We present an improved numerical relativity (NR) calibration of the new effective-one-body (EOB) model for coalescing nonprecessing spinning black hole binaries recently introduced by Damour and ...Nagar Phys. Rev. D 90, 044018 (2014). We do so by comparing the EOB predictions to both the phasing and the energetics provided by two independent sets of NR data covering mass ratios 1< or =q< or =9.989 and dimensionless spin range -0.95< or = chi < or =+0.994. One set of data is a subset of the Simulating eXtreme Spacetimes (SXS) catalog of public waveforms; the other set consists of new simulations obtained with the Llama code plus Cauchy characteristic evolution. We present the first systematic computation of the gauge-invariant relation between the binding energy and the total angular momentum, E sub(b)j), for a large sample of, spin-aligned, SXS and Llama data. The dynamics of the EOB model presented here involves only two free functional parameters, one (ProQuest: Formulae and/or non-USASCII text omitted) entering the nonspinning sector, as a 5PN effective correction to the interaction potential, and one c sub(3)(a sub(1),a sub(2),nu) in the spinning sector, as an effective next-to-next-to-next-to-leading order correction to the spin-orbit coupling. These parameters are determined together with a third functional parameter Delta t sub(NQC)( chi ) entering the waveform by comparing the EOB phasing with the SXS phasing, the consistency of the energetics being checked afterwards. The quality of the analytical model for gravitational wave data analysis purposes is assessed by computing the EOB/NR faithfulness. Over the NR data sample and when varying the total mass between 20 and 200 M sub(middot in circle) the EOB/NR unfaithfulness (integrated over the NR frequency range) is found to vary between 99.493% and 99.984% with a median value of 99.944%.
The final evolution of a binary-black-hole system gives rise to a recoil velocity if an asymmetry is present in the emitted gravitational radiation. Measurements of this effect for nonspinning ...binaries with unequal masses have pointed out that kick velocities approximately 175 km/s can be reached for a mass ratio approximately 0.36. However, a larger recoil can be obtained for equal-mass binaries if the asymmetry is provided by the spins. Using two independent methods we show that the merger of such binaries yields velocities as large as approximately 440 km/s for black holes having unequal spins that are antialigned and parallel to the orbital angular momentum.
Significant advances in numerical simulations of black-hole binaries have recently been achieved using the puncture method. We examine how and why this method works by evolving a single black hole. ...The coordinate singularity and hence the geometry at the puncture are found to change during evolution, from representing an asymptotically flat end to being a cylinder. We construct an analytic solution for the stationary state of a black hole in spherical symmetry that matches the numerical result and demonstrates that the evolution is not dominated by artefacts at the puncture but indeed finds the analytical result.
Determining the final spin of a black hole (BH) binary is a question of key importance in astrophysics. Modeling this quantity in general is made difficult by the fact that it depends on the ...seven-dimensional space of parameters characterizing the two initial black holes. However, in special cases, when symmetries can be exploited, the description can become simpler. For BH binaries with unequal masses but with equal spins which are aligned with the orbital angular momentum, we show that the use of recent simulations and basic but exact constraints derived from the extreme mass-ratio limit allow us to model this quantity with a simple analytic expression. Despite the simple dependence, the expression models very accurately all of the available estimates, with errors of a couple of percent at most. We also discuss how to use the fit to predict when a Schwarzschild BH is produced by the merger of two spinning BHs, when the total angular momentum of the spacetime "flips" sign, or under what conditions the final BH is "spun up" by the merger. Finally, we suggest an extension of the fit to include unequal-spin binaries, thus potentially providing a complete description of the final spin from the coalescence of generic BH binaries with spins aligned to the orbital angular momentum.
In addition to the dominant oscillatory gravitational wave signals produced during binary inspirals, a non-oscillatory component arises from the nonlinear 'memory' effect, sourced by the emitted ...gravitational radiation. The memory grows significantly during the late-inspiral and merger, modifying the signal by an almost step-function profile, and making it difficult to model by approximate methods. We use numerical evolutions of binary black holes (BHs) to evaluate the nonlinear memory during late-inspiral, merger, and ringdown. We identify two main components of the signal: the monotonically growing portion corresponding to the memory, and an oscillatory part which sets in roughly at the time of merger and is due to the BH ringdown. Counterintuitively, the ringdown is most prominent for models with the lowest total spin. Thus, the case of maximally spinning BHs anti-aligned to the orbital angular momentum exhibits the highest signal-to-noise ratio (S/N) for interferometric detectors. The largest memory offset, however, occurs for highly spinning BHs, with an estimated value of h tot 20 0.24 in the maximally spinning case. These results are central to determining the detectability of nonlinear memory through pulsar timing array measurements.
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 E ...and the (reduced) angular momentum j of the system. We show that the relation E(j) is an accurate diagnostic of the dynamics of a black-hole binary in a highly relativistic regime. By comparing the numerical-relativity E(NR)(j) curve with the predictions of several analytic approximation schemes, we find that, while the canonically defined, nonresummed post-Newtonian-expanded E(PN)(j) relation exhibits large and growing deviations from E(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.
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