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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.