Small-mass-ratio corrections to the binding energy during transition to plunge*

The small-mass-ratio (SMR) approximation describes binary motion by perturbing off geodesic motion. Originally developed to describe extreme-mass-ratio inspirals, comparisons to numerical simulations have shown that this approach is remarkably successful even for binaries with comparable masses. In the past these comparisons have been limited to the adiabatic inspiral phase. Here we extend these comparisons into the transition to plunge, which can last for many gravitational wave cycles before merger. By examining the binding energy in binary black hole simulations over a range of mass ratios, we find that the systems can be described by the leading SMR prediction for transition dynamics. We extract higher-order SMR corrections and demonstrate that a combination of inspiral and transition SMR models can describe the simulations up until a half cycle before merger, even at equal mass.