A. Buonanno

Effective one-body approach to general relativistic two-body dynamics

We map the general relativistic two-body problem onto that of a test particle moving in an effective external metric. This effective-one-body approach defines, in a non-perturbative manner, the late dynamical evolution of a coalescing binary system of compact objects. The transition from the adiabatic inspiral, driven by gravitational radiation damping, to an unstable plunge, induced by strong spacetime curvature, is predicted to occur for orbits more tightly bound than the innermost stable circular orbit in a Schwarzschild metric of mass M 5m11m2 . The binding energy, angular momentum and orbital frequency of the innermost stable circular orbit for the time-symmetric two-body problem are determined as a function of the mass ratio. @S0556-2821~99!04806-7#

Transition from inspiral to plunge in binary black hole coalescences

Combining recent techniques giving non-perturbative re-summed estimates of the damping and conservative parts of the two-body dynamics, we describe the transition between the adiabatic phase and the plunge, in coalescing binary black holes with comparable masses moving on quasi-circular orbits. We give initial dynamical data for numerical relativity investigations, with a fraction of an orbit left, and provide, for data analysis purposes, an estimate of the gravitational wave-form emitted throughout the inspiral, plunge and coalescence phases.

Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors

It has long been thought that the sensitivity of laser interferometric gravitational-wave detectors is limited by the free-mass standard quantum limit, unless radical redesigns of the interferometers or modifications of their input or output optics are introduced. Within a fully quantum-mechanical approach we show that in a second-generation interferometer composed of arm cavities and a signal recycling cavity, e.g., the LIGO-II configuration, (i) quantum shot noise and quantum radiation-pressure-fluctuation noise are dynamically correlated, (ii) the noise curve exhibits two resonant dips, (iii) the standard quantum limit can be beaten by a factor of 2, over a frequency range Δf/f∼1, but at the price of increasing noise at lower frequencies.

Toward faithful templates for non-spinning binary black holes using the effective-one-body approach

im izing only overtim eofarrivaland initialphase.W eobtain thisresultby sim ply adding a 4-post- Newtonian ordercorrection in theEO B radialpotentialand determ iningthe(constant)coecientby im posing high-m atching perform anceswith num ericalwaveform sofm assratios m 1=m 2 = 1;3=2;2 and 4, m 1 and m 2 being the individualblack-hole m asses. Thenalblack-hole m ass and spin predicted by the num ericalsim ulations are used to determ ine the ringdown frequency and decay tim eofthreequasi-norm al-m ode dam ped sinusoidsthatare attached to theEO B inspiral-(plunge) waveform at the EO B light-ring. The EO B waveform s m ight be tested and further im proved in thefutureby com parison with extrem ely long and accurateinspiralnum erical-relativity waveform s. They m ay already be em ployed for coherent searches and param eter estim ation ofgravitational wavesem itted by non-spinningcoalescing binary black holeswith ground-based laser-interferom eter detectors.

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.

Estimating spinning binary parameters and testing alternative theories of gravity with LISA

We investigate the effect of spin-orbit and spin-spin couplings on the estimation of parameters for inspiralling compact binaries of massive black holes, and for neutron stars inspiralling into intermediate-mass black holes, using hypothetical data from the proposed Laser Interferometer Space Antenna (LISA). We work both in Einstein’s theory and in alternative theories of gravity of the scalar-tensor and massive-graviton types. We restrict the analysis to non-precessing spinning binaries, i.e. to cases where the spins are aligned normal to the orbital plane. We find that the accuracy with which intrinsic binary parameters such as chirp mass and reduced mass can be estimated within general relativity is degraded by between one and two orders of magnitude. We find that the bound on the coupling parameter ωBD of scalar-tensor gravity is significantly reduced by the presence of spin couplings, while the reduction in the graviton-mass bound is milder. Using fast Monte-Carlo simulations of 10 4 binaries, we show that inclusion of spin terms in massive blackhole binaries has little effect on the angular resolution or on distance determination accuracy. For stellar mass inspirals into intermediate-mass black holes, the angular resolution and the distance are determined only poorly, in all cases considered. We also show that, if LISA’s low-frequency noise sensitivity can be extrapolated from 10 −4 Hz to as low as 10 −5 Hz, the accuracy of determining both extrinsic parameters (distance, sky location) and intrinsic parameters (chirp mass, reduced mass) of massive binaries may be greatly improved.

Signal recycled laser-interferometer gravitational-wave detectors as optical springs

Using the force-susceptibility formalism of linear quantum measurements, we study the dynamics of signal recycled interferometers, such as LIGO-II. We show that, although the antisymmetric mode of motion of the four arm-cavity mirrors is originally described by a free mass, when the signal-recycling mirror is added to the interferometer, the radiation-pressure force not only disturbs the motion of that “free mass” randomly due to quantum fluctuations, but also, and more fundamentally, makes it respond to forces as though it were connected to a spring with a specific optical-mechanical rigidity. This oscillatory response gives rise to a much richer dynamics than previously known for SR interferometers, which enhances the possibilities for reshaping the noise curves and, if thermal noise can be pushed low enough, enables the standard quantum limit to be beaten. We also show the possibility of using servo systems to suppress the instability associated with the optical-mechanical interaction without compromising the sensitivity of the interferometer.

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.

Higher-order spin effects in the dynamics of compact binaries. I. Equations of motion

We derive the equations of motion of spinning compact binaries including the spin-orbit (SO) coupling terms one post-Newtonian (PN) order beyond the leading-order effect. For black holes maximally spinning this corresponds to 2.5PN order. Our result for the equations of motion essentially confirms the previous result by Tagoshi, Ohashi and Owen. We also compute the spin-orbit effects up to 2.5PN order in the conserved (Noetherian) integrals of motion, namely the energy, the total angular momentum, the linear momentum and the center-of-mass integral. We obtain the spin precession equations at 1PN order beyond the leading term, as well. Those results will be used in a future paper to derive the time evolution of the binary orbital phase, providing more accurate templates for LIGO-Virgo-LISA type interferometric detectors.

The Distribution of Recoil Velocities from Merging Black Holes

We calculate the linear momentum flux from merging black holes (BHs) with arbitrary masses and spin orientations, using the effective-one-body (EOB) model. This model includes an analytic description of the inspiral phase, a short merger, and a superposition of exponentially damped quasi-normal ring-down modes of a Kerr BH. By varying the matching point between inspiral and ring-down, we can estimate the systematic errors generated with this method. Within these confidence limits, we find close agreement with previously reported results from numerical relativity. Using a Monte Carlo implementation of the EOB model, we are able to sample a large volume of BH parameter space and estimate the distribution of recoil velocities. For a range of mass ratios 1 ≤ m1/m2 ≤ 10, spin magnitudes of a1, 2 = 0.9, and uniform random spin orientations, we find that a fraction f500 = 0.12 of binaries have recoil velocities greater than 500 km s-1 and that a fraction f1000 = 0.027 of binaries have kicks greater than 1000 km s-1. These velocities likely are capable of ejecting the final BH from its host galaxy. Limiting the sample to comparable-mass binaries with m1/m2 ≤ 4, the typical kicks are even larger, with f500 = 0.31 and f1000 = 0.079.