Multipolar Waveform Research Articles

Exploiting Newton-factorized, 2PN-accurate waveform multipoles in effective-one-body models for spin-aligned noncircularized binaries

We present a new approach to factorize and resum the post-Newtonian (PN) waveform for generic equatorial motion to be used within effective-one-body (EOB-)based waveform models. The new multipolar waveform factorization improves previous prescriptions in that (i) the generic Newtonian contribution is factored out from each multipole; (ii) the circular part is factored out and resummed using standard EOB methods; and (iii) the residual, 2PN-accurate, noncircular part, and in particular the tail contribution, is additionally resummed using Pad\'e approximants. The resulting waveform is validated in the extreme-mass-ratio limit by comparisons with nine (mostly nonspinning) numerical waveforms either from eccentric inspirals, with eccentricities up to $e=0.9$, or dynamical captures. The resummation of the noncircular tail contribution is found essential to obtain excellent ($\ensuremath{\lesssim}0.05\text{ }\text{ }\mathrm{rad}$ at periastron for $e=0.9$) analytical/numerical agreement and to considerably improve the prescription with just the Newtonian prefactor. In the comparable mass case, the new 2PN waveform shows only a marginal improvement over the previous Newtonian factorization, though yielding maximal unfaithfulness $\ensuremath{\simeq}{10}^{\ensuremath{-}3}$ with the 28 publicly available numerical relativity simulations with eccentricity up to $\ensuremath{\sim}0.3$ (except for a single outlier that grazes ${10}^{\ensuremath{-}2}$). We finally use test-particle data to validate the waveform factorization proposed by Khalil et al. [Phys. Rev. 104, 024046 (2021)] and conclude that its amplitude can be considered reliable (though less accurate, $\ensuremath{\sim}6%$ fractional difference versus 1.5% of our method) only up to eccentricities $\ensuremath{\sim}0.3$.

Effective-one-body multipolar waveforms for eccentric binary black holes with nonprecessing spins

We construct an inspiral-merger-ringdown eccentric gravitational-wave (GW) model for binary black holes with non-precessing spins within the effective-one-body formalism. This waveform model, SEOBNRv4EHM, extends the accurate quasi-circular SEOBNRv4HM model to eccentric binaries by including recently computed eccentric corrections up to 2PN order in the gravitational waveform modes, notably the $(l,|m|)=(2,2),(2,1),(3,3),(4,4),(5,5)$ multipoles. The waveform model reproduces the zero eccentricity limit with an accuracy comparable to the underlying quasi-circular model, with the unfaithfulness of $\lesssim1\%$ against quasi-circular numerical-relativity (NR) simulations. When compared against 28 public eccentric NR simulations from the Simulating eXtreme Spacetimes catalog with initial orbital eccentricities up to $e\simeq0.3$ and dimensionless spin magnitudes up to $+0.7$, the model provides unfaithfulness $<1\%$, showing that both the $(2,|2|)$-modes and the higher-order modes are reliably described without calibration to NR datasets in the eccentric sector. The waveform model SEOBNRv4EHM is able to qualitatively reproduce the phenomenology of dynamical captures, and can be extended to include spin-precession effects. It can be employed for upcoming observing runs with the LIGO-Virgo-KAGRA detectors and used to re-analyze existing GW catalogs to infer the eccentricity parameters for binaries with $e\lesssim0.3$ (at 20 Hz or lower) and spins up to $\lesssim 0.9-0.95$. The latter is a promising region of the parameter space where some astrophysical formation scenarios of binaries predict mild eccentricity in the ground-based detectors' bandwidth. Assessing the accuracy and robustness of the eccentric waveform model SEOBNRv4EHM for larger eccentricities and spins will require comparisons with, and, likely, calibration to eccentric NR waveforms in a larger region of the parameter space.

Fast post-adiabatic waveforms in the time domain: Applications to compact binary coalescences in LIGO and Virgo

We present a computationally efficient (time-domain) multipolar waveform model for quasicircular spin-aligned compact binary coalescences. The model combines the advantages of the numerical-relativity informed, effective-one-body (EOB) family of models with a post-adiabatic solution of the equations of motion for the inspiral part of the two-body dynamics. We benchmark this model against other state-of-the-art waveforms in terms of efficiency and accuracy. We find a speed-up of one to two orders of magnitude compared to the underlying time-domain eob model for the total mass range $2--100\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. More specifically, for a low total-mass system, such as a binary neutron star with equal masses of $1.4\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, like GW170817, the computational speedup is around 100 times; for an event with total mass $\ensuremath{\sim}40\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ and mass ratio $\ensuremath{\sim}3$, like GW190412, the speedup is by a factor of $\ensuremath{\sim}20$, while for a binary system of comparable masses and total mass of $\ensuremath{\sim}70\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, like GW150914, it is by a factor of $\ensuremath{\sim}10$. We demonstrate that the new model is extremely faithful to the underlying eob model with unfaithfulness less than 0.01% across the entire applicable region of parameter space. Finally, we present successful applications of this new waveform model to parameter estimation studies and tests of general relativity.

Assessment of consistent next-to-quasicircular corrections and postadiabatic approximation in effective-one-body multipolar waveforms for binary black hole coalescences

The use of effective-one-body (EOB) waveforms for black hole binaries analysis in gravitational-wave astronomy requires faithful models and fast generation times. A key aspect to achieve faithfulness is the inclusion of numerical-relativity (NR) informed next-to-quasicircular corrections (NQC), dependent on the radial momentum, to the waveform and radiation reaction. A robust method to speed up the waveform generation is the postadiabatic iteration to approximate the solution of the EOB Hamiltonian equations. In this work, we assess the performances of a fast NQC prescription in combination to the postadiabatic method for generating multipolar gravitational waves. The outlined approach allows a consistent treatment of NQC in both the waveform and the radiation-reaction, does not require iterative procedures to achieve high faithfulness, and can be efficiently employed for parameter estimation. Comparing to 611 NR simulations, for total mass $10\text{ }\text{ }{M}_{\ensuremath{\bigodot}}\ensuremath{\le}M\ensuremath{\le}200\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ and using the Advanced LIGO noise, the model has EOB/NR unfaithfulness well below 0.01, with 78.5% of the cases below 0.001. We apply the model to the parameter estimation of GW150914 exploring the impact of the new NQC and of the higher modes up to $\ensuremath{\ell}=m=8$.

Effective one-body model for extreme-mass-ratio spinning binaries on eccentric equatorial orbits: Testing radiation reaction and waveform

We provide a systematic analysis of the multipolar gravitational waveform, energy and angular momentum fluxes emitted by a nonspinning test particle orbiting a Kerr black hole along equatorial, eccentric orbits. These quantities are computed by numerically solving the Teukolsky equation in the time domain and are then used to test and improve the radiation reaction (and waveform) of an effective-one-body (EOB) model. Eccentricity is incorporated into EOB by replacing the quasi-circular Newtonian (or leading-order) prefactors in the EOB-factorized multipolar waveform (and fluxes) with their generic counterparts. The comparison between numerical and analytical quantities is carried out over a large portion of the parameter space, notably for orbits close to the separatrix and with high eccentricities. The analytical model agrees to $\sim 1\%$ with the numerical data for orbits with moderate eccentricities ($e\lesssim 0.3$) and moderate spins ($\hat{a}\lesssim 0.5$), although this increases up to $\sim 33\%$ for large, positive, black hole spins ($\sim 0.9$) and large eccentricities ($\sim 0.9$). For moderate eccentricities, the new EOB fluxes can be used to drive the dynamics through the nonadiabatic transition from eccentric inspiral to plunge, merger and ringdown, thus providing accurate an description of the merger. We also show that the same technique can be applied to hyperbolic encounters. In general, our approach to radiation reaction for eccentric inspirals should be seen as a first step toward EOB modelization of extreme-mass-ratio-inspirals waveforms for LISA.

Radiation-reaction force and multipolar waveforms for eccentric, spin-aligned binaries in the effective-one-body formalism

While most binary inspirals are expected to have circularized before they enter the LIGO/Virgo frequency band, a small fraction of those binaries could have non-negligible orbital eccentricity depending on their formation channel. Hence, it is important to accurately model eccentricity effects in waveform models used to detect those binaries, infer their properties, and shed light on their astrophysical environment. We develop a multipolar effective-one-body (EOB) eccentric waveform model for compact binaries whose components have spins aligned or antialigned with the orbital angular momentum. The waveform model contains eccentricity effects in the radiation-reaction force and gravitational modes through second post-Newtonian (PN) order, including tail effects, and spin-orbit and spin-spin couplings. We recast the PN-expanded, eccentric radiation-reaction force and modes in factorized form so that the newly derived terms can be directly included in the state-of-the-art, quasi-circular--orbit EOB model currently used in LIGO/Virgo analyses (i.e., the SEOBNRv4HM model).

Effective one-body multipolar waveform model for spin-aligned, quasicircular, eccentric, hyperbolic black hole binaries

Building upon recent work, we present an improved effective-one-body (EOB) model for spin-aligned, coalescing, black hole binaries with generic orbital configurations, i.e. quasi-circular, eccentric or hyperbolic orbits. The model relies on the idea of incorporating general Newtonian prefactors, instead of the usual quasi-circular ones, in both radiation reaction and waveform. The major advance with respect to previous work is that the quasi-circular limit of the model is now correctly informed by numerical relativity (NR) quasi-circular simulation. This provides EOB/NR unfaithfulness for the dominant quadrupolar waveform, calculated with Advanced LIGO noise, at most of the order of $1\%$ over a meaningful portion of the quasi-circular NR simulations calculated by the Simulating eXtreme Spacetime (SXS) collaboration. In the presence of eccentricity, the model is similarly NR-faithful, $\lesssim 1\%$, all over the 28 public SXS NR datasets, with initial eccentricity up to $\simeq 0.2$ , mass ratio up to $q=3$ and dimensionless spin magnitudes as large as $+0.7$. Higher multipoles, up to $\ell=5$ are also reliably modeled through the eccentric inspiral, plunge merger and ringdown. For hyperbolic-like configurations, we also show that the EOB computed scattering angle is in excellent agreement with all currently available NR results.

Multipolar effective one body waveform model for spin-aligned black hole binaries

We introduce \TEOBiResumSM{}, an improved version of the effective-one-body (EOB) waveform model \TEOBResumS{} for spin-aligned, coalescing black hole binaries, that includes subdominant gravitational waveform modes completed through merger and ringdown. Beyond the dominant $(\ell,|m|)=(2,2)$ one, the more robust multipoles all over the parameter space are: $(2,1)$, $(3,3)$, $(3,2)$, $(4,4)$ and $(5,5)$. The multipolar ringdown EOB waveform stems from suitably fitting many numerical relativity (NR) waveform data from the Simulating eXtreme Spacetimes (SXS) collaboration together with test-mass waveform data. Mode-mixing effects are not incorporated. The orbital (nonspinning) part of the multipolar waveform amplitudes includes test-mass results up to (relative) 6PN order and, for most modes,is Pad\'e resummed. The $m$=odd waveform multipoles (up to $\ell=5$) incorporate most of the currently available spin-dependent analytical information. Improving on previous work, we confirm that certain $m=\text{odd}$ modes, e.g. the $(2,1)$, and even the $(3,1)$, may develop a zero (or a minimum) in the amplitude for nearly equal-mass binaries and for several combinations of the individual spins. A remarkable EOB/NR agreement around such zero is found for these modes. The new waveform, and radiation reaction, prompts a new NR-calibration of the spinning sector of the model, done with only $32$ datasets.The maximum $(2,2)$ EOB/NR unfaithfulness $\bar{F}$ with Advanced LIGO noise against the SXS catalog ($\sim 595$ datasets) is always below $0.5\%$ for binaries with total mass $M$ as $10M_\odot\leq M \leq 200M_\odot$, except for a single outlier with $\max{(\bar{F})}\sim 0.85\%$. When $(2,1)$, $(3,3)$ and $(4,4)$ modes are included, one finds an excellent EOB/NR agreement up to $M\sim 120M_\odot$, above which the performance degrades slightly and moves above $3\%$

Testing the multipole structure and conservative dynamics of compact binaries using gravitational wave observations: The spinning case

In an earlier work [S. Kastha et al., Phys. Rev. D 98, 124033 (2018)], we developed the parametrized multipolar gravitational wave phasing formula to test general relativity, for the nonspinning compact binaries in quasicircular orbit. In this paper, we extend the method and include the important effect of spins in the inspiral dynamics. Furthermore, we consider parametric scaling of post-Newtonian (PN) coefficients of the conserved energy for the compact binary, resulting in the parametrized phasing formula for nonprecessing spinning compact binaries in quasicircular orbit. We also compute the projected accuracies with which the second and third generation ground-based gravitational wave detector networks as well as the planned space-based detector LISA will be able to measure the multipole deformation parameters and the binding energy parameters. Based on different source configurations, we find that a network of third-generation detectors would have comparable ability to that of LISA in constraining the conservative and dissipative dynamics of the compact binary systems. This parametrized multipolar waveform would be extremely useful not only in deriving the first upper limits on any deviations of the multipole and the binding energy coefficients from general relativity using the gravitational wave detections, but also for science case studies of next generation gravitational wave detectors.

Effective-one-body multipolar waveform for tidally interacting binary neutron stars up to merger

Gravitational-wave astronomy with coalescing binary neutron star sources requires the availability of gravitational waveforms with tidal effects accurate up to merger. This article presents an improved version of \TEOBResum, a nonspinning effective-one-body (EOB) waveform model with enhanced analytical information in its tidal sector. The tidal potential governing the conservative dynamics employs resummed expressions based on post-Newtonian (PN) and gravitational self-force (GSF) information. In particular, we compute a GSF-resummed expression for the leading-order octupolar gravitoelectric term and incorporate the leading-order gravitomagnetic term (either in PN-expanded or GSF-resummed form). The multipolar waveform and fluxes are augmented with gravitoelectric and magnetic terms recently obtained in PN. The new analytical information enhances tidal effects toward merger accelerating the coalescence. We quantify the impact on the gravitational-wave phasing of each physical effect. The most important contribution is given by the resummed gravitoelectric octupolar term entering the EOB interaction potential, that can yield up to 1~rad of dephasing (depending on the NS model) with respect to its nonresummed version. The model's energetics and the gravitational wave phasing are validated with eccentricity-reduced and multi-resolution numerical relativity simulations with different equations of state and mass ratios. We also present EOB-NR waveform comparisons for higher multipolar modes beyond the dominant quadrupole one.

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 $(\ell,|m|) = (2,2)$ 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.

Multipolar gravitational waveforms and ringdowns generated during the plunge from the innermost stable circular orbit into a Schwarzschild black hole

We study the gravitational radiation emitted by a massive point particle plunging from slightly below the innermost stable circular orbit into a Schwarzschild black hole. We consider both even- and odd-parity perturbations and describe them using the two gauge-invariant master functions of Cunningham, Price, and Moncrief. We obtain, for arbitrary directions of observation and, in particular, outside the orbital plane of the plunging particle, the regularized multipolar waveforms, i.e., the waveforms constructed by summing over of a large number of modes, and their unregularized counterparts constructed from the quasinormal-mode spectrum. They are in excellent agreement and our results permit us to especially emphasize the impact on the distortion of the waveforms of (i) the harmonics beyond the dominant $(\ell=2,m=\pm 2)$ modes and (ii) the direction of observation, and therefore the necessity to take them into account in the analysis of the last phase of binary black hole coalescence.

Alternative description of gravitational radiation from black holes based on the Regge poles of the S -matrix and the associated residues

We advocate for an alternative description of gravitational radiation from black holes based on complex angular momentum techniques (analytic continuation of partial wave expansions, duality of the ${\cal S}$-matrix and effective resummations involving its Regge poles and the associated residues, Regge trajectories, semiclassical interpretations, etc.). Such techniques, which proved to be very helpful in various areas of physics to describe and analyze resonant scattering, were only marginally used in the context of black hole physics. Here, by considering the multipolar waveform generated by a massive particle falling radially from infinity into a Schwarzschild black hole, we show that they could play a fundamental role in gravitational-wave physics. More precisely, from the multipole expansion defining the Weyl scalar $\Psi_4$, we extract the Fourier transform of a sum over Regge poles and their residues which can be evaluated numerically from the associated Regge trajectories. This Regge pole approximation permits us to reconstruct, for an arbitrary direction of observation, a large part of the multipolar waveform $\Psi_4$. In particular, it can reproduce with very good agreement the quasinormal ringdown as well as with rather good agreement the tail of the signal. This is achieved even if we take into account only one Regge pole and, if a large number of modes are excited, the result can be improved by considering additional poles. Moreover, while quasinormal-mode contributions do not provide physically relevant results at "early times" due to their exponentially divergent behavior as time decreases, it is not necessary to determine from physical considerations a starting time for the Regge ringdown.

Electromagnetic radiation generated by a charged particle plunging into a Schwarzschild black hole: Multipolar waveforms and ringdowns

Electromagnetic radiation emitted by a charged particle plunging from slightly below the innermost stable circular orbit into a Schwarzschild black hole is examined. Both even- and odd-parity electromagnetic perturbations are considered. They are described by using gauge invariant master functions and the regularized multipolar waveforms as well as their unregularized counterparts constructed from the quasinormal-mode spectrum are obtained for arbitrary directions of observation and, in particular, outside the orbital plane of the plunging particle. They are in excellent agreement and the results especially emphasize the impact of higher harmonics on the distortion of the waveforms.

A new gravitational wave generation algorithm for particle perturbations of the Kerr spacetime

We present a new approach to solve the 2+1 Teukolsky equation for gravitational perturbations of a Kerr black hole. Our approach relies on a new horizon penetrating, hyperboloidal foliation of Kerr spacetime and spatial compactification. In particular, we present a framework for waveform generation from point-particle perturbations. Extensive tests of a time domain implementation in the Teukode code are presented. The code can efficiently deliver waveforms at future null infinity. The accuracy and convergence of the waveforms’ phase and amplitude is demonstrated. As a first application of the method, we compute the gravitational waveforms from inspiraling and coalescing black-hole binaries in the large-mass-ratio limit. The smaller mass black hole is modeled as a point particle whose dynamics is driven by an effective-one-body-resummed analytical radiation reaction force. We compare the analytical, mechanical angular momentum loss (computed using two different prescriptions) to the gravitational wave angular momentum flux. We find that higher-order post-Newtonian corrections are needed to improve the consistency for rapidly spinning binaries. We characterize the multipolar waveform as a function of the black-hole spin. Close to merger, the subdominant multipolar amplitudes (notably the m = 0 ones) are enhanced for retrograde orbits with respect to prograde ones. We argue that this effect mirrors nonnegligible deviations from the circularity of the dynamics during the late-plunge and merger phase. For the first time, we compute the gravitational wave energy flux flowing into the black hole during the inspiral using a time-domain formalism proposed by Poisson. Finally, a self-consistent, iterative method to compute the gravitational wave fluxes at leading-order in the mass of the particle is developed. The method can be used alternatively to the analytical radiation reaction in cases where the analytical information is poor or not sufficient. Specifically, we apply it to compute dynamics and waveforms for a rapidly rotating black hole with dimensionless spin parameter . For this case, the simulation with the consistent flux differs from the one with the analytical flux by gravitational wave cycles over a total of about 250 cycles. In this simulation the horizon absorption accounts for about gravitational wave cycles.

Impact of higher harmonics in searching for gravitational waves from nonspinning binary black holes

Current searches for gravitational waves from coalescing binary black holes (BBH) use templates that only include the dominant harmonic. In this study we use effective-one-body multipolar waveforms calibrated to numerical-relativity simulations to quantify the effect of neglecting subdominant harmonics on the sensitivity of searches. We consider both signal-to-noise ratio (SNR) and the signal-based vetoes that are used to reweight SNR. We find that neglecting subdominant modes when searching for nonspinning BBHs with component masses $3\text{ }\text{ }{\mathrm{M}}_{\ensuremath{\bigodot}}\ensuremath{\le}{m}_{1}$, ${m}_{2}\ensuremath{\le}200\text{ }\text{ }{\mathrm{M}}_{\ensuremath{\bigodot}}$ and total mass $M&lt;360\text{ }\text{ }{\mathrm{M}}_{\ensuremath{\bigodot}}$ in advanced LIGO results in a negligible reduction of the reweighted SNR at detection thresholds. Subdominant modes therefore have no effect on the detection rates predicted for advanced LIGO. Furthermore, we find that if subdominant modes are included in templates the sensitivity of the search becomes worse if we use current search priors, due to an increase in false alarm probability. Templates would need to be weighted differently than what is currently done to compensate for the increase in false alarms. If we split the template bank such that subdominant modes are only used when $M\ensuremath{\gtrsim}100\text{ }\text{ }{\mathrm{M}}_{\ensuremath{\bigodot}}$ and mass ratio $q\ensuremath{\gtrsim}4$, we find that the sensitivity does improve for these intermediate mass-ratio BBHs, but the sensitive volume associated with these systems is still small compared to equal-mass systems. Using subdominant modes is therefore unlikely to substantially increase the probability of detecting gravitational waves from nonspinning BBH signals unless there is a relatively large population of intermediate mass-ratio BBHs in the universe.

Erratum: Post-Newtonian factorized multipolar waveforms for spinning, nonprecessing black-hole binaries [Phys. Rev. D83, 064003 (2011)

Erratum: Post-Newtonian factorized multipolar waveforms for spinning, nonprecessing black-hole binaries [Phys. Rev. D<b>83</b>, 064003 (2011)

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

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 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 Msun 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 50Msun are considered, the mismatch for mass ratio 6 (1) can be as high as 5% (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 50Msun 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.

Binary black hole coalescence in the extreme-mass-ratio limit: Testing and improving the effective-one-body multipolar waveform

We discuss the properties of the effective-one-body (EOB) multipolar gravitational waveform emitted by nonspinning black-hole binaries of masses $\ensuremath{\mu}$ and $M$ in the extreme-mass-ratio limit $\ensuremath{\mu}/M=\ensuremath{\nu}\ensuremath{\ll}1$. We focus on the transition from quasicircular inspiral to plunge, merger, and ringdown. We compare the EOB waveform to a Regge-Wheeler-Zerilli waveform computed using the hyperboloidal layer method and extracted at null infinity. Because the EOB waveform keeps track analytically of most phase differences in the early inspiral, we do not allow for any arbitrary time or phase shift between the waveforms. The dynamics of the particle, common to both wave-generation formalisms, is driven by a leading-order $\mathcal{O}(\ensuremath{\nu})$ analytically resummed radiation reaction. The EOB and the Regge-Wheeler-Zerilli waveforms have an initial dephasing of about $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\text{ }\text{ }\mathrm{rad}$ and maintain then a remarkably accurate phase coherence during the long inspiral ($\ensuremath{\sim}33$ orbits), accumulating only about $\ensuremath{-}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\text{ }\text{ }\mathrm{rad}$ until the last stable orbit, i.e. $\ensuremath{\Delta}\ensuremath{\phi}/\ensuremath{\phi}\ensuremath{\sim}\ensuremath{-}5.95\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. We obtain such accuracy without calibrating the analytically resummed EOB waveform to numerical data, which indicates the aptitude of the EOB waveform for studies concerning the Laser Interferometer Space Antenna. We then improve the behavior of the EOB waveform around merger by introducing and tuning next-to-quasicircular corrections in both the gravitational wave amplitude and phase. For each multipole we tune only four next-to-quasicircular parameters by requiring compatibility between EOB and Regge-Wheeler-Zerilli waveforms at the light ring. The resulting phase difference around the merger time is as small as $\ifmmode\pm\else\textpm\fi{}0.015\text{ }\text{ }\mathrm{rad}$, with a fractional amplitude agreement of 2.5%. This suggest that next-to-quasicircular corrections to the phase can be a useful ingredient in comparisons between EOB and numerical-relativity waveforms.

Post-Newtonian factorized multipolar waveforms for spinning, nonprecessing black-hole binaries

We generalize the factorized resummation of multipolar waveforms introduced by Damour, Iyer, and Nagar to spinning black holes. For a nonspinning test particle spiraling a Kerr black hole in the equatorial plane, we find that factorized multipolar amplitudes which replace the residual relativistic amplitude ${f}_{\ensuremath{\ell}m}$ with its $\ensuremath{\ell}$th root, ${\ensuremath{\rho}}_{\ensuremath{\ell}m}={f}_{\ensuremath{\ell}m}^{1/\ensuremath{\ell}}$, agree quite well with the numerical amplitudes up to the Kerr-spin value $q\ensuremath{\le}0.95$ for orbital velocities $v\ensuremath{\le}0.4$. The numerical amplitudes are computed solving the Teukolsky equation with a spectral code. The agreement for prograde orbits and large spin values of the Kerr black-hole can be further improved at high velocities by properly factoring out the lower-order post-Newtonian contributions in ${\ensuremath{\rho}}_{\ensuremath{\ell}m}$. The resummation procedure results in a better and systematic agreement between numerical and analytical amplitudes (and energy fluxes) than standard Taylor-expanded post-Newtonian approximants. This is particularly true for higher-order modes, such as (2,1), (3,3), (3,2), and (4,4), for which less spin post-Newtonian terms are known. We also extend the factorized resummation of multipolar amplitudes to generic mass-ratio, nonprecessing, spinning black holes. Lastly, in our study we employ new, recently computed, higher-order post-Newtonian terms in several subdominant modes and compute explicit expressions for the half and one-and-half post-Newtonian contributions to the odd-parity (current) and even-parity (odd) multipoles, respectively. Those results can be used to build more accurate templates for ground-based and space-based gravitational-wave detectors.