Compact Binary Waveform Center-of-Mass Corrections

Abstract

We present a detailed study of the center-of-mass (COM) motion seen in simulations produced by the Simulating eXtreme Spacetimes (SXS) collaboration. We investigate potential physical sources for the large COM motion in binary black hole (BBH) simulations and find that a significant fraction of the COM motion cannot be explained physically, thus concluding that it is largely a gauge effect. These large COM displacements cause mode mixing in the gravitational waveform, most easily recognized as amplitude oscillations caused by the dominant (2,$\pm$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 COM-correction method used by the SXS collaboration, which is based on counteracting the motion of the COM 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 COM correction or evaluating any other COM transformation based solely on the asymptotic waveform data