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

We present the first attempt at calibrating the effective-one-body (EOB) model to accurate numerical relativity simulations of spinning, nonprecessing black-hole binaries. Aligning the EOB and numerical waveforms at low frequency over a time interval of $1000M$, we first estimate the phase and amplitude errors in the numerical waveforms and then minimize the difference between numerical and EOB waveforms by calibrating a handful of EOB-adjustable parameters. In the equal-mass, spin aligned case, we find that phase and fractional amplitude differences between the numerical and EOB $(2,2)$ mode can be reduced to 0.01 radian and 1%, respectively, over the entire inspiral waveforms. In the equal-mass, spin antialigned case, these differences can be reduced to 0.13 radian and 1% during inspiral and plunge, and to 0.4 radian and 10% during merger and ringdown. The waveform agreement is within numerical errors in the spin aligned case while slightly over numerical errors in the spin antialigned case. Using Enhanced LIGO and Advanced LIGO noise curves, we find that the overlap between the EOB and the numerical $(2,2)$ mode, maximized over the initial phase and time of arrival, is larger than 0.999 for binaries with total mass $30{M}_{\ensuremath{\bigodot}}--200{M}_{\ensuremath{\bigodot}}$. In addition to the leading $(2,2)$ mode, we compare four subleading modes. We find good amplitude and frequency agreements between the EOB and numerical modes for both spin configurations considered, except for the $(3,2)$ mode in the spin antialigned case. We believe that the larger difference in the $(3,2)$ mode is due to the lack of knowledge of post-Newtonian spin effects in the higher modes.