Small mass plunging into a Kerr black hole: Anatomy of the inspiral-merger-ringdown waveforms

We numerically solve the Teukolsky equation in the time domain to obtain the gravitational-wave emission of a small mass inspiraling and plunging into the equatorial plane of a Kerr black hole. We account for the dissipation of orbital energy using the Teukolsky frequency-domain gravitational-wave fluxes for circular, equatorial orbits, down to the light-ring. We consider Kerr spins $-0.99 \leq q \leq 0.99$, and compute the inspiral-merger-ringdown (2,2), (2,1), (3,3), (3,2), (4,4), and (5,5) modes. We study the large-spin regime, and find a great simplicity in the merger waveforms, thanks to the extremely circular character of the plunging orbits. We also quantitatively examine the mixing of quasinormal modes during the ringdown, which induces complicated amplitude and frequency modulations in the waveforms. Finally, we explain how the study of small mass-ratio black-hole binaries helps extending effective-one-body models for comparable-mass, spinning black-hole binaries to any mass ratio and spin magnitude.Comment: 20 pages, 15 figure

Surrogate model for an aligned-spin effective one body waveform model of binary neutron star inspirals using Gaussian process regression

Fast and accurate waveform models are necessary for measuring the properties of inspiraling binary neutron star systems such as GW170817. We present a frequency-domain surrogate version of the aligned-spin binary neutron star waveform model using the effective one body formalism known as SEOBNRv4T. This model includes the quadrupolar and octopolar adiabatic and dynamical tides. The version presented here is improved by the inclusion of the spin-induced quadrupole moment effect, and completed by a prescription for tapering the end of the waveform to qualitatively reproduce numerical relativity simulations. The resulting model has 14 intrinsic parameters. We reduce its dimensionality by using universal relations that approximate all matter effects in terms of the leading quadrupolar tidal parameters. The implementation of the time-domain model can take up to an hour to evaluate using a starting frequency of 20Hz, and this is too slow for many parameter estimation codes that require $O(10^7)$ sequential waveform evaluations. We therefore construct a fast and faithful frequency-domain surrogate of this model using Gaussian process regression. The resulting surrogate has a maximum mismatch of $4.5\times 10^{-4}$ for the Advanced LIGO detector, and requires 0.13s to evaluate for a waveform with a starting frequency of 20Hz. Finally, we perform an end-to-end test of the surrogate with a set of parameter estimation runs, and find that the surrogate accurately recovers the parameters of injected waveforms.Comment: 19 pages, 10 figures, submitted to PR

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.Comment: 28 page

Inspiral-merger-ringdown models for spinning black-hole binaries at the interface between analytical and numerical relativity

The long-sought direct detection of gravitational waves may only be a few years away, as a new generation of interferometric experiments of unprecedented sensitivity will start operating in 2015. These experiments will look for gravitational waves with frequencies from 10 to about 1000 Hz, thus targeting astrophysical sources such as coalescing binaries of compact objects, core collapse supernovae, and spinning neutron stars, among others. The search strategy for gravitational waves emitted by compact-object binaries consists in filtering the output of the detectors with template waveforms that describe plausible signals, as predicted by general relativity, in order to increase the signal-to-noise ratio. In this work, we modeled these systems through the effective-one-body approach to the general-relativistic 2-body problem. This formalism rests on the idea that binary coalescence is universal across different mass ratios, from the test-particle limit to the equal-mass regime. It bridges the gap between post-Newtonian theory (valid in the slow-motion, weak-field limit) and black-hole perturbation theory (valid in the small mass-ratio limit, but not limited to slow motion). The project unfolded along two main avenues of inquiry, with the goal of developing faithful inspiral-merger-ringdown waveforms for generic spinning, stellar-mass black-hole binaries. On the one hand, we studied the motion and gravitational radiation of test masses orbiting Kerr black holes in perturbation theory, with the goal of extracting strong-field information that can be incorporated into effective-one-body models. On the other hand, we worked at the interface between analytical and numerical relativity by calibrating effective-one-body models against numerical solutions of Einstein's equations, and testing their accuracy when extrapolated to different regions of the parameter space. In the course of this project, we also studied conservative effects of the 2-body dynamics, namely the periastron advance, and devised algorithms for generating realistic initial conditions for spinning, precessing black-hole binaries. The waveform models developed in this project will be employed in data-analysis pipelines and gravitational-wave searches of advanced LIGO and Virgo. In the near future, natural extensions of this work will be the inclusion of tidal effects in the comparable-mass regime (relevant for neutron-star/black-hole binaries), and spin precession in the test-particle limit

Reducing orbital eccentricity of precessing black-hole binaries

Building initial conditions for generic binary black-hole evolutions without initial spurious eccentricity remains a challenge for numerical-relativity simulations. This problem can be overcome by applying an eccentricity-removal procedure which consists in evolving the binary for a couple of orbits, estimating the eccentricity, and then correcting the initial conditions. The presence of spins can complicate this procedure. As predicted by post-Newtonian theory, spin-spin interactions and precession prevent the binary from moving along an adiabatic sequence of spherical orbits, inducing oscillations in the radial separation and in the orbital frequency. However, spin-induced oscillations occur at approximately twice the orbital frequency, therefore they can be distinguished from the initial spurious eccentricity, which occurs at approximately the orbital frequency. We develop a new removal procedure based on the derivative of the orbital frequency and find that it is successful in reducing the eccentricity measured in the orbital frequency to less than 0.0001 when moderate spins are present. We test this new procedure using numerical-relativity simulations of binary black holes with mass ratios 1.5 and 3, spin magnitude 0.5 and various spin orientations. The numerical simulations exhibit spin-induced oscillations in the dynamics at approximately twice the orbital frequency. Oscillations of similar frequency are also visible in the gravitational-wave phase and frequency of the dominant mode.Comment: 17 pages, 11 figures, fixed typo

Numerical relativity reaching into post-Newtonian territory: a compact-object binary simulation spanning 350 gravitational-wave cycles

We present the first numerical-relativity simulation of a compact-object binary whose gravitational waveform is long enough to cover the entire frequency band of advanced gravitational-wave detectors, such as LIGO, Virgo and KAGRA, for mass ratio 7 and total mass as low as $45.5\,M_\odot$. We find that effective-one-body models, either uncalibrated or calibrated against substantially shorter numerical-relativity waveforms at smaller mass ratios, reproduce our new waveform remarkably well, with a negligible loss in detection rate due to modeling error. In contrast, post-Newtonian inspiral waveforms and existing calibrated phenomenological inspiral-merger-ringdown waveforms display greater disagreement with our new simulation. The disagreement varies substantially depending on the specific post-Newtonian approximant used

Inspiral-merger-ringdown waveforms of spinning, precessing black-hole binaries in the effective-one-body formalism

We describe a general procedure to generate spinning, precessing waveforms that include inspiral, merger and ringdown stages in the effective-one-body (EOB) approach. The procedure uses a precessing frame in which precession-induced amplitude and phase modulations are minimized, and an inertial frame, aligned with the spin of the final black hole, in which we carry out the matching of the inspiral-plunge to merger-ringdown waveforms. As a first application, we build spinning, precessing EOB waveforms for the gravitational modes l=2 such that in the nonprecessing limit those waveforms agree with the EOB waveforms recently calibrated to numerical-relativity waveforms. Without recalibrating the EOB model, we then compare EOB and post-Newtonian precessing waveforms to two numerical-relativity waveforms produced by the Caltech-Cornell-CITA collaboration. The numerical waveforms are strongly precessing and have 35 and 65 gravitational-wave cycles. We find a remarkable agreement between EOB and numerical-relativity precessing waveforms and spins' evolutions. The phase difference is ~ 0.2 rad at merger, while the mismatches, computed using the advanced-LIGO noise spectral density, are below 2% when maximizing only on the time and phase at coalescence and on the polarization angle.Comment: 17 pages, 10 figure

Prototype effective-one-body model for nonprecessing spinning inspiral-merger-ringdown waveforms

We first use five non-spinning and two mildly spinning (chi_i \simeq -0.44, +0.44) numerical-relativity waveforms of black-hole binaries and calibrate an effective-one-body (EOB) model for non-precessing spinning binaries, notably its dynamics and the dominant (2,2) gravitational-wave mode. Then, we combine the above results with recent outcomes of small-mass-ratio simulations produced by the Teukolsky equation and build a prototype EOB model for detection purposes, which is capable of generating inspiral-merger-ringdown waveforms for non-precessing spinning black-hole binaries with any mass ratio and individual black-hole spins -1 \leq chi_i \lesssim 0.7. We compare the prototype EOB model to two equal-mass highly spinning numerical-relativity waveforms of black holes with spins chi_i = -0.95, +0.97, which were not available at the time the EOB model was calibrated. In the case of Advanced LIGO we find that the mismatch between prototype-EOB and numerical-relativity waveforms is always smaller than 0.003 for total mass 20-200 M_\odot, the mismatch being computed by maximizing only over the initial phase and time. To successfully generate merger waveforms for individual black-hole spins chi_i \gtrsim 0.7, the prototype-EOB model needs to be improved by (i) better modeling the plunge dynamics and (ii) including higher-order PN spin terms in the gravitational-wave modes and radiation-reaction force.Comment: 20 pages, 8 figures. Minor changes to match version accepted for publication in PR

Approaching the Post-Newtonian Regime with Numerical Relativity: A Compact-Object Binary Simulation Spanning 350 Gravitational-Wave Cycles

We present the first numerical-relativity simulation of a compact-object binary whose gravitational waveform is long enough to cover the entire frequency band of advanced gravitational-wave detectors, such as LIGO, Virgo, and KAGRA, for mass ratio 7 and total mass as low as 45.5M_⊙. We find that effective-one-body models, either uncalibrated or calibrated against substantially shorter numerical-relativity waveforms at smaller mass ratios, reproduce our new waveform remarkably well, with a negligible loss in detection rate due to modeling error. In contrast, post-Newtonian inspiral waveforms and existing calibrated phenomenological inspiral-merger-ringdown waveforms display greater disagreement with our new simulation. The disagreement varies substantially depending on the specific post-Newtonian approximant used