Fixing the BMS frame of numerical relativity 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-ofmass frame is not as effective as previously thought. Consequently, we also develop an improved correction that utilizes asymptotic Poincaré 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 Poincaré transformations.

The SpECTRE Cauchy-characteristic evolution system for rapid, precise waveform extraction

“…SpECTRE CCE has already begun to be used to extract valuable insights from gravitational wave data. The gains available from highly precise gravitational wave extraction and the rich data encoded in the Weyl scalars have enabled a number of valuable early investigations of waveform properties and BMS gauge transformations [29,54,66,67]. We anticipate that precise waveform extraction will play an important role in the gravitational wave modelling pipeline as next-generation ground-based and the near future space-based gravitational wave detectors will demand extremely high quality gravitational wave models [12].…”

“…The main remaining deficit in the accuracy of the waveforms determined by SpECTRE CCE is the initial-data transient near the beginning of every characteristic evolution. Without a better method to fix the CCE data on the first hypersurface, waveform data analysis methods are typically forced to discard the first ≈ 3 − 5 orbits of the resulting strain waveform, and to correct for the long-lived BMS frame shift following the initial data transient [54]. The BMS shift is primarily noticeable in the strain waveform, which displays a visually apparent offset during the inspiral.…”

Gyroscopic Gravitational Memory

“…The balance equations (10) will play an important role in section 4, allowing us to relate gyroscopic memory to angular momentum fluxes. We stress once more that the timedependence of news is arbitrary, unless a specific gravitational source has been chosen.…”

“…Remarkably, memory is a Newtonian addition to the oscillatory waveforms emitted by bounded gravitational sources [7]. As a result, the effect may realistically be quite large for binary systems [8][9][10], but its detection is hampered by the poor sensitivity of gravitational wave detectors at low frequencies. It is nevertheless conceivable that future experiments will be able to detect it: see e.g.…”

Gravitational-Wave Energy Flux for Compact Binaries through Second Order in the Mass Ratio

“…After further subtracting the 2SF fluxes we expect the residual to scale as ν 4 (shown as a solid red curve). For the (2,2)-mode the residual broadly follows the ν 4 trend, but the comparison is complicated by small oscillations in the NR waveform (likely from residual eccentricity and/or centre-of-mass motion in the NR simulation[40,41]). For the (3,3)-mode the residual is less subdominant and clearly follows the expected ν 4 behavior.…”