Fixing the BMS Frame of Numerical Relativity Waveforms

TL;DR

This paper develops methods to analyze and align numerical relativity waveforms within the BMS frame, improving the accuracy of waveform modeling and hybridization for gravitational wave analysis.

Contribution

It introduces a general approach to map numerical waveforms to the BMS frame, including an improved center-of-mass correction and a method to find the optimal BMS transformation.

Findings

Current center-of-mass correction is less effective than previously thought.

An improved correction using asymptotic Poincaré charges is developed.

Waveforms mapped to the PN BMS frame hybridize more effectively with PN waveforms.

Abstract

Understanding the Bondi-Metzner-Sachs (BMS) frame of the gravitational waves produced by numerical relativity is crucial for ensuring that analyses on such waveforms are performed properly. It is also important that models are built from waveforms in the same BMS frame. Up until now, however, the BMS frame of numerical waveforms has not been thoroughly examined, largely because the necessary tools have not existed. In this paper, we show how to analyze and map to a suitable BMS frame for numerical waveforms calculated with the Spectral Einstein Code (SpEC). However, the methods and tools that we present are general and can be applied to any numerical waveforms. We present an extensive study of 13 binary black hole systems that broadly span parameter space. From these simulations, we extract the strain and also the Weyl scalars using both SpECTRE's Cauchy-characteristic extraction module and also the standard extrapolation procedure with a displacement memory correction applied during postprocessing. First, we show that the current center-of-mass correction used to map these waveforms to the center-of-mass frame is not as effective as previously thought. Consequently, we also develop an improved correction that utilizes asymptotic Poincar\'e charges instead of a Newtonian center-of-mass trajectory. Next, we map our waveforms to the post-Newtonian (PN) BMS frame using a PN strain waveform. This helps us find the unique BMS transformation that minimizes the $L^{2}$ norm of the difference between the numerical and PN strain waveforms during the early inspiral phase. We find that once the waveforms are mapped to the PN BMS frame, they can be hybridized with a PN strain waveform much more effectively than if one used any of the previous alignment schemes, which only utilize the Poincar\'e transformations.