introduces an algorithm to evaluate hybrid waveform errors using equivalent PN models and common data, reducing reliance on existing NR simulations.

Findings

Approximately 10 NR orbits before merger are sufficient for accurate waveform models in most cases.

Nonspinning systems with high mass ratios are well modeled with these waveforms.

Parameter biases are around 1% for total mass and less than 0.1 for spin magnitude.

Abstract

With recent advances in post-Newtonian (PN) theory and numerical relativity (NR) it has become possible to construct inspiral-merger-ringdown waveforms by combining both descriptions into one hybrid signal. While addressing the reliability of such waveforms, previous studies have identified the PN contribution as the dominant source of error, which can be reduced by incorporating longer NR simulations. Here we overcome the two outstanding issues that make it difficult to determine the minimum NR simulation length necessary to produce suitably accurate hybrids: (1) the criteria for a GW search is the mismatch between the true waveform and a set of model waveforms, optimized over all waveforms in the model, but for discrete hybrids this optimization was not yet possible. (2) these calculations typically require that numerical waveforms already exist, while we develop an algorithm to estimate hybrid mismatches errors without numerical data. Our procedure relies on combining supposedly equivalent PN models at highest available order with common data in the NR regime, and their difference serves as a measure of the uncertainty assumed in each waveform. Contrary to some earlier studies, we estimate that ~10 NR orbits before merger should allow for the construction of waveform families that are accurate enough for detection in a broad range of parameters, only excluding highly spinning, unequal-mass systems. Nonspinning systems, even with high mass-ratio (q>=20) are well modeled for astrophysically reasonable component masses. The parameter bias is only of the order of 1% for total mass and symmetric mass-ratio and less than 0.1 for the dimensionless spin magnitude. We take the view that similar NR waveform lengths will remain the state of the art in the advanced detector era, and begin to assess the limits of the science that can be done with them.