Compact binary waveform center-of-mass corrections

Abstract

We present a detailed study of the center-of-mass (c.m.) motion seen in simulations produced by the Simulating eXtreme Spacetimes (SXS) collaboration. We investigate potential physical sources for the large c.m. motion in binary black hole simulations and find that a significant fraction of the c.m. motion cannot be explained physically, thus concluding that it is largely a gauge effect. These large c.m. displacements cause mode mixing in the gravitational waveform, most easily recognized as amplitude oscillations caused by the dominant (2, ±2) modes mixing into subdominant modes. This mixing does not diminish with increasing distance from the source; it is present even in asymptotic waveforms, regardless of the method of data extraction. We describe the current c.m.-correction method used by the SXS collaboration, which is based on counteracting the motion of the c.m. as measured by the trajectories of the apparent horizons in the simulations, and investigate potential methods to improve that correction to the waveform. We also present a complementary method for computing an optimal c.m. correction or evaluating any other c.m. transformation based solely on the asymptotic waveform data.

The Poincaré and BMS flux-balance laws with application to binary systems

“…The consequences of the global super-Lorentz flux balance laws and their related spin and center-of-mass memory effects remain to be exploited for numerical simulations of compact binary mergers (see the latest SXS catalog [114] which can be analysed using tools defined in Bondi gauge [115]). The Poincaré flux-balance laws allow to deduce the final recoil and angular momentum [116] or allow to establish the balance of the center-ofmass [117]. The detectability of displacement, spin and center-of-mass memory effects has been partly analyzed but certainly deserves more attention, in particular for space-based gravitational wave observatories.…”

Intermediate Mass-Ratio Black Hole Binaries: Applicability of Small Mass-Ratio Perturbation Theory

“…Because of the use of spectral methods and a dual-frame approach [66], SpEC achieves very high accuracies even for long inspiral simulations that cover a comparatively large range in orbital frequencies. Gravitational radiation is extracted using the Regge-Wheeler-Zerilli formalism, extrapolated to future null infinity [27,67] and corrected for center of mass drifts [68].…”

Extending gravitational wave extraction using Weyl characteristic fields

“…While λ parametrizes the boost freedom of the tetrad, there is still a spin freedom on the choice of m a , for which we can see that m a ↦ e iΘ m a does not affect the normalization m am a ¼ s 0 . Therefore, we absorb this freedom, parametrized by 0 ≤ Θ < 2π, into the definition of m a , 3 The divergence of the Weyl tensor is properly sourced by the stress-energy tensor,…”

“…Part of this improvement must come from a systematic understanding of gauge effects inherent in the waveforms. Gauge effects in a waveform, if erroneously interpreted as physical effects, can have a direct and adverse impact on parameter estimation from a detected gravitational wave [2][3][4][5]. Both phenomenological and surrogate waveform models depend heavily on numerical relativity (NR) for their construction [6,7].…”

“…And because gauge conditions used in NR simulations are complicated and widely varied, we can expect to find significant effects in waveforms due to gauge choices. In addition to the standard time offset and rotation gauges, important effects due to boost and translation have already been found in numerical waveforms [2][3][4]11]. To move beyond this basic analysis-and to understand supertranslations-we need more information than is currently produced by most NR codes.…”