A. Taracchini

Effective-one-body model for black-hole binaries with generic mass ratios and spins

Gravitational waves emitted by black-hole binary systems have the highest signal-to-noise ratio in LIGO and Virgo detectors when black-hole spins are aligned with the orbital angular momentum and extremal. For such systems, we extend the effective-one-body inspiral-merger-ringdown waveforms to generic mass ratios and spins calibrating them to 38 numerical-relativity nonprecessing waveforms produced by the SXS Collaboration. The numerical-relativity simulations span mass ratios from 1 to 8, spin magnitudes up to 98% of extremality, and last for 40 to 60 gravitational-wave cycles. When the total mass of the binary is between 20 and 200M_⊙, the effective-one-body nonprecessing (dominant mode) waveforms have overlap above 99% (using the advanced-LIGO design noise spectral density) with all of the 38 nonprecessing numerical waveforms, when maximizing only on initial phase and time. This implies a negligible loss in event rate due to modeling. We also show that—without further calibration— the precessing effective-one-body (dominant mode) waveforms have overlap above 97% with two very long, strongly precessing numerical-relativity waveforms, when maximizing only on the initial phase and time.

Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration

The Numerical–Relativity–Analytical–Relativity (NRAR) collaboration is a joint effort between members of the numerical relativity, analytical relativity and gravitational-wave data analysis communities. The goal of the NRAR collaboration is to produce numerical-relativity simulations of compact binaries and use them to develop accurate analytical templates for the LIGO/Virgo Collaboration to use in detecting gravitational-wave signals and extracting astrophysical information from them. We describe the results of the first stage of the NRAR project, which focused on producing an initial set of numerical waveforms from binary black holes with moderate mass ratios and spins, as well as one non-spinning binary configuration which has a mass ratio of 10. All of the numerical waveforms are analysed in a uniform and consistent manner, with numerical errors evaluated using an analysis code created by members of the NRAR collaboration. We compare previously-calibrated, non-precessing analytical waveforms, notably the effective-one-body (EOB) and phenomenological template families, to the newly-produced numerical waveforms. We find that when the binarys total mass is ~100–200M⊙, current EOB and phenomenological models of spinning, non-precessing binary waveforms have overlaps above 99% (for advanced LIGO) with all of the non-precessing-binary numerical waveforms with mass ratios ≤4, when maximizing over binary parameters. This implies that the loss of event rate due to modelling error is below 3%. Moreover, the non-spinning EOB waveforms previously calibrated to five non-spinning waveforms with mass ratio smaller than 6 have overlaps above 99.7% with the numerical waveform with a mass ratio of 10, without even maximizing on the binary parameters.

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 gravitationalwave 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.

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

This paper presents a tunable effective-one-body (EOB) model for black-hole (BH) binaries of arbitrary mass ratio and aligned spins. This new EOB model incorporates recent results of small-mass-ratio simulations based on Teukolsky’s perturbative formalism. The free parameters of the model are calibrated to numerical-relativity simulations of nonspinning BH-BH systems of five different mass ratios and to equal-mass nonprecessing BH-BH systems with dimensionless BH spins χ_i≃±0.44. The present analysis focuses on the orbital dynamics of the resulting EOB model, and on the dominant (l,m)=(2,2) gravitational-wave mode. The calibrated EOB model can generate inspiral-merger-ringdown waveforms for nonprecessing, spinning BH binaries with any mass ratio and with individual BH spins -1≤χ_i≲0.7. Extremizing only over time and phase shifts, the calibrated EOB model has overlaps larger than 0.997 with each of the seven numerical-relativity waveforms for total masses between 20M_⊙ and 200M_⊙, using the Advanced LIGO noise curve. We compare the calibrated EOB model with two additional equal-mass highly spinning (χ_i≃-0.95,+0.97) numerical-relativity waveforms, which were not used during calibration. We find that the calibrated model has an overlap larger than 0.995 with the simulation with nearly extremal antialigned spins. Extension of this model to black holes with aligned spins χ_i≳0.7 requires improvements of our modeling of the plunge dynamics and inclusion of higher-order PN spin terms in the gravitational-wave modes and radiation-reaction force.

Improved effective-one-body model of spinning, nonprecessing binary black holes for the era of gravitational-wave astrophysics with advanced detectors

We improve the accuracy of the effective-one-body (EOB) waveforms that were employed during the first observing run of Advanced LIGO for binaries of spinning, nonprecessing black holes by calibrating them to a set of 141 numerical-relativity (NR) waveforms. The NR simulations expand the domain of calibration toward larger mass ratios and spins, as compared to the previous EOBNR model. Merger-ringdown waveforms computed in black-hole perturbation theory for Kerr spins close to extremal provide additional inputs to the calibration. For the inspiral-plunge phase, we use a Markov-chain Monte Carlo algorithm to efficiently explore the calibration space. For the merger-ringdown phase, we fit the NR signals with phenomenological formulae. After extrapolation of the calibrated model to arbitrary mass ratios and spins, the (dominant-mode) EOBNR waveforms have faithfulness—at design Advanced-LIGO sensitivity—above 99% against all the NR waveforms, including 16 additional waveforms used for validation, when maximizing only on initial phase and time. This implies a negligible loss in event rate due to modeling for these binary configurations. We find that future NR simulations at mass ratios ≳4 and double spin ≳0.8 will be crucial to resolving discrepancies between different ways of extrapolating waveform models. We also find that some of the NR simulations that already exist in such region of parameter space are too short to constrain the low-frequency portion of the models. Finally, we build a reduced-order version of the EOBNR model to speed up waveform generation by orders of magnitude, thus enabling intensive data-analysis applications during the upcoming observation runs of Advanced LIGO.

Periastron advance in black-hole binaries.

The general relativistic (Mercury-type) periastron advance is calculated here for the first time with exquisite precision in full general relativity. We use accurate numerical relativity simulations of spinless black-hole binaries with mass ratios 1/8≤m(1)/m(2)≤1 and compare with the predictions of several analytic approximation schemes. We find the effective-one-body model to be remarkably accurate and, surprisingly, so also the predictions of self-force theory [replacing m(1)/m(2)→m(1)m(2)/(m(1)+m(2))(2)]. Our results can inform a universal analytic model of the two-body dynamics, crucial for ongoing and future gravitational-wave searches.

Dynamical Tides in General Relativity: Effective Action and Effective-One-Body Hamiltonian

Tidal effects have an important impact on the late inspiral of compact binary systems containing neutron stars. Most current models of tidal deformations of neutron stars assume that the tidal bulge is directly related to the tidal field generated by the companion, with a constant response coefficient. However, if the orbital motion approaches a resonance with one of the internal modes of the neutron star, this adiabatic description of tidal effects starts to break down, and the tides become dynamical. In this paper, we consider dynamical tides in general relativity due to the quadrupolar fundamental oscillation mode of a neutron star. We devise a description of the effects of the neutron star’s finite size on the orbital dynamics based on an effective point-particle action augmented by dynamical quadrupolar degrees of freedom. We analyze the post-Newtonian and test-particle approximations of this model and incorporate the results into an effective-one-body Hamiltonian. This enables us to extend the description of dynamical tides over the entire inspiral. We demonstrate that dynamical tides give a significant enhancement of matter effects compared to adiabatic tides, at least for neutron stars with large radii and for low mass-ratio systems, and should therefore be included in accurate models for gravitational-wave data analysis.

Validating the effective-one-body model of spinning, precessing binary black holes against numerical relativity

In Ref. [1], the properties of the first gravitational wave detected by LIGO, GW150914, were measured by employing an effective-one-body (EOB) model of precessing binary black holes whose underlying dynamics and waveforms were calibrated to numerical-relativity (NR) simulations. Here, we perform the first extensive comparison of such EOBNR model to 70 precessing NR waveforms that span mass ratios from 1 to 5, dimensionless spin magnitudes up to 0.5, generic spin orientations, and length of about 20 orbits. We work in the observers inertial frame and include all

Reducing orbital eccentricity of precessing black-hole binaries

\ell=2

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

modes in the gravitational-wave polarizations. We introduce new prescriptions for the EOB ringdown signal concerning its spectrum and time of onset. For total masses between 10Msun and 200Msun, we find that precessing EOBNR waveforms have unfaithfulness within about 3% to NR waveforms when considering the Advanced-LIGO design noise curve. This result is obtained without recalibration of the inspiral-plunge of the underlying nonprecessing EOBNR model. The unfaithfulness is computed with maximization over time and phase of arrival, sky location and polarization of the EOBNR waveform and it is averaged over sky location and polarization of the NR signal. We also present comparisons between NR and EOBNR waveforms in a frame that tracks the orbital precession.