Inspiral-merger-ringdown multipolar waveforms of nonspinning black-hole binaries using the effective-one-body formalism

Abstract

We calibrate an effective-one-body (EOB) model to numerical-relativity simulations of mass ratios 1, 2, 3, 4, and 6, by maximizing phase and amplitude agreement of the leading (2, 2) mode and of the subleading modes (2, 1), (3, 3), (4, 4) and (5, 5). Aligning the calibrated EOB waveforms and the numerical waveforms at low frequency, the phase difference of the (2, 2) mode between model and numerical simulation remains below $\ensuremath{\sim}0.1$ rad throughout the evolution for all mass ratios considered. The fractional amplitude difference at peak amplitude of the (2, 2) mode is 2% and grows to 12% during the ringdown. Using the Advanced LIGO noise curve we study the effectualness and measurement accuracy of the EOB model, and stress the relevance of modeling the higher-order modes for parameter estimation. We find that the effectualness, measured by the mismatch between the EOB and numerical-relativity polarizations which include only the (2, 2) mode, is smaller than 0.2% for binaries with total mass $20--200{M}_{\ensuremath{\bigodot}}$ and mass ratios 1, 2, 3, 4, and 6. When numerical-relativity polarizations contain the strongest seven modes, and stellar-mass black holes with masses less than $50{M}_{\ensuremath{\bigodot}}$ are considered, the mismatch for mass ratio 6 (1) can be as high as 7% (0.2%) when only the EOB (2, 2) mode is included, and an upper bound of the mismatch is 0.5% (0.07%) when all the four subleading EOB modes calibrated in this paper are taken into account. For binaries with intermediate-mass black holes with masses greater than $50{M}_{\ensuremath{\bigodot}}$ the mismatches are larger. We also determine for which signal-to-noise ratios the EOB model developed here can be used to measure binary parameters with systematic biases smaller than statistical errors due to detector noise.