James R. van Meter

GETTING A KICK OUT OF NUMERICAL RELATIVITY

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-1, and the most reliable runs give kicks between 86 and 97 km s-1. This is intermediate between the estimates from two recent post-Newtonian analyses and suggests that at redshifts z 10, halos with masses 109 M☉ will have difficulty retaining coalesced black holes after major mergers.

Toward faithful templates for non-spinning binary black holes using the effective-one-body approach

im izing only overtim eofarrivaland initialphase.W eobtain thisresultby sim ply adding a 4-post- Newtonian ordercorrection in theEO B radialpotentialand determ iningthe(constant)coecientby im posing high-m atching perform anceswith num ericalwaveform sofm assratios m 1=m 2 = 1;3=2;2 and 4, m 1 and m 2 being the individualblack-hole m asses. Thenalblack-hole m ass and spin predicted by the num ericalsim ulations are used to determ ine the ringdown frequency and decay tim eofthreequasi-norm al-m ode dam ped sinusoidsthatare attached to theEO B inspiral-(plunge) waveform at the EO B light-ring. The EO B waveform s m ight be tested and further im proved in thefutureby com parison with extrem ely long and accurateinspiralnum erical-relativity waveform s. They m ay already be em ployed for coherent searches and param eter estim ation ofgravitational wavesem itted by non-spinningcoalescing binary black holeswith ground-based laser-interferom eter detectors.

Binary black hole merger dynamics and waveforms

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 Einsteins 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.

Black-hole binaries, gravitational waves, and numerical relativity

Understanding the predictions of general relativity for the dynamical interactions of two black holes has been a long-standing unsolved problem in theoretical physics. Black-hole mergers are monumental astrophysical events, releasing tremendous amounts of energy in the form of gravitational radiation, and are key sources for both ground- and space-based gravitational-wave detectors. The black-hole merger dynamics and the resulting gravitational wave forms can only be calculated through numerical simulations of Einsteins equations of general relativity. For many years, numerical relativists attempting to model these mergers encountered a host of problems, causing their codes to crash after just a fraction of a binary orbit could be simulated. Recently, however, a series of dramatic advances in numerical relativity has allowed stable, robust black-hole merger simulations. This remarkable progress in the rapidly maturing field of numerical relativity and the new understanding of black-hole binary dynamics that is emerging is chronicled. Important applications of these fundamental physics results to astrophysics, to gravitational-wave astronomy, and in other areas are also discussed.

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.

How to move a black hole without excision: Gauge conditions for the numerical evolution of a moving puncture

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.

A data-analysis driven comparison of analytic and numerical coalescing binary waveforms: nonspinning case

We compare waveforms obtained by numerically evolving nonspinning binary black holes to postNewtonian (PN) template families currently used in the search for gravitational waves by groundbased detectors. We find that the time-domain 3.5PN template family, which includes the inspiral phase, has fitting factors (FFs) ≥ 0.96 for binary systems with total mass M = 10–20M⊙. The timedomain 3.5PN effective-one-body template family, which includes the inspiral, merger and ring-down phases, gives satisfactory signal-matching performance with FFs ≥ 0.96 for binary systems with total mass M = 10–120M⊙. If we introduce a cutoff frequency properly adjusted to the final black-hole ring-down frequency, we find that the frequency-domain stationary-phase-approximated template family at 3.5PN order has FFs ≥ 0.96 for binary systems with total mass M = 10–20M⊙. However, to obtain high matching performances for larger binary masses, we need to either extend this family to unphysical regions of the parameter space or introduce a 4PN order coefficient in the frequencydomain GW phase. Finally, we find that the phenomenological Buonanno-Chen-Vallisneri family has FFs ≥ 0.97 with total mass M = 10–120M⊙. The main analyses use the noise spectral-density of LIGO, but several tests are extended to VIRGO and advanced LIGO noise-spectral densities.

Modeling Kicks from the Merger of Nonprecessing Black Hole Binaries

Several groups have recently computed the gravitational radiation recoil produced by the merger of two spinning black holes. The results suggest that spin can be the dominant contributor to the kick, with reported recoil speeds of hundreds to even thousands of kilometers per second. The parameter space of spin kicks is large, however, and it is ultimately desirable to have a simple formula that gives the approximate magnitude of the kick given a mass ratio, spin magnitudes, and spin orientations. As a step toward this goal, we perform a systematic study of the recoil speeds from mergers of black holes with mass ratio q ? m1/m2 = 2/3 and dimensionless spin parameters of a1/m1 and a2/m2 equal to 0 or 0.2, with directions aligned or antialigned with the orbital angular momentum. We also run an equal-mass a1/m1 = -a2/m2 = 0.2 case, and find good agreement with previous results. We find that, for currently reported kicks from aligned or antialigned spins, a simple kick formula inspired by post-Newtonian analyses can reproduce the numerical results to better than ~10%.

Consistency of post-Newtonian waveforms with numerical relativity.

General relativity predicts the gravitational wave signatures of coalescing binary black holes. Explicit waveform predictions for such systems, required for optimal analysis of observational data, have so far been achieved primarily using the post-Newtonian (PN) approximation. The quality of this treatment is unclear, however, for the important late-inspiral portion. We derive late-inspiral waveforms via a complementary approach, direct numerical simulation of Einsteins equations. We compare waveform phasing from simulations of the last approximately 14 cycles of gravitational radiation from equal-mass, nonspinning black holes with the corresponding 2.5PN, 3PN, and 3.5PN orbital phasing. We find phasing agreement consistent with internal error estimates for either approach, suggesting that PN waveforms for this system are effective until the last orbit prior to final merger.

Mergers of non-spinning black-hole binaries: Gravitational radiation characteristics

We present a detailed descriptive analysis of the gravitational radiation from black-hole binary mergers of nonspinning black holes, based on numerical simulations of systems varying from equal mass to a