We present a new algorithm for evolving orbiting black-hole binaries that does not require excision or a corotating shift. Our algorithm is based on a novel technique to handle the singular puncture conformal factor. This system, based on the BSSN formulation of Einstein's equations, when used with a 'pre-collapsed' initial lapse, is non-singular at the start of the evolution, and remains nonsingular and stable provided that a good choice is made for the gauge. As a test case, we use this technique to fully evolve orbiting black-hole binaries from near the Innermost Stable Circular Orbit (ISCO) regime. We show fourth order convergence of waveforms and compute the radiated gravitational energy and angular momentum from the plunge. These results are in good agreement with those predicted by the Lazarus approach.PACS numbers: 04.25. Dm, 04.25.Nx, 04.30.Db, 04.70.Bw One of the most significant goals of numerical relativity is to compute accurate gravitational waveforms from astrophysically realistic simulations of merging black-hole binaries. The expectation of very strong gravitational wave emission from the merger of two black holes, and some of the newest astrophysical observations, from supermassive galactic nuclei just about to merge [1] to stellar size black-hole binaries, make these systems one of the most extraordinary astrophysical objects under study today. Binary black hole mergers are expected not only to provide information about the history and formation of the binary system but also to provide important precise tests of strong-field, highly dynamical relativity.Motivated by the forthcoming observations of groundbased gravitational wave detectors, such as LIGO [2], and by the next generation of space-based detectors, such as LISA [3], the numerical relativity community has dedicated a great deal of effort to solving the binary-blackhole problem over the past few decades. After the 'Binary Black Hole Grand Challenge' [4] several new approaches have been pursued in the attempt to produce stable three-dimensional (3D) numerical codes capable of evolving the full Einstein field equations in the absence of any symmetry. This includes the introduction of new formulations of these equations and the development of numerical techniques for accurate evolutions of black-hole binaries, such as higher order finite differencing, spectral methods, and adaptive mesh refinement (AMR) (see Ref.[5] and references therein).The calculation of the gravitational radiation emitted from plunging black-hole binaries was pioneered through the use of the Lazarus approach, which bridges numerical relativity and perturbative techniques to extract approximate gravitational waveforms [6,7,8]. More recently important progress has been made toward evolving orbiting binary-black-hole spacetimes with the use of stable full 3D numerical relativity codes using corotating gauge conditions and singularity excision [9,10,11].Here we present a novel technique for evolving orbiting black holes based on puncture data. This technique does not ...

We describe a numerical method for calculating the (3+1) dimensional general relativistic hydrodynamics of a coalescing neutron-star binary system. The relativistic field equations are solved at each time slice with a spatial 3-metric chosen to be conformally flat. Against this solution to the general relativistic field equations the hydrodynamic variables and gravitational radiation are allowed to respond. The gravitational radiation signal is derived via a multipole expansion of the metric perturbation to the hexadecapole (l = 4) order including both mass and current moments and a correction for the slow motion approximation. Using this expansion, the effect of gravitational radiation on the system evolution can also be recovered by introducing an acceleration term in the matter evolution. In the present work we illustrate the method by applying this model to evaluate various orbits of two neutron stars with a gravitational mass of 1.45 M⊙ near the time of the final merger. We discuss the evidence that, for a realistic neutron star equation of state, general relativistic effects may cause the stars to individually collapse into black holes prior to merging. Also, the strong fields cause the last stable orbit to occur at a larger separation distance and lower frequency than previously estimated.PACS Numbers: 04.20.Jb, 04.30.+x, 47.75+f,, 95.30.Lz, 95.30.Sf 97.60.Jd,

We have performed ab initio neutrino radiation hydrodynamics simulations in three and two spatial dimensions (3D and 2D) of core-collapse supernovae from the same 15 M progenitor through 440 ms after core bounce. Both 3D and 2D models achieve explosions, however, the onset of explosion (shock revival) is delayed by ∼100 ms in 3D relative to the 2D counterpart and the growth of the diagnostic explosion energy is slower. This is consistent with previously reported 3D simulations utilizing iron-core progenitors with dense mantles. In the ∼100 ms before the onset of explosion, diagnostics of neutrino heating and turbulent kinetic energy favor earlier explosion in 2D. During the delay, the angular scale of convective plumes reaching the shock surface grows and explosion in 3D is ultimately lead by a single, large-angle plume, giving the expanding shock a directional orientation not dissimilar from those imposed by axial symmetry in 2D simulations. We posit that shock revival and explosion in the 3D simulation may be delayed until sufficiently large plumes form, whereas such plumes form more rapidly in 2D, permitting earlier explosions.

We present four ab initio axisymmetric core-collapse supernova simulations initiated from 12, 15, 20, and 25 M  zero-age main sequence progenitors. All of the simulations yield explosions and havebeen evolved for at least 1.2 s after core bounce and 1 s after material first becomes unbound. These simulations were computed with our CHIMERA code employing RbR spectral neutrino transport, special and general relativistic transport effects, and state-of-the-art neutrino interactions. Continuing the evolution beyond 1 s after core bounce allows the explosions to develop more fully and the processes involved in powering the explosions to become more clearly evident. We compute explosion energy estimates, including the negative gravitational binding energy of the stellar envelope outside the expanding shock, of 0.34, 0.88, 0.38, and 0.70 Bethe (B≡10 51 erg) and increasing at 0.03, 0.15, 0.19, and 0.52 B s 1 -, respectively, for the 12, 15, 20, and 25 M  models at the endpoint of this report. We examine the growth of the explosion energy in our models through detailed analyses of the energy sources and flows. We discuss how the explosion energies may be subject to stochastic variations as exemplfied by the effect of the explosion geometry of the 20 M  model in reducing its explosion energy. We compute the proto-neutron star masses and kick velocities. We compare our results for the explosion energies and ejected Ni 56 masses against some observational standards despite the large error bars in both models and observations.

We present an overview of four ab initio axisymmetric core-collapse supernova simulations employing detailed spectral neutrino transport computed with our CHIMERA code and initiated from Woosley & Heger (2007) progenitors of mass 12, 15, 20, and 25 M ⊙ . All four models exhibit shock revival over ∼ 200 ms (leading to the possibility of explosion), driven by neutrino energy deposition. Hydrodynamic instabilities that impart substantial asymmetries to the shock aid these revivals, with convection appearing first in the 12 M ⊙ model and the standing accretion shock instability (SASI) appearing first in the 25 M ⊙ model. Three of the models have developed pronounced prolate morphologies (the 20 M ⊙ model has remained approximately spherical). By 500 ms after bounce the mean shock radii in all four models exceed 3,000 km and the diagnostic explosion energies are 0.33, 0.66, 0.65, and 0.70 Bethe (B = 10 51 ergs) for the 12, 15, 20, and 25 M ⊙ models, respectively, and are increasing. The three least massive of our models are already sufficiently energetic to completely unbind the envelopes of their progenitors (i.e., to explode), as evidenced by our best estimate of their explosion energies, which first become positive at 320, 380, and 440 ms after bounce. By 850 ms the 12 M ⊙ diagnostic explosion energy has saturated at 0.38 B, and our estimate for the final kinetic energy of the ejecta is ∼ 0.3 B, which is comparable to observations for lower-mass progenitors.

We consider black holes resulting from binary black hole mergers. By fitting to numerical results we construct analytic formulas that predict the mass and spin of the final black hole. Our formulas are valid for arbitrary initial spins and mass ratios and agree well with available numerical simulations. We use our spin formula in the context of two common merger scenarios for supermassive galactic black holes. We consider the case of isotropically distributed initial spin orientations (when no surrounding matter is present) and also the case when matter closely aligns the spins with the orbital angular momentum. The spin magnitude of black holes resulting from successive generations of mergers (with symmetric mass ratio η) has a mean of 1.73η + 0.28 in the isotropic case and 0.94 for the closely aligned case.

We study identical mass black hole binaries with spins perpendicular to the binary's orbital plane. These binaries have individual spins ranging from s/m 2 = −0.90 to 0.90, (s1 = s2 in all cases) which is near the limit possible with standard Bowen-York puncture initial data. The extreme cases correspond to the largest initial spin simulations to date. Our results expand the parameter space covered by Rezzolla et al. and, when combining both data sets, we obtain estimations for the minimum and maximum values for the intrinsic angular momenta of the remnant of binary black hole mergers of J/M 2 = 0.341 ± 0.004 and 0.951 ± 0.004 respectively. Note, however, that these values are reached through extrapolation to the singular cases |s1| = |s2| = 1 and thus remain as estimates until full-fledged numerical simulations provide confirmation.

The Numerical–Relativity–Analytical–Relativity (NRAR) collaboration is a joint effort between members of the numerical relativity, analytical relativity and gravitational-wave data analysis communities. The goal of the NRAR collaboration is to produce numerical-relativity simulations of compact binaries and use them to develop accurate analytical templates for the LIGO/Virgo Collaboration to use in detecting gravitational-wave signals and extracting astrophysical information from them. We describe the results of the first stage of the NRAR project, which focused on producing an initial set of numerical waveforms from binary black holes with moderate mass ratios and spins, as well as one non-spinning binary configuration which has a mass ratio of 10. All of the numerical waveforms are analysed in a uniform and consistent manner, with numerical errors evaluated using an analysis code created by members of the NRAR collaboration. We compare previously-calibrated, non-precessing analytical waveforms, notably the effective-one-body (EOB) and phenomenological template families, to the newly-produced numerical waveforms. We find that when the binary's total mass is ∼100–200M⊙, current EOB and phenomenological models of spinning, non-precessing binary waveforms have overlaps above 99% (for advanced LIGO) with all of the non-precessing-binary numerical waveforms with mass ratios ⩽4, when maximizing over binary parameters. This implies that the loss of event rate due to modelling error is below 3%. Moreover, the non-spinning EOB waveforms previously calibrated to five non-spinning waveforms with mass ratio smaller than 6 have overlaps above 99.7% with the numerical waveform with a mass ratio of 10, without even maximizing on the binary parameters.