Optimizing post-Newtonian parameters and fixing the BMS frame for numerical relativity waveform hybridizations

Numerical relativity (NR) simulations of binary black holes (BBH) provide precise waveforms, but are typically too computationally expensive to produce waveforms long enough to cover the whole frequency band of gravitational wave observatories. Consequently, it is important to be able to hybridize NR waveforms with analytic, post-Newtonian (PN) waveforms. We show that to build such hybrids, it is important to both optimize over the PN parameters as well as fix the Bondi-van~der~Burg-Metzner-Sachs (BMS) frame of the NR waveforms to match that of PN theory. With this procedure, we find that for spin-aligned systems, we can reduce the typical mismatches between NR and PN over 20-orbit-long waveforms to the error caused by non-zero eccentricities of NR systems, which is around e² ~10^-7. And for precessing systems, we can obtain typical mismatches of 10^-5, which are limited by the truncation of spin-asymmetric memory terms in PN waveforms at 2PN order.