Faithful effective-one-body waveforms of small-mass-ratio coalescing black hole binaries

Abstract

We address the problem of constructing high-accuracy, faithful analytic waveforms describing the gravitational wave signal emitted by inspiralling and coalescing binary black holes. We work within the effective-one-body (EOB) framework and propose a methodology for improving the current (waveform) implementations of this framework based on understanding, element by element, the physics behind each feature of the waveform and on systematically comparing various EOB-based waveforms with exact waveforms obtained by numerical relativity approaches. The present paper focuses on small-mass-ratio nonspinning binary systems, which can be conveniently studied by Regge-Wheeler-Zerilli-type methods. Our results include (i) a resummed, 3 PN-accurate description of the inspiral waveform, (ii) a better description of radiation reaction during the plunge, (iii) a refined analytic expression for the plunge waveform, (iv) an improved treatment of the matching between the plunge and ring-down waveforms. This improved implementation of the EOB approach allows us to construct complete analytic waveforms which exhibit a remarkable agreement with the exact ones in modulus, frequency, and phase. In particular, the analytic and numerical waveforms stay in phase, during the whole process, within $\ifmmode\pm\else\textpm\fi{}1.1%$ of a cycle. We expect that the extension of our methodology to the comparable-mass case will be able to generate comparably accurate analytic waveforms of direct use for the ground-based network of interferometric detectors of gravitational waves.