Adding gravitational memory to waveform catalogs using BMS balance laws

Abstract

Accurate models of gravitational waves from merging binary black holes are crucial for detectors to measure events and extract new science. One important feature that is currently missing from the Simulating eXtreme Spacetimes (SXS) Collaboration's catalog of waveforms for merging black holes, and other waveform catalogs, is the gravitational memory effect: a persistent, physical change to spacetime that is induced by the passage of transient radiation. We find, however, that by exploiting the Bondi-Metzner-Sachs (BMS) balance laws, which come from the extended BMS transformations, we can correct the strain waveforms in the SXS catalog to include the missing displacement memory. Our results show that these corrected waveforms satisfy the BMS balance laws to a much higher degree of accuracy. Furthermore, we find that these corrected strain waveforms coincide especially well with the waveforms obtained from Cauchy-characteristic extraction (CCE) that already exhibit memory effects. These corrected strain waveforms also evade the transient junk effects that are currently present in CCE waveforms. Lastly, we make our code for computing these contributions to the BMS balance laws and memory publicly available as a part of the python package sxs, thus enabling anyone to evaluate the expected memory effects and violation of the BMS balance laws.

Fixing the BMS frame of numerical relativity waveforms

“…Note that this convention differs from the related works of [18,19,25], which in contrast do not include the 1= ffiffi ffi 2 p normalization factor on the dyads in Eq. (6).…”

“…We denote the Weyl scalars by Ψ 0−4 . The conversion from the convention of [18,19,25] (denoted NR 8 ) to ours (denoted MB 9 ) is…”

“…6 Previously, the BMS freedom of numerical waveforms has not been important because the SXS Collaboration's waveforms did not exhibit the displacement memory [18]. However, because waveforms with memory effects can now easily be produced by numerical relativity [18] or can even have memory effects added to them via a correction [19], fixing this Bondi frame has become crucial, seeing as it is absolutely necessary for performing hybridizations between numerical and PN strain waveforms. We find that by mapping numerical waveforms to the PN BMS frame, we can significantly improve NR/PN strain hybridizations.…”

Eccentric binary black hole surrogate models for the gravitational waveform and remnant properties: Comparable mass, nonspinning case

“…Therefore, we model all nonzero l ≤ 3 and ð4; AE4Þ modes, except the m ¼ 0 modes. We exclude m ¼ 0 memory modes because (nonoscillatory) Christodoulou memory is not accumulated sufficiently in our NR simulations [82]; this defect was recently addressed in both Cauchy characteristic extraction (CCE) [83][84][85] and extrapolation [86] approaches. The (4,2) mode, on the other hand, was found to have significant numerical error in the extrapolation procedure [77,79].…”

Comparing remnant properties from horizon data and asymptotic data in numerical relativity

“…These systems all begin orbiting in the x − y plane. For further details, see [88]. The waveforms from these systems are made publicly available at [53].…”