Analytical Black-Hole Binary Merger Waveforms

Abstract

We present a highly accurate, fully analytical model for the late inspiral, merger, and ringdown of black-hole binaries with arbitrary mass ratios and spin vectors, including the contributions of harmonics beyond the fundamental mode. This model assumes only that nonlinear effects remain small throughout the entire coalescence, and is developed based on a physical understanding of the dynamics of late stage binary evolution, in particular on the tendency of the dynamical binary spacetime to behave like a linear perturbation of the static merger-remnant spacetime, even at times before the merger has occurred. We demonstrate that our model agrees with the most accurate numerical relativity results to within their own uncertainties throughout the merger-ringdown phase, and it does so for example cases spanning the full range of binary parameter space that is currently testable with numerical relativity. Furthermore, our model maintains accuracy back to the innermost stable circular orbit of the merger-remnant spacetime over much of the relevant parameter space, greatly decreasing the need to introduce phenomenological degrees of freedom to describe the late inspiral.