Effective-one-body waveforms calibrated to numerical relativity simulations: Coalescence of nonspinning, equal-mass black holes

Abstract

We calibrate the effective-one-body (EOB) model to an accurate numerical simulation of an equal-mass, nonspinning binary black-hole coalescence produced by the Caltech-Cornell Collaboration. Aligning the EOB and numerical waveforms at low frequency over a time interval of $\ensuremath{\sim}1000M$, and taking into account the uncertainties in the numerical simulation, we investigate the significance and degeneracy of the EOB-adjustable parameters during inspiral, plunge, and merger, and determine the minimum number of EOB-adjustable parameters that achieves phase and amplitude agreements on the order of the numerical error. We find that phase and fractional amplitude differences between the numerical and EOB values of the dominant gravitational-wave mode ${h}_{22}$ can be reduced to 0.02 radians and 2%, respectively, until a time $20M$ before merger, and to 0.04 radians and 7%, respectively, at a time $20M$ after merger (during ringdown). Using LIGO, Enhanced LIGO, and Advanced LIGO noise curves, we find that the overlap between the EOB and the numerical ${h}_{22}$, maximized only over the initial phase and time of arrival, is larger than 0.999 for equal-mass binary black holes with total mass $30--150{M}_{\ensuremath{\bigodot}}$. In addition to the leading gravitational mode (2, 2), we compare the dominant subleading modes (4, 4) and (3, 2) for the inspiral and find phase and amplitude differences on the order of the numerical error. We also determine the mass-ratio dependence of one of the EOB-adjustable parameters by calibrating to numerical inspiral waveforms for black-hole binaries with mass ratios $2\ensuremath{\mathbin:}1$ and $3\ensuremath{\mathbin:}1$. The results presented in this paper improve and extend recent successful attempts aimed at providing gravitational-wave data analysts the best analytical EOB model capable of interpolating accurate numerical simulations.