Success of the small mass-ratio approximation during the final orbits of binary black hole simulations

Recent studies have shown the surprising effectiveness of small mass-ratio approximation (SMR) in modeling relativistic two-body problem even at comparable masses. Up to now this has been demonstrated only during inspiral, before binary transitions into plunge and merger. Here we examine binding energy nonspinning black hole simulations with mass ratios from $20\ensuremath{\mathbin:}1$ equal mass. We show for first time that binaries undergo a transition as predicted by analytic theory, estimate size region, which is $\ensuremath{\sim}10$ gravitational wave cycles binaries. By including transition, SMR expansion accurate until last cycle emission. This true such those observed current detectors, where often makes up much signal. Our work provides further evidence can be directly applied observations.