Length requirements for numerical-relativity waveforms

TL;DR

This paper determines the minimum length of numerical relativity waveforms needed to produce accurate hybrid gravitational wave signals for black-hole binaries, ensuring they meet detection accuracy standards.

Contribution

It provides specific length requirements for NR waveforms across different binary configurations to achieve less than 3% mismatch error in hybrid waveforms.

Findings

3 to 10 orbits needed before merger depending on binary parameters

Longer waveforms reduce PN error contribution in hybrids

Guidelines for waveform length improve gravitational wave detection accuracy

Abstract

One way to produce complete inspiral-merger-ringdown gravitational waveforms from black-hole-binary systems is to connect post-Newtonian (PN) and numerical-relativity (NR) results to create "hybrid" waveforms. Hybrid waveforms are central to the construction of some phenomenological models for GW search templates, and for tests of GW search pipelines. The dominant error source in hybrid waveforms arises from the PN contribution, and can be reduced by increasing the number of NR GW cycles that are included in the hybrid. Hybrid waveforms are considered sufficiently accurate for GW detection if their mismatch error is below 3% (i.e., a fitting factor about 0.97). We address the question of the length requirements of NR waveforms such that the final hybrid waveforms meet this requirement, considering nonspinning binaries with q = M_2/M_1 \in [1,4] and equal-mass binaries with \chi = S_i/M_i^2 \in [-0.5,0.5]. We conclude that for the cases we study simulations must contain between three (in the equal-mass nonspinning case) and ten (the \chi = 0.5 case) orbits before merger, but there is also evidence that these are the regions of parameter space for which the least number of cycles will be needed.