Richard A. Matzner

Gravitational Recoil from Spinning Binary Black Hole Mergers

The inspiraling and merger of binary black holes will likely involve black holes with not only unequal masses but also arbitrary spins. The gravitational radiation emitted by these binaries will carry angular as well as linear momentum. A net flux of emitted linear momentum implies that the black hole produced by the merger will experience a recoil or kick. Previous studies have focused on the recoil velocity from unequal-mass, nonspinning binaries. We present results from simulations of equal-mass but spinning black hole binaries and show how a significant gravitational recoil can also be obtained in these situations. We consider the case of black holes with opposite spins of magnitude a aligned and antialigned with the orbital angular momentum, with a the dimensionless spin parameter of the individual holes. For the initial setups under consideration, we find a recoil velocity of V = 475a km s-1. Supermassive black hole mergers producing kicks of this magnitude could result in the ejection of the final hole produced by the collision from the core of a dwarf galaxy.

Testing gravitational-wave searches with numerical relativity waveforms: results from the first Numerical INJection Analysis (NINJA) project

The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational-wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search algorithms using numerically generated waveforms and to foster closer collaboration between the numerical relativity and data analysis communities. We describe the results of the first NINJA analysis which focused on gravitational waveforms from binary black hole coalescence. Ten numerical relativity groups contributed numerical data which were used to generate a set of gravitational-wave signals. These signals were injected into a simulated data set, designed to mimic the response of the initial LIGO and Virgo gravitational-wave detectors. Nine groups analysed this data using search and parameter-estimation pipelines. Matched filter algorithms, un-modelled-burst searches and Bayesian parameter estimation and model-selection algorithms were applied to the data. We report the efficiency of these search methods in detecting the numerical waveforms and measuring their parameters. We describe preliminary comparisons between the different search methods and suggest improvements for future NINJA analyses.

Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration

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 binarys 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.

Binary black holes : Spin dynamics and gravitational recoil

We present a study of spinning black hole binaries focusing on the spin dynamics of the individual black holes as well as on the gravitational recoil acquired by the black hole produced by the merger. We consider two series of initial spin orientations away from the binary orbital plane. In one of the series, the spins are antialigned; for the second series, one of the spins points away from the binary along the line separating the black holes. We find a remarkable agreement between the spin dynamics predicted at 2nd post-Newtonian order and those from numerical relativity. For each configuration, we compute the kick of the final black hole. We use the kick estimates from the series with antialigned spins to fit the parameters in the Kidder kick formula, and verify that the recoil in the direction of the orbital angular momentum is {proportional_to}sin{theta} and on the orbital plane {proportional_to}cos{theta}, with {theta} the angle between the spin directions and the orbital angular momentum. We also find that the black hole spins can be well estimated by evaluating the isolated horizon spin on spheres of constant coordinate radius.

Testing General Relativity and gravitational physics using the LARES satellite

The discovery of the accelerating expansion of the Universe, thought to be driven by a mysterious form of “dark energy” constituting most of the Universe, has further revived the interest in testing Einstein’s theory of General Relativity. At the very foundation of Einstein’s theory is the geodesic motion of a small, structureless test-particle. Depending on the physical context, a star, planet or satellite can behave very nearly like a test-particle, so geodesic motion is used to calculate the advance of the perihelion of a planet’s orbit, the dynamics of a binary pulsar system and of an Earth-orbiting satellite. Verifying geodesic motion is then a test of paramount importance to General Relativity and other theories of fundamental physics. On the basis of the first few months of observations of the recently launched satellite LARES, its orbit shows the best agreement of any satellite with the test-particle motion predicted by General Relativity. That is, after modelling its known non-gravitational perturbations, the LARES orbit shows the smallest deviations from geodesic motion of any artificial satellite: its residual mean acceleration away from geodesic motion is less than

Interaction of U(1) cosmic strings: numerical intercommunication

\ensuremath 0.5\times10^{-12}

Big Bang Nucleosynthesis and the Quark - Hadron Transition

m/s^2. LARES-type satellites can thus be used for accurate measurements and for tests of gravitational and fundamental physics. Already with only a few months of observation, LARES provides smaller scatter in the determination of several low-degree geopotential coefficients (Earth gravitational deviations from sphericity) than available from observations of any other satellite or combination of satellites.

LIGHT PROPAGATION IN INHOMOGENEOUS UNIVERSES. I. METHODOLOGY AND PRELIMINARY RESULTS

The putative ability of cosmic strings to act as seeds for galaxies depends on the efficiency of a number of processes that produce an initial network of strings and then allow them to evolve to a population that can act as condensation centers. Here the classical field theory of the interaction of cosmic strings is studied. A limited survey of numerical evolutions has been carried out. Calculations have been carried out showing parallel string–string repulsion; string–antistring (i.e., antiparallel string) annihilation with initial velocity v=0 and v=0.75; string–string collision at right angles with v/c=0.1, 0.5, 0.75, 0.85, 0.9c, with v/c=0.75 at θ=π/4 and at θ=3π/4, and with v/c=0.9 at θ=7π/8; and string–string and string–antistring collisions with v/c=0.9 and v/c=0.95. Intercommutation occurs in all situations so far investigated except that string–antistring collision with v/c≳0.90 apparently leads to reemergence, i.e., no intercommutation. All simulations have a ‘‘sombrero’’ potential V (φ)=λ(‖φ‖2−σ2)2 and a gauge field coupling e. (The numerical results are obtained with λ=0.01, e=0.2, giving the gauge field a slightly longer scale length than that of the scalar field.)

Superkicks in hyperbolic encounters of binary black holes.

An examination and brief review is made of the effects of quark-hadron transition induced fluctuations on Big Bang nucleosynthesis. It is shown that cosmologically critical densities in baryons are difficult to reconcile with observation, but the traditional baryon density constraints from homogeneous calculations might be loosened by as much as 50 percent, to 0.3 of critical density, and the limit on the number of neutrino flavors remains about N(sub nu) is less than or approximately 4. To achieve baryon densities of greater than or approximately 0.3 of critical density would require initial density contrasts R is much greater the 10(exp e), whereas the simplest models for the transition seem to restrict R to less than of approximately 10(exp 2). 43 refs.

Boosted three-dimensional black-hole evolutions with singularity excision

We describe a numerical algorithm that simulates the propagation of light in inhomogeneous universes. This algorithm computes the trajectories of light rays between the observer, located at redshift z = 0, and distant sources located at high redshift using the multiple lens plane method. The deformation and deflection of light beams as they interact with each lens plane are computed using the filled-beam approximation. We use a particle-particle/particle-mesh (P3M) N-body numerical code to simulate the formation of large-scale structure in the universe. We extend the length resolution of the simulations to submegaparsec scales by using a Monte Carlo method for locating galaxies inside the computational volume according to the underlying distribution of background matter. The observed galaxy two-point correlation function is reproduced. This algorithm constitutes a major improvement over previous methods, which either neglected the presence of large-scale structure, neglected the presence of galaxies, neglected the contribution of distant matter (matter located far from the beam), or used the Zeldovich approximation for simulating the formation of large-scale structure. In addition, we take into account the observed morphology-density relation when assigning morphological types to galaxies, something that was ignored in all previous studies. To test this algorithm, we perform 1981 simulations for three different cosmological models: an Einstein-de Sitter model with density parameter Ω0 = 1, an open model with Ω0 = 0.2, and a flat, low-density model with Ω0 = 0.2 and a cosmological constant of λ0 = 0.8. In all models, the initial density fluctuations correspond to a cold dark matter power spectrum normalized to COBE. In each simulation, we compute the shear and magnification resulting from the presence of inhomogeneities. Our results are the following: (1) The magnification is totally dominated by the convergence, with the shear contributing less than one part in 104. (2) Most of the cumulative shear and magnification is contributed by matter located at intermediate redshifts, z = 1-2. (3) The actual value of the redshift at which the largest contribution to shear and magnification occurs depends on the cosmological model. In particular, the lens planes contributing the most are located at larger redshift for models with smaller Ω0. (4) The number of galaxies directly hit by the beam increases with redshift, while the contribution of lens planes to the shear and magnification decrease with increasing lens plane redshift for z > 2, which indicates that the bulk of the shear and magnification does not originate from direct hits, but rather from the tidal influence of nearby and more distant galaxies and background matter. (5) The average contributions of background matter and nearby galaxies to the shear is comparable for models with small Ω0. For the Einstein-de Sitter model, the contribution of the background matter exceeds the contribution of nearby galaxies by nearly 1 order of magnitude.