The Effective One-Body Description of the Two-Body Problem

Damour, Thibault; Nagar, Alessandro

doi:10.1007/978-90-481-3015-3_7

Cited by 110 publications

(199 citation statements)

References 132 publications

(472 reference statements)

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“…A successful way to recast PN results and combine them with information from NR simulations is the effective-one-body (EOB) formalism [35,36]. This framework has been refined to devise an accurate, semi-analytical description of the dynamics and GW signals of coalescing BHs with arbitrary spins and mass ratios [37][38][39]. Tidal effects have also been included in the EOB model, starting with the first analysis [40] that used Newtonian and partial 1PN tidal information [41] and was compared against NR simulations in [42].…”

Section: Introductionmentioning

confidence: 99%

Comprehensive comparison of numerical relativity and effective-one-body results to inform improvements in waveform models for binary neutron star systems

Dietrich

Hinderer

2017

Phys. Rev. D

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We present a detailed comparison between tidal effective-one-body (EOB) models and new stateof-the-art numerical relativity simulations for non-spinning binary neutron star systems. This comparison is the most extensive one to date, covering a wide range in the parameter space and encompassing the energetics of the binary, the periastron advance, the time and frequency evolution of the gravitational wave phase for the dominant mode, and several subdominant modes. We consider different EOB models with tidal effects that have been proposed, including the model with dynamical tides of [Phys.Rev.Lett. 116 (2016) no.18, 181101] and the gravitational self-force (GSF) inspired tidal EOB model of [Phys.Rev.Lett. 114 (2015) no.16, 161103]. The EOB model with dynamical tides leads to the best representation of the systems considered here, however, the differences to the GSF-inspired model are small. A common feature is that for systems where matter effects are large, i.e. stiff equations of state or small total masses, all EOB models underestimate the tidal effects and differences to the results from numerical relativity simulations become noticeable near the merger. We analyze this regime to diagnose the shortcomings of the models in the late inspiral, where the two neutron stars are no longer isolated bodies moving in vacuum. Our work will serve to guide further advances in modeling these systems.

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Section: Introductionmentioning

confidence: 99%

Comprehensive comparison of numerical relativity and effective-one-body results to inform improvements in waveform models for binary neutron star systems

Dietrich

Hinderer

2017

Phys. Rev. D

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“…A more recent approach, effective-one-body (EOB) theory, maps the binary's motion to that of a particle moving in an effective metric, generalizing the Newtonian reduced-mass treatment of the two-body problem [8,9]. This theory encompasses information from the former three approaches to calibrate the parameters that go into the theory, which allows it to model a binary system of any given mass-ratio.…”

Section: Introductionmentioning

confidence: 99%

Experimental mathematics meets gravitational self-force

2015

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It is now possible to compute linear in mass-ratio terms in the post-Newtonian (PN) expansion for compact binaries to very high orders using linear black hole perturbation theory applied to various invariants. For instance, a computation of the redshift invariant of a point particle in a circular orbit about a black hole in linear perturbation theory gives the linear-in-mass-ratio portion of the binding energy of a circular binary with arbitrary mass ratio. This binding energy, in turn, encodes the system's conservative dynamics. We give a method for extracting the analytic forms of these post-Newtonian coefficients from high-accuracy numerical data using experimental mathematics techniques, notably an integer relation algorithm. Such methods should be particularly important when the calculations progress to the considerably more difficult case of perturbations of the Kerr metric. As an example, we apply this method to the redshift invariant in Schwarzschild. Here we obtain analytic coefficients to 12.5PN, and higher-order terms in mixed analytic-numerical form to 21.5PN, including analytic forms for the complete 13.5PN coefficient, and all the logarithmic terms at 13PN. We have computed the individual modes to over 5000 digits, of which we use at most 1240 in the present calculation. At these high orders, an individual coefficient can have over 30 terms, including a wide variety of transcendental numbers, when written out in full. We are still able to obtain analytic forms for such coefficients from the numerical data through a careful study of the structure of the expansion. The structure we find also allows us to predict certain "leading logarithm"-type contributions to all orders. The additional terms in the expansion we obtain improve the accuracy of the PN series for the redshift observable, even in the very strongfield regime inside the innermost stable circular orbit, particularly when combined with exponential resummation.

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“…Despite the mathematical complexity of the problem, many results of the NR simulations can be reproduced accurately using semianalytical prescriptions (Damour & Nagar 2009;Buonanno et al 2009) based on post-Newtonian (PN) and BH perturbation theory. It is therefore not entirely surprising that the dimensionless spin of the remnant from a BH-binary merger, a fin = S fin /M 2 fin , can be described, with increasing accuracy, via simple prescriptions based on point particles (Hughes & Blandford 2003;Buonanno et al 2008;Kesden 2008), on fits to the NR data (Rezzolla et al 2008b(Rezzolla et al , 2008cTichy & Marronetti 2008;, or on a combination of the two approaches (Rezzolla et al 2008a;see Rezzolla 2009 for a review).…”

Section: Introductionmentioning

confidence: 99%

Predicting the Direction of the Final Spin From the Coalescence of Two Black Holes

Barausse

Rezzolla

2009

ApJ

196

265

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Knowledge of the spin of the black hole resulting from the merger of a generic black-hole binary is of great importance for studying the cosmological evolution of supermassive black holes. Several attempts have been made to model the spin via simple expressions exploiting the results of numerical-relativity simulations. While these expressions are in reasonable agreement with the simulations, they neglect the precession of the binary's orbital plane, and cannot therefore be applied directly-i.e., without evolving the system to small separations using post-Newtonian theory-to binaries with separations larger than a few hundred gravitational radii. While not a problem in principle, this may be impractical if the formulas are employed in cosmological merger trees or N-body simulations, which provide the spins and angular momentum of the two black holes when their separation is of hundreds or thousands of gravitational radii. The formula that we propose is instead built on improved assumptions and gives, for any separation, a very accurate prediction both for the norm of the final spin and for its direction. By comparing with the numerical data, we also show that the final-spin direction is very accurately aligned with the binary's total angular momentum at large separation. Hence, observations of the final-spin direction (e.g., via a jet) can provide information on the binary's orbital plane at large separations and could be relevant, for instance, for studying X-shaped radio sources.

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The Effective One-Body Description of the Two-Body Problem

Cited by 110 publications

References 132 publications

Comprehensive comparison of numerical relativity and effective-one-body results to inform improvements in waveform models for binary neutron star systems

Comprehensive comparison of numerical relativity and effective-one-body results to inform improvements in waveform models for binary neutron star systems

Experimental mathematics meets gravitational self-force

Predicting the Direction of the Final Spin From the Coalescence of Two Black Holes

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