Abdul H. Mroué

High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions

Numerical simulations of 15 orbits of an equal-mass binary black-hole system are presented. Gravitational waveforms from these simulations, covering more than 30 cycles and ending about 1.5 cycles before merger, are compared with those from quasicircular zero-spin post-Newtonian (PN) formulae. The cumulative phase uncertainty of these comparisons is about 0.05 radians, dominated by effects arising from the small residual spins of the black holes and the small residual orbital eccentricity in the simulations. Matching numerical results to PN waveforms early in the run yields excellent agreement (within 0.05 radians) over the first ~15 cycles, thus validating the numerical simulation and establishing a regime where PN theory is accurate. In the last 15 cycles to merger, however, generic time-domain Taylor approximants build up phase differences of several radians. But, apparently by coincidence, one specific post-Newtonian approximant, TaylorT4 at 3.5PN order, agrees much better with the numerical simulations, with accumulated phase differences of less than 0.05 radians over the 30-cycle waveform. Gravitational-wave amplitude comparisons are also done between numerical simulations and post-Newtonian, and the agreement depends on the post-Newtonian order of the amplitude expansion: the amplitude difference is about 6%–7% for zeroth order and becomes smaller for increasing order. A newly derived 3.0PN amplitude correction improves agreement significantly (<1% amplitude difference throughout most of the run, increasing to 4% near merger) over the previously known 2.5PN amplitude terms.

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.

Testing gravitational-wave searches with numerical relativity waveforms: results from the first Numerical INJection Analysis (NINJA) project

The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational-wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search algorithms using numerically generated waveforms and to foster closer collaboration between the numerical relativity and data analysis communities. We describe the results of the first NINJA analysis which focused on gravitational waveforms from binary black hole coalescence. Ten numerical relativity groups contributed numerical data which were used to generate a set of gravitational-wave signals. These signals were injected into a simulated data set, designed to mimic the response of the initial LIGO and Virgo gravitational-wave detectors. Nine groups analysed this data using search and parameter-estimation pipelines. Matched filter algorithms, un-modelled-burst searches and Bayesian parameter estimation and model-selection algorithms were applied to the data. We report the efficiency of these search methods in detecting the numerical waveforms and measuring their parameters. We describe preliminary comparisons between the different search methods and suggest improvements for future NINJA analyses.

Catalog of 174 Binary Black Hole Simulations for Gravitational Wave Astronomy

This Letter presents a publicly available catalog of 174 numerical binary black hole simulations following up to 35 orbits. The catalog includes 91 precessing binaries, mass ratios up to 8∶1, orbital eccentricities from a few percent to 10(-5), black hole spins up to 98% of the theoretical maximum, and radiated energies up to 11.1% of the initial mass. We establish remarkably good agreement with post-Newtonian precession of orbital and spin directions for two new precessing simulations, and we discuss other applications of this catalog. Formidable challenges remain: e.g., precession complicates the connection of numerical and approximate analytical waveforms, and vast regions of the parameter space remain unexplored.

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.

High-accuracy numerical simulation of black-hole binaries: Computation of the gravitational-wave energy flux and comparisons with post-Newtonian approximants

Expressions for the gravitational wave (GW) energy flux and center-of-mass energy of a compact binary are integral building blocks of post-Newtonian (PN) waveforms. In this paper, we compute the GW energy flux and GW frequency derivative from a highly accurate numerical simulation of an equal-mass, non-spinning black hole binary. We also estimate the (derivative of the) center- of-mass energy from the simulation by assuming energy balance. We compare these quantities with the predictions of various PN approximants (adiabatic Taylor and Pade models; non-adiabatic effective-one-body (EOB) models). We find that Pade summation of the energy flux does not accelerate the convergence of the flux series; nevertheless, the Pade flux is markedly closer to the numerical result for the whole range of the simulation (about 30 GW cycles). Taylor and Pade models overestimate the increase in flux and frequency derivative close to merger, whereas EOB models reproduce more faithfully the shape of and are closer to the numerical flux, frequency derivative and derivative of energy. We also compare the GW phase of the numerical simulation with Pade and EOB models. Matching numerical and untuned 3.5 PN order waveforms, we find that the phase difference accumulated until Mω = 0.1 is -0.12 radians for Pade approximants, and 0.50 (0.45) radians for an EOB approximant with Keplerian (non-Keplerian) flux. We fit free parameters within the EOB models to minimize the phase difference, and confirm the presence of degeneracies among these parameters. By tuning the pseudo 4PN order coefficients in the radial potential or in the flux, or, if present, the location of the pole in the flux, we find that the accumulated phase difference at Mω = 0.1 can be reduced—if desired—to much less than the estimated numerical phase error (0.02 radians).

Extrapolating gravitational-wave data from numerical simulations

Two complementary techniques are developed for obtaining the asymptotic form of gravitational-wave data at large radii from numerical simulations, in the form of easily implemented algorithms. It is shown that, without extrapolation, near-field effects produce errors in extracted waveforms that can significantly affect LIGO data analysis. The extrapolation techniques are discussed in the context of Newman-Penrose data applied to extrapolation of waveforms from an equal-mass, nonspinning black-hole binary simulation. The results of the two methods are shown to agree within error estimates. The various benefits and deficiencies of the methods are discussed.

Status of NINJA: the Numerical INJection Analysis project

The 2008 NRDA conference introduced the Numerical INJection Analysis project (NINJA), a new collaborative effort between the numerical relativity community and the data analysis community. NINJA focuses on modeling and searching for gravitational wave signatures from the coalescence of binary system of compact objects. We review the scope of this collaboration and the components of the first NINJA project, where numerical relativity groups, shared waveforms and data analysis teams applied various techniques to detect them when embedded in colored Gaussian noise.

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.