Enriching the symphony of gravitational waves from binary black holes by tuning higher harmonics

For the first time, we construct an inspiral-merger-ringdown waveform model within the effective-one-body formalism for spinning, nonprecessing binary black holes that includes gravitational modes beyond the dominant $(\ensuremath{\ell},|m|)=(2,2)$ mode, specifically $(\ensuremath{\ell},|m|)=(2,1),(3,3),(4,4),(5,5)$. Our multipolar waveform model incorporates recent (resummed) post-Newtonian results for the inspiral and information from 157 numerical-relativity simulations, and 13 waveforms from black-hole perturbation theory for the (plunge-)merger and ringdown. We quantify the improvement in accuracy when including higher-order modes by computing the faithfulness of the waveform model against the numerical-relativity waveforms used to construct the model. We define the faithfulness as the match maximized over time, phase of arrival, gravitational-wave polarization and sky position of the waveform model, and averaged over binary orientation, gravitational-wave polarization and sky position of the numerical-relativity waveform. When the waveform model contains only the (2,2) mode, we find that the averaged faithfulness to numerical-relativity waveforms containing all modes with $\ensuremath{\ell}\ensuremath{\le}5$ ranges from 90% to 99.9% for binaries with total mass $20--200\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ (using the Advanced LIGO's design noise curve). By contrast, when the (2,1), (3,3), (4,4), (5,5) modes are also included in the model, the faithfulness improves to 99% for all but four configurations in the numerical-relativity catalog, for which the faithfulness is greater than 98.5%. Starting from the complete inspiral-merger-ringdown model, we develop also a (stand-alone) waveform model for the merger-ringdown signal, calibrated to numerical-relativity waveforms, which can be used to measure multiple quasi-normal modes. The multipolar waveform model can be extended to include spin-precessional effects, and will be employed in upcoming observing runs of Advanced LIGO and Virgo.