We study dynamics and radiation generation in the last few orbits and merger of a binary black hole system, applying recently developed techniques for simulations of moving black holes. Our analysis of the gravitational radiation waveforms and dynamical black hole trajectories produces a consistent picture for a set of simulations with black holes beginning on circular-orbit trajectories at a variety of initial separations. We find profound agreement at the level of 1% among the simulations for the last orbit, merger and ringdown. We are confident that this part of our waveform result accurately represents the predictions from Einstein's General Relativity for the final burst of gravitational radiation resulting from the merger of an astrophysical system of equal-mass nonspinning black holes. The simulations result in a final black hole with spin parameter a/m = 0.69. We also find good agreement at a level of roughly 10% for the radiation generated in the preceding few orbits.

We present new techniqes for evolving binary black hole systems which allow the accurate determination of gravitational waveforms directly from the wave zone region of the numerical simulations. Rather than excising the black hole interiors, our approach follows the "puncture" treatment of black holes, but utilzing a new gauge condition which allows the black holes to move successfully through the computational domain. We apply these techniques to an inspiraling binary, modeling the radiation generated during the final plunge and ringdown. We demonstrate convergence of the waveforms and good conservation of mass-energy, with just over 3% of the system's mass converted to gravitional radiation.PACS numbers: 04.25. Dm, 04.30.Db, 04.70.Bw, 95.30.Sf, 97.60.Lf Coalescing comparable mass black hole binaries are prodigious sources of gravitational waves. The final merger of these systems, in which the black holes leave their quasicircular orbits and plunge together to produce a highly distorted black hole that "rings down" to a quiescent Kerr state, will produce a strong burst of gravitational radiation. Such mergers are expected to be among the strongest sources for ground-based gravitational wave detectors, which will observe the mergers of stellar-mass and intermediate mass black hole binaries, and the spacebased LISA, which will detect mergers of massive black hole binaries. Observations of these systems will provide an unprecedented look into the strong-field dynamical regime of general relativity. With the first-generation of ground-based interferometers reaching maturity and LISA moving forward through the formulation phase, the need for accurate merger waveforms has become urgent.Such waveforms can only be obtained through 3-D numerical relativity simulations of the full Einstein equations. While this has proven to be a very challenging undertaking, new developments allow an optimistic outlook. Full 3-D evolutions of binary black holes, in which regions within the horizons have been excised from the computational grid, have recently been carried out. Using co-rotating coordinates, so that the holes remain fixed on the grid as the system evolves, a binary has been evolved through a little more than a full orbit [1] as well as through a plunge, merger, and ringdown [2], though without being able to extract gravitational waveforms. More recently, a simulation in which excised black holes move through the grid in a single plunge-orbit, merger, and ringdown has been accomplished, with the calculation of a waveform [3].In this Letter, we report the results of new simulations of inspiraling binary black holes through merger and ringdown. These have been carried out using new techniques which allow the black holes to move through the coordinate grid without the need for excision [17].Using fixed mesh refinement, we are able to resolve both the dynamical region where the black holes inspiral (with length scales ∼ M , where M is the total system mass) and the outer regions where the gravitational waves propagate (leng...

Recent developments in numerical relativity have made it possible to reliably follow the coalescence of two black holes from near the innermost stable circular orbit to final ringdown. This opens up a wide variety of exciting astrophysical applications of these simulations. Chief among these is the net kick received when two unequal mass or spinning black holes merge. The magnitude of this kick has bearing on the production and growth of supermassive black holes during the epoch of structure formation, and on the retention of black holes in stellar clusters. Here we report the first accurate numerical calculation of this kick, for two nonspinning black holes in a 1.5 : 1 mass ratio, which is expected on the basis of analytic considerations to give a significant fraction of the maximum possible recoil. We have performed multiple runs with different initial separations, orbital angular momenta, resolutions, extraction radii, and gauges. The full range of our kick speeds is 86-116 km s , and the Ϫ1 most reliable runs give kicks between 86 and 97 km s . This is intermediate between the estimates from two Ϫ1 recent post-Newtonian analyses and suggests that at redshifts , halos with masses Շ will have 9 z տ 10 10 M , difficulty retaining coalesced black holes after major mergers.

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Coalescing binary black hole mergers are expected to be the strongest gravitational wave sources for ground-based interferometers, such as the LIGO, VIRGO, and GEO600, as well as the space-based interferometer LISA. Until recently it has been impossible to reliably derive the predictions of general relativity for the final merger stage, which takes place in the strong-field regime. Recent progress in numerical relativity simulations is, however, revolutionizing our understanding of these systems. We examine here the specific case of merging equal-mass Schwarzschild black holes in detail, presenting new simulations in which the black holes start in the late-inspiral stage on orbits with very low eccentricity and evolve for 1200M through 7 orbits before merging. We study the accuracy and consistency of our simulations and the resulting gravitational waveforms, which encompass 14 cycle before merger, and highlight the importance of using frequency (rather than time) to set the physical reference when comparing models. Matching our results to post-Newtonian (PN) calculations for the earlier parts of the inspiral provides a combined waveform with less than one cycle of accumulated phase error through the entire coalescence. Using this waveform, we calculate signal-to-noise ratios (SNRs) for iLIGO, adLIGO, and LISA, highlighting the contributions from the late-inspiral and merger-ringdown parts of the waveform, which can now be simulated numerically. Contour plots of SNR as a function of z and M show that adLIGO can achieve SNR * 10 for some intermediate mass binary black holes (IMBBHs) out to z 1, and that LISA can see massive binary black holes (MBBHs) in the range 3 10 4 & M=M & 10 7 at SNR > 100 out to the earliest epochs of structure formation at z > 15.

Recent demonstrations of unexcised black holes traversing across computational grids represent a significant advance in numerical relativity. Stable and accurate simulations of multiple orbits, and their radiated waves, result. This capability is critically undergirded by a careful choice of gauge. Here we present analytic considerations which suggest certain gauge choices, and numerically demonstrate their efficacy in evolving a single moving puncture black hole.

We present convergent gravitational waveforms extracted from three-dimensional, numerical simulations in the wave zone and with causally disconnected boundaries. These waveforms last for multiple periods and are very accurate, showing a peak error to peak amplitude ratio of 2% or better. Our approach includes defining the Weyl scalar Ψ4 in terms of a three-plus-one decomposition of the Einstein equations; applying, for the first time, a novel algorithm due to Misner for computing spherical harmonic components of our wave data; and using fixed mesh refinement to focus resolution on non-linear sources while simultaneously resolving the wave zone and maintaining a causally disconnected computational boundary. We apply our techniques to a (linear) Teukolsky wave, and then to an equal mass, head-on collision of two black holes. We argue both for the quality of our results and for the value of these problems as standard test cases for wave extraction techniques.

We present an algorithm for treating mesh refinement interfaces in numerical relativity. We detail the behavior of the solution near such interfaces located in the strong field regions of dynamical black hole spacetimes, with particular attention to the convergence properties of the simulations. In our applications of this technique to the evolution of puncture initial data with vanishing shift, we demonstrate that it is possible to simultaneously maintain second order convergence near the puncture and extend the outer boundary beyond 100M, thereby approaching the asymptotically flat region in which boundary condition problems are less difficult and wave extraction is meaningful.Comment: 18 pages, 12 figures. Minor changes, final PRD versio