要旨
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 $(\ell,|m|) =
(2,2)$ mode, specifically $(\ell,|m|)=(2,1),(3,3),(4,4),(5,5)$. 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 improved accuracy 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 $\ell \leq$ 5 ranges
from $90\%$ to $99.9\%$ for binaries with total mass $20-200 M_\odot$ (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
$98.5\%$. Using our results, we also 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-precession, and will
be employed in upcoming observing runs of Advanced LIGO and Virgo.
