by Barausse, Enrico and Buonanno, Alessandra and Tiec, Alexandre Le
11 pages, 2 figures

Using the main result of a companion paper, in which the binding energy of a circular-orbit non-spinning compact binary system is computed at leading-order beyond the test-particle approximation, the exact expression of the effective-one-body (EOB) metric component $latex g^\text{eff}_{tt}$ is obtained through first order in the mass ratio. Combining these results with the recent gravitational self-force calculation of the periastron advance for circular orbits in the Schwarzschild geometry, the EOB metric component $latex g^\text{eff}_{rr}$ is also determined at linear order in the mass ratio. These results assume that the mapping between the real and effective Hamiltonians at the second and third post-Newtonian (PN) orders holds at all PN orders. Our findings also confirm the advantage of resumming the PN dynamics around the test-particle limit if the goal is to obtain a flexible model that can smoothly connect the test-mass and equal-mass limits.

by Barausse, Enrico and Buonanno, Alessandra and Hughes, Scott A. and Khanna, Gaurav and O’Sullivan, Stephen and Pan, Yi
19 pages, 14 figures, 6 tables

Using the effective-one-body (EOB) formalism and a time-domain Teukolsky code, we generate inspiral, merger, and ringdown waveforms in the small mass-ratio limit. We use EOB inspiral and plunge trajectories to build the Teukolsky equation source term, and compute full coalescence waveforms for a range of black hole spins. By comparing EOB waveforms that were recently developed for comparable mass binary black holes to these Teukolsky waveforms, we improve the EOB model for the (2,2), (2,1), (3,3), and (4,4) modes. Our results can be used to quickly and accurately extract useful information about merger waves for binaries with spin, and should be useful for improving analytic models of such binaries. Although in this analysis we only consider equatorial inspirals (orbital angular momentum parallel to spin), there is no issue of principle preventing us from considering inclined binaries. We will extend this analysis to examine misaligned spin-orbit configurations in future work.

by Damour, Thibault and Nagar, Alessandro and Pollney, Denis and Reisswig, Christian
4 pages, 2 figures

Using accurate numerical relativity simulations of (nonspinning) black-hole binaries with mass ratios 1:1, 2:1 and 3:1 we compute the gauge invariant relation between the (reduced) binding energy $latex E$ and the (reduced) angular momentum $latex j$ of the system. We show that the relation $latex E(j)$ is an accurate diagnostic of the dynamics of a black-hole binary in a highly relativistic regime. By comparing the numerical-relativity $latex E^{\rm NR} (j)$ curve with the predictions of several analytic approximation schemes, we find that, while the usual, non-resummed post-Newtonian-expanded $latex E^{\rm PN} (j)$ relation exhibits large and growing deviations from $latex E^{\rm NR} (j)$, the prediction of the effective one-body formalism, based purely on known analytical results (without any calibration to numerical relativity), agrees strikingly well with the numerical-relativity results.

by Han, Wen-Biao and Cao, Zhoujian
11 pages, 7 figures and 2 tables

A new scheme for computing dynamical evolutions and gravitational radiations for intermediate-mass-ratio inspirals (IMRIs) based on an effective one-body (EOB) dynamics plus Teukolsky perturbation theory is built in this paper. In the EOB framework, the dynamics essentially affects the resulted gravitational waveform for binary compact star system. This dynamics includes two parts. One is the conservative part which comes from effective one-body reduction. The other part is the gravitational back reaction which contributes to the shrinking process of the inspiral of binary compact star system. Previous works used analytical waveform to construct this back reaction term. Since the analytical form is based on post-Newtonian expansion, the consistency of this term is always checked by numerical energy flux. Here we directly use numerical energy flux by solving the Teukolsky equation via the frequency-domain method to construct this back reaction term. And the conservative correction to the leading order terms in mass-ratio is included in the deformed-Kerr metric and the EOB Hamiltonian. We try to use this method to simulate not only quasi-circular adiabatic inspiral but also the nonadiabatic plunge phase. For several different spinning black holes, we demonstrate and compare the resulted dynamical evolutions and gravitational waveforms.

by Nagar, Alessandro
11 pages, no figures. Submitted to Phys. Rev. D

Building on the recently computed next-to-next-to-leading order (NNLO) post-Newtonian (PN) spin-orbit Hamiltonian for spinning binaries \cite{Hartung:2011te} we extend the effective-one-body (EOB) description of the dynamics of two spinning black-holes to NNLO in the spin-orbit interaction. The calculation that is presented extends to NNLO the next-to-leading order (NLO) spin-orbit Hamiltonian computed in Ref. \cite{Damour:2008qf}. The present EOB Hamiltonian reproduces the spin-orbit coupling through NNLO in the test-particle limit case. In addition, in the case of spins parallel or antiparallel to the orbital angular momentum, when circular orbits exist, we find that the inclusion of NNLO spin-orbit terms moderates the effect of the NLO spin-orbit coupling.

by Tiec, Alexandre Le and Mroué, Abdul H. and Barack, Leor and Buonanno, Alessandra and Pfeiffer, Harald P. and Sago, Norichika and Taracchini, Andrea
5 pages, 3 figures

The general relativistic periastron advance of non-spinning black hole binaries on quasi-circular orbits has been computed using black hole perturbation theory, post-Newtonian expansions, and the effective-one-body formalism. We compare these approximations with accurate numerical relativity simulations of mass ratios 1/8 < m1/m2 m1m2/(m1+m2)^2. The effective-one-body prediction also agrees very well over the entire mass-ratio range considered.

by Pan, Yi and Buonanno, Alessandra and Boyle, Michael and Buchman, Luisa T. and Kidder, Lawrence E. and Pfeiffer, Harald P. and Scheel, Mark A.
26 pages, 25 figures

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.

by Kocsis, Bence and Yunes, Nicolas and Loeb, Abraham
42 pages, 8 figures, 3 tables, submitted to Phys. Rev. D

We examine the electromagnetic (EM) and gravitational wave (GW) signatures of stellar-mass compact objects (COs) spiraling into a supermassive black hole (extreme mass-ratio inspirals or EMRIs), embedded in a thin, radiation-pressure dominated, accretion disk. At large separations, the tidal effect of the secondary CO clears a gap. We show that the gap refills during the late GW-driven phase of the inspiral, leading to a sudden EM brightening of the source. The accretion disk leaves an imprint on the GW through its angular momentum exchange with the binary, the mass increase of the binary members due to accretion, and its gravity. We compute the disk-modified GWs both in an analytical Newtonian approximation and in a numerical effective-one-body approach. We find that disk-induced migration provides the dominant perturbation to the inspiral, with weaker effects from the mass accretion onto the CO and hydrodynamic drag. Depending on whether a gap is present, the perturbation of the GW phase is between 10 and 1000 radians per year, detectable with the future Laser Interferometer Space Antenna (LISA) at high significance. The Fourier transform of the disk-modified GW in the stationary phase approximation is sensitive to disk parameters with a frequency trend different from post-Newtonian vacuum corrections. Our results suggest that observations of EMRIs may place new sensitive constraints on the physics of accretion disks.

by Bernuzzi, Sebastiano and Nagar, Alessandro and Zenginoglu, Anil

We discuss the properties of the effective-one-body (EOB) multipolar gravitational waveform emitted by nonspinning black-hole binaries of masses $latex \mu$ and $latex M$ in the extreme-mass-ratio limit, $latex \mu/M=\nu\ll 1$. We focus on the transition from quasicircular inspiral to plunge, merger and ringdown.We compare the EOB waveform to a Regge-Wheeler-Zerilli (RWZ) 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 leading-order $latex {\cal O}(\nu)$ analytically–resummed radiation reaction. The EOB and the RWZ waveforms have an initial dephasing of about $latex 5\times 10^{-4}$ rad and maintain then a remarkably accurate phase coherence during the long inspiral ($latex \sim 33$ orbits), accumulating only about $latex -2\times 10^{-3}$ rad until the last stable orbit, i.e. $latex \Delta\phi/\phi\sim -5.95\times 10^{-6}$. We obtain such accuracy without calibrating the analytically-resummed EOB waveform to numerical data, which indicates the aptitude of the EOB waveform for LISA-oriented studies. We then improve the behavior of the EOB waveform around merger by introducing and tuning next-to-quasi-circular corrections both in the gravitational wave amplitude and phase. For each multipole we tune only four next-to-quasi-circular parameters by requiring compatibility between EOB and RWZ waveforms at the light-ring. The resulting phase difference around merger time is as small as $latex \pm 0.015$ rad, with a fractional amplitude agreement of $latex 2.5%$. This suggest that next-to-quasi-circular corrections to the phase can be a useful ingredient in comparisons between EOB and numerical relativity waveforms.

by Favata, Marc
17 pages, 2 figures, 1 table

The innermost stable circular orbit (ISCO) delimits the transition from circular orbits to those that plunge into a black hole. In the test-mass limit, well-defined ISCO conditions exist for the Kerr and Schwarzschild spacetimes. In the finite-mass case, there are a large variety of ways to define an ISCO in a post-Newtonian (PN) context. Here I generalize the gauge-invariant ISCO condition of Blanchet & Iyer (2003) to the case of spinning (non-precessing) binaries. The Blanchet-Iyer ISCO condition has two desirable and unexpected properties: (1) it exactly reproduces the Schwarzschild ISCO in the test-mass limit, and (2) it accurately approximates the recently-calculated shift in the Schwarzschild ISCO frequency due to the conservative-piece of the gravitational self-force [Barack & Sago (2009)]. The generalization of this ISCO condition to spinning binaries has the property that it also exactly reproduces the Kerr ISCO in the test-mass limit (up to the order at which PN spin corrections are currently known). The shift in the ISCO due to the spin of the test-particle is also calculated. Remarkably, the gauge-invariant PN ISCO condition exactly reproduces the ISCO shift predicted by the Papapetrou equations for a fully-relativistic spinning particle. It is surprising that an analysis of the stability of the standard PN equations of motion is able (without any form of “resummation”) to accurately describe strong-field effects of the Kerr spacetime. The ISCO frequency shift due to the conservative self-force in Kerr is also calculated from this new ISCO condition, as well as from the effective-one-body Hamiltonian of Barausse & Buonanno (2010). These results serve as a useful point-of-comparison for future gravitational self-force calculations in the Kerr spacetime.

by Yunes, Nicolas and Buonanno, Alessandra and Hughes, Scott A. and Pan, Yi and Barausse, Enrico and Miller, M. Coleman and Throwe, William
21 pages, 8 figures, submitted to Phys. Rev. D

We construct effective-one-body waveform models suitable for data analysis with LISA for extreme-mass ratio inspirals in quasi-circular, equatorial orbits about a spinning supermassive black hole. The accuracy of our model is established through comparisons against frequency-domain, Teukolsky-based waveforms in the radiative approximation. The calibration of eight high-order post-Newtonian parameters in the energy flux suffices to obtain a phase and fractional amplitude agreement of better than 1 radian and 1 % respectively over a period between 2 and 6 months depending on the system considered. This agreement translates into matches higher than 97 % over a period between 4 and 9 months, depending on the system. Better agreements can be obtained if a larger number of calibration parameters are included. Higher-order mass ratio terms in the effective-one-body Hamiltonian and radiation-reaction introduce phase corrections of at most 30 radians in a one year evolution. These corrections are usually one order of magnitude larger than those introduced by the spin of the small object in a one year evolution. These results suggest that the effective-one-body approach for extreme mass ratio inspirals is a good compromise between accuracy and computational price for LISA data analysis purposes.

by Damour, T. and Trias, M. and Nagar, A.
29 pages, 7 figures, 1 table

The coalescences of binary black hole (BBH) systems, here taken to be non-spinning, are among the most promising sources for gravitational wave (GW) ground-based detectors, such as LIGO and Virgo. To detect the GW signals emitted by BBHs, and measure the parameters of the source, one needs to have in hand a bank of GW templates that are both effectual (for detection), and accurate (for measurement). We study the effectualness and the accuracy of the two types of parametrized banks of templates that are directly defined in the frequency-domain by means of closed-form expressions, namely ‘post-Newtonian’ (PN) and ‘phenomenological’ models. In absence of knowledge of the exact waveforms, our study assumes as fiducial, target waveforms the ones generated by the most accurate version of the effective one body (EOB) formalism. We find that, for initial GW detectors the use, at each point of parameter space, of the best closed-form template (among PN and phenomenological models) leads to an effectualness >97% over the entire mass range and >99% in an important fraction of parameter space; however, when considering advanced detectors, both of the closed-form frequency-domain models fail to be effectual enough in significant domains of the two-dimensional [total mass and mass ratio] parameter space. Moreover, we find that, both for initial and advanced detectors, the two closed-form frequency-domain models fail to satisfy the minimal required accuracy standard in a very large domain of the two-dimensional parameter space. In addition, a side result of our study is the determination, as a function of the mass ratio, of the maximum frequency at which a frequency-domain PN waveform can be ‘joined’ onto a NR-calibrated EOB waveform without undue loss of accuracy.

by Favata, Marc
26 pages, 2 figures, 2 tables

[abridged] Barack & Sago have recently computed the shift of the innermost stable circular orbit (ISCO) due to the conservative self-force that arises from the finite-mass of an orbiting test-particle. This is one of the first concrete results of the self-force program, and provides an exact point of comparison with approximate post-Newtonian (PN) computations of the ISCO. Here this exact ISCO shift is compared with nearly all known PN-based methods. These include both “non-resummed” and “resummed” approaches (the latter reproduce the test-particle limit by construction). The best agreement with the exact result is found from effective-one-body (EOB) calculations that are fit to numerical relativity simulations. However, if one considers uncalibrated methods based only on the currently-known 3PN-order conservative dynamics, the best agreement is found from the gauge-invariant ISCO condition of Blanchet and Iyer (2003). This method reproduces the exact test-particle limit without any resummation. A comparison of PN methods with the equal-mass ISCO is also performed. The results of this study suggest that the EOB approach—while exactly incorporating the conservative test-particle dynamics—does not (in the absence of calibration) incorporate conservative self-force effects more accurately than standard PN methods. I also consider how the conservative self-force ISCO shift, combined with numerical relativity computations of the ISCO, can be used to constrain our knowledge of (1) the EOB effective metric, (2) phenomenological inspiral-merger-ringdown templates, and (3) 4PN and 5PN order terms in the PN orbital energy. These constraints could help in constructing better gravitational-wave templates. Lastly, I suggest a new method to calibrate unknown PN-terms in inspiral templates using “low-cost” numerical-relativity calculations.

by Barack, Leor and Damour, Thibault and Sago, Norichika
25 pages, 5 eps figures

Using a recently presented numerical code for calculating the Lorenz-gauge gravitational self-force (GSF), we compute the $latex O(m)$ conservative correction to the precession rate of the small-eccentricity orbits of a particle of mass $latex m$ moving around a Schwarzschild black hole of mass $latex {\mathsf M}\gg m$. Specifically, we study the gauge-invariant function $latex \rho(x)$, where $latex \rho$ is defined as the $latex O(m)$ part of the dimensionless ratio $latex (\hat\Omega_r/\hat\Omega_{\varphi})^2$ between the squares of the radial and azimuthal frequencies of the orbit, and where $latex x=[Gc^{-3}({\mathsf M}+m)\hat\Omega_{\varphi}]^{2/3}$ is a gauge-invariant measure of the dimensionless gravitational potential (mass over radius) associated with the mean circular orbit. Our GSF computation of the function $latex \rho(x)$ in the interval $latex 0<x\leq 1/6$ determines, for the first time, the {\em strong-field behavior} of a combination of two of the basic functions entering the Effective One Body (EOB) description of the conservative dynamics of binary systems. We show that our results agree well in the weak-field regime (small $latex x$) with the 3rd post-Newtonian (PN) expansion of the EOB results, and that this agreement is improved when taking into account the analytic values of some of the logarithmic-running terms occurring at higher PN orders. Furthermore, we demonstrate that GSF data give access to higher-order PN terms of $latex \rho(x)$ and can be used to set useful new constraints on the values of yet-undetermined EOB parameters. Most significantly, we observe that an {\em excellent global representation} of $latex \rho(x)$ can be obtained using a simple `two-point' Pad\'{e} approximant which combines 3PN knowledge at $latex x=0$ with GSF information at a single strong-field point (say, $latex x=1/6$).

by Barausse, Enrico and Buonanno, Alessandra
22 pages, 9 figures

Building on a recent paper in which we computed the canonical Hamiltonian of a spinning test particle in curved spacetime, at linear order in the particle’s spin, we work out an improved effective-one-body (EOB) Hamiltonian for spinning black-hole binaries. As in previous descriptions, we endow the effective particle not only with a mass m, but also with a spin S*. Thus, the effective particle interacts with the effective Kerr background (having spin S_Kerr) through a geodesic-type interaction and an additional spin-dependent interaction proportional to S*. When expanded in post-Newtonian (PN) orders, the EOB Hamiltonian reproduces the leading order spin-spin coupling and the spin-orbit coupling through 2.5PN order, for any mass-ratio. Also, it reproduces all spin-orbit couplings in the test-particle limit. Similarly to the test-particle limit case, when we restrict the EOB dynamics to spins aligned or antialigned with the orbital angular momentum, for which circular orbits exist, the EOB dynamics has several interesting features, such as the existence of an innermost stable circular orbit, a photon circular orbit, and a maximum in the orbital frequency during the plunge subsequent to the inspiral. These properties are crucial for reproducing the dynamics and gravitational-wave emission of spinning black-hole binaries, as calculated in numerical relativity simulations.

by Pan, Yi and Buonanno, Alessandra and Buchman, Luisa T. and Chu, Tony and Kidder, Lawrence E. and Pfeiffer, Harald P. and Scheel, Mark A.
15 pages, 8 figures

We present the first attempt at calibrating the effective-one-body (EOB) model to accurate numerical-relativity simulations of spinning, non-precessing black-hole binaries. Aligning the EOB and numerical waveforms at low frequency over a time interval of 1000M, we first estimate the phase and amplitude errors in the numerical waveforms and then minimize the difference between numerical and EOB waveforms by calibrating a handful of EOB-adjustable parameters. In the equal-mass, spin aligned case, we find that phase and fractional amplitude differences between the numerical and EOB (2,2) mode can be reduced to 0.01 radians and 1%, respectively, over the entire inspiral waveforms. In the equal-mass, spin anti-aligned case, these differences can be reduced to 0.13 radians and 1% during inspiral and plunge, and to 0.4 radians and 10% during merger and ringdown. The waveform agreement is within numerical errors in the spin aligned case while slightly over numerical errors in the spin anti-aligned case. Using Enhanced LIGO and Advanced LIGO noise curves, we find that the overlap between the EOB and the numerical (2,2) mode, maximized over the initial phase and time of arrival, is larger than 0.999 for binaries with total mass 30-200Ms. In addition to the leading (2,2) mode, we compare four subleading modes. We find good amplitude and frequency agreements between the EOB and numerical modes for both spin configurations considered, except for the (3,2) mode in the spin anti-aligned case. We believe that the larger difference in the (3,2) mode is due to the lack of knowledge of post-Newtonian spin effects in the higher modes.

by Damour, Thibault and Nagar, Alessandro
21 pages, 5 figures. Submitted to Phys. Rev. D

The late part of the gravitational wave signal of binary neutron star inspirals can in principle yield crucial information on the nuclear equation of state via its dependence on relativistic tidal parameters. In the hope of analytically describing the gravitational wave phasing during the late inspiral (essentially up to contact) we propose an extension of the effective one body (EOB) formalism which includes tidal effects. We compare the prediction of this tidal-EOB formalism to recently computed nonconformally flat quasi-equilibrium circular sequences of binary neutron star systems. Our analysis suggests the importance of higher-order (post-Newtonian) corrections to tidal effects, even beyond the first post-Newtonian order, and their tendency to {\it significantly} increase the “effective tidal polarizability” of neutron stars. We compare the EOB predictions to some recently advocated, nonresummed, post-Newtonian based (“Taylor-T4”) description of the phasing of inspiralling systems. This comparison shows the strong sensitivity of the late-inspiral phasing to the choice of the analytical model, but raises the hope that a sufficiently accurate numerical–relativity–“calibrated” EOB model might give us a reliable handle on the nuclear equation of state

by Damour, Thibault
44 pages

We discuss various ways in which the computation of conservative Gravitational Self Force (GSF) effects on a point mass moving in a Schwarzschild background can inform us about the basic building blocks of the Effective One-Body (EOB) Hamiltonian. We display the information which can be extracted from the recently published GSF calculation of the first-GSF-order shift of the orbital frequency of the last stable circular orbit, and we combine this information with the one recently obtained by comparing the EOB formalism to high-accuracy numerical relativity (NR) data on coalescing binary black holes. The information coming from GSF data helps to break the degeneracy (among some EOB parameters) which was left after using comparable-mass NR data to constrain the EOB formalism. We suggest various ways of obtaining more information from GSF computations: either by studying eccentric orbits, or by focussing on a special zero-binding zoom-whirl orbit. We show that logarithmic terms start entering the post-Newtonian expansions of various (EOB and GSF) functions at the fourth post-Newtonian (4PN) level, and we analytically compute the first logarithm entering a certain, gauge-invariant “redshift” GSF function (defined along the sequence of circular orbits).

by Yunes, Nicolas and Buonanno, Alessandra and Hughes, Scott A. and Miller, M. Coleman and Pan, Yi
4 pages, 3 figures, submitted to Phys. Rev. Letters

We present the first models of extreme-mass-ratio inspirals within the effective-one-body (EOB) formalism, focusing on quasi-circular orbits into non-rotating black holes. We show that the phase difference and (Newtonian normalized) amplitude difference between EOB and Teukolsky-based gravitational waveforms can be reduced to < 0.1 rads and < 0.002, respectively, after a 2-year evolution. The inclusion of post-Newtonian self-force terms in the EOB approach leads to a phase disagreement of ~6-27 rads after a 2-year evolution. Such inclusion could also allow for the EOB modeling of waveforms from intermediate-mass ratio, quasi-circular inspirals.

by Buonanno, Alessandra and Iyer, Bala and Ochsner, Evan and Pan, Yi and Sathyaprakash, B. S.
27 pages, 8 figures, 4 tables, submitted to PRD

The two-body dynamics in general relativity has been solved perturbatively using the post-Newtonian (PN) approximation. The evolution of the orbital phase and the emitted gravitational radiation are now known to a rather high order up to O(v^8), v being the characteristic velocity of the binary. The orbital evolution, however, cannot be specified uniquely due to the inherent freedom in the choice of parameter used in the PN expansion as well as the method pursued in solving the relevant differential equations. The goal of this paper is to determine the (dis)agreement between different PN waveform families in the context of initial and advanced gravitational-wave detectors. The waveforms employed in our analysis are those that are currently used by Initial LIGO/Virgo, that is the time-domain PN models TaylorT1, TaylorT2, TaylorT3, TaylorT4 and TaylorEt, the effective one-body (EOB) model, and the Fourier-domain representation TaylorF2. We examine the overlaps of these models with one another and with the prototype effective one-body model (calibrated to numerical relativity simulations, as currently used by initial LIGO) for a number of different binaries at 2PN, 3PN and 3.5PN orders to quantify their differences and to help us decide whether there exist preferred families that are the most appropriate as search templates. We conclude that as long as the total mass remains less than a certain upper limit M_crit, all template families at 3.5PN order (except TaylorT3 and TaylorEt) are equally good for the purpose of detection. The value of M_crit is found to be ~ 12M_Sun for Initial, Enhanced and Advanced LIGO. From a purely computational point of view we recommend that 3.5PN TaylorF2 be used below Mcrit and EOB calibrated to numerical relativity simulations be used for total binary mass M > Mcrit.

by Favata, Marc
4 pages, 3 figures

Some astrophysical sources of gravitational-waves can produce a “memory effect,” which causes a permanent displacement of the test masses in a freely-falling gravitational-wave detector. The Christodoulou memory is a particularly interesting nonlinear form of memory that arises from the gravitational-wave stress-energy tensor’s contribution to the distant gravitational-wave field. This nonlinear memory contributes a non-oscillatory component to the gravitational-wave signal at leading (Newtonian-quadrupole) order in the waveform amplitude. Previous computations of the memory and its detectability considered only the inspiral phase of binary black hole coalescence. Using an “effective-one-body” (EOB) approach calibrated to numerical relativity simulations, as well as a simple fully-analytic model, the Christodoulou memory is computed for the inspiral, merger, and ringdown. The memory will be very difficult to detect with ground-based interferometers, but is likely to be observable in supermassive black hole mergers with LISA out to a redshift of two. Detection of the nonlinear memory could serve as an experimental test of the ability of gravity to “gravitate.”

by Buonanno, Alessandra and Pan, Yi and Pfeiffer, Harald P. and Scheel, Mark A. and Buchman, Luisa T. and Kidder, Lawrence E.
19 pages, 19 figures

We calibrate the effective-one-body (EOB) model to an accurate numerical simulation of an equal-mass, non-spinning binary black-hole coalescence produced by the Caltech-Cornell collaboration. Aligning the EOB and numerical waveforms at low frequency over a time interval of ~1000M, and taking into account the uncertainties in the numerical simulation, we investigate the significance and degeneracy of the EOB adjustable parameters during inspiral, plunge and merger, and determine the minimum number of EOB adjustable parameters that achieves phase and amplitude agreements on the order of the numerical error. We find that phase and fractional amplitude differences between the numerical and EOB values of the dominant gravitational wave mode h_{22} can be reduced to 0.02 radians and 2%, respectively, until a time 26 M before merger, and to 0.1 radians and 10%, at a time 16M after merger (during ringdown), respectively. Using LIGO, Enhanced LIGO and Advanced LIGO noise curves, we find that the overlap between the EOB and the numerical h_{22}, maximized only over the initial phase and time of arrival, is larger than 0.999 for equal-mass binary black holes with total mass 30-150 Msun. In addition to the leading gravitational mode (2,2), we compare the dominant subleading modes (4,4) and (3,2) and find phase and amplitude differences on the order of the numerical error. We also determine the mass-ratio dependence of one of the EOB adjustable parameters by fitting to numerical {\it inspiral} waveforms for black-hole binaries with mass ratios 2:1 and 3:1. These results improve and extend recent successful attempts aimed at providing gravitational-wave data analysts the best analytical EOB model capable of interpolating accurate numerical simulations.

by Damour, Thibault and Nagar, Alessandro
5 pages, 5 figures, to apper as a Phys. Rev. D Rapid Communication

We present an analytical formalism, within the Effective-One-Body framework, which predicts gravitational-wave signals from inspiralling and coalescing black-hole binaries that agree, within numerical errors, with the results of the currently most accurate numerical relativity simulations for several different mass ratios. In the equal-mass case, the gravitational wave energy flux predicted by our formalism agrees, within numerical errors, with the most accurate numerical-relativity energy flux. We think that our formalism opens a realistic possibility of constructing a sufficiently accurate, large bank of gravitational wave templates, as needed both for detection and data analysis of (non spinning) coalescing binary black holes.

by Walther, Benny and Bruegmann, Bernd and Mueller, Doreen
20 pages, 11 figures, pdflatex

Black hole binaries on non-eccentric orbits form an important subclass of gravitational wave sources, but it is a non-trivial issue to construct numerical initial data with minimal initial eccentricity for numerical simulations. We compute post-Newtonian orbital parameters for quasi-spherical orbits using the method of Buonanno, Chen and Damour (2006) and examine the resulting eccentricity in numerical simulations. Four different methods are studied resulting from the choice of Taylor-expanded or effective-one-body Hamiltonians, and from two choices for the energy flux. The eccentricity increases for unequal masses and for spinning black holes, but remains smaller than that obtained from previous post-Newtonian approaches. The effective-one-body Hamiltonian offers advantages for decreasing initial separation as expected, but in the context of this study also performs significantly better than the Taylor-expanded Hamiltonian for binaries with spin.