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

Abstract

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 ( , |m|) = (2, 2) mode, specifically ( , |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 ≤ 5 ranges from 90% to 99.9% for binaries with total mass 20 − 200M (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.

Factorization and resummation: A new paradigm to improve gravitational wave amplitudes. III. The spinning test-body terms

“…Test-mass results have been crucial to devise robust resummation techniques for the truncated post-Newtonian expansion that give access to analytical gravitational waveform and fluxes for circularized, nonprecessing, binaries [1][2][3][4][5]. Such resummed waveform, and related fluxes, are one of the crucial building blocks of effectiveone-body (EOB) waveform models for coalescing relativistic binaries [6][7][8][9][10][11]. Up to now, resummation of PN-expanded analytical result is the only approach that can be adopted to improve the behavior of the PNexpansions in the strong-field, fast velocity regime up to merger [12].…”

LISA parameter estimation and source localization with higher harmonics of the ringdown

“…Combined measurement of the inspiral and of the ringdown could reduce the errors on the individual spin components. These qualitative arguments should be supported by explicit calculations using state-of-the-art inspiral/merger/ringdown models including higher harmonics [7][8][9][10][11][12], a task beyond the scope of this work. ity: New frontiers in Einstein's theory" grant agreement no.…”

“…For systems with mass M 10 6 M , high-frequency harmonics can lie closer to the noise "bucket" of LISA than the fundamental (low-frequency) modes, and therefore they can have relatively large SNR. This is particularly important for large-q mergers, because then higher modes can have relatively large amplitudes relative to the (2, 2) mode [9,15,18]. In fact, the SNR in higher harmonics for massive binaries with large q is comparable to (or greater than) the (2, 2) mode SNR.…”

Including higher order multipoles in gravitational-wave models for precessing binary black holes

“…This motivated the study in Ref. [11], where the authors analysed GW170729 with two new aligned-spin and higher mode models (SEOBNRv4HM [40] and PhenomHM [10]). They found that the models preferred to interpret the data as the GW signal coming from a higher mass-ratio system with estimates for the mass-ratio changing from 0.62 +0.…”