S. Husa

Maximum kick from nonspinning black-hole binary inspiral.

When unequal-mass black holes merge, the final black hole receives a kick due to the asymmetric loss of linear momentum in the gravitational radiation emitted during the merger. The magnitude of this kick has important astrophysical consequences. Recent breakthroughs in numerical relativity allow us to perform the largest parameter study undertaken to date in numerical simulations of binary black-hole inspirals. We study nonspinning black-hole binaries with mass ratios from q=M1/M2=1 to q=0.25 (eta=q/(1+q)2 from 0.25 to 0.16). We accurately calculate the velocity of the kick to within 6%, and the final spin of the black holes to within 2%. A maximum kick of 175.2+/-11 km s(-1) is achieved for eta=0.195+/-0.005.

Supermassive recoil velocities for binary black-hole mergers with antialigned spins

Recent calculations of the recoil velocity in binary black-hole mergers have found the kick velocity to be of the order of a few hundred km/s in the case of nonspinning binaries and about 500 km/s in the case of spinning configurations, and have lead to predictions of a maximum kick of up to 1300 km/s. We test these predictions and demonstrate that kick velocities of at least 2500 km/s are possible for equal-mass binaries with antialigned spins in the orbital plane. Kicks of that magnitude are likely to have significant repercussions for models of black-hole formation, the population of intergalactic black holes, and the structure of host galaxies.

Inspiral-merger-ringdown waveforms for black-hole binaries with nonprecessing spins

We present the first analytical inspiral-merger-ringdown gravitational waveforms from binary black holes (BBHs) with nonprecessing spins, that is based on a description of the late-inspiral, merger and ringdown in full general relativity. By matching a post-Newtonian description of the inspiral to a set of numerical-relativity simulations, we obtain a waveform family with a conveniently small number of physical parameters. These waveforms will allow us to detect a larger parameter space of BBH coalescence, including a considerable fraction of precessing binaries in the comparable-mass regime, thus significantly improving the expected detection rates.

Inspiral, merger, and ringdown of unequal mass black hole binaries: A multipolar analysis

We study the inspiral, merger, and ringdown of unequal mass black hole binaries by analyzing a catalogue of numerical simulations for seven different values of the mass ratio (from q=M2/M1=1 to q=4). We compare numerical and post-Newtonian results by projecting the waveforms onto spin-weighted spherical harmonics, characterized by angular indices (l,m). We find that the post-Newtonian equations predict remarkably well the relation between the wave amplitude and the orbital frequency for each (l,m), and that the convergence of the post-Newtonian series to the numerical results is nonmonotonic. To leading order, the total energy emitted in the merger phase scales like η2 and the spin of the final black hole scales like η, where η=q/(1+q)2 is the symmetric mass ratio. We study the multipolar distribution of the radiation, finding that odd-l multipoles are suppressed in the equal mass limit. Higher multipoles carry a larger fraction of the total energy as q increases. We introduce and compare three different definitions for the ringdown starting time. Applying linear-estimation methods (the so-called Prony methods) to the ringdown phase, we find resolution-dependent time variations in the fitted parameters of the final black hole. By cross correlating information from different multipoles, we show that ringdown fits can be used to obtain precise estimates of the mass and spin of the final black hole, which are in remarkable agreement with energy and angular momentum balance calculations.

Matching post-Newtonian and numerical relativity waveforms: Systematic errors and a new phenomenological model for nonprecessing black hole binaries

We present a new phenomenological gravitational waveform model for the inspiral and coalescence of nonprecessing spinning black hole binaries. Our approach is based on a frequency-domain matching of post-Newtonian inspiral waveforms with numerical relativity based binary black hole coalescence waveforms. We quantify the various possible sources of systematic errors that arise in matching post-Newtonian and numerical relativity waveforms, and we use a matching criteria based on minimizing these errors; we find that the dominant source of errors are those in the post-Newtonian waveforms near the merger. An analytical formula for the dominant mode of the gravitational radiation of nonprecessing black hole binaries is presented that captures the phenomenology of the hybrid waveforms. Its implementation in the current searches for gravitational waves should allow cross-checks of other inspiral-merger-ringdown waveform families and improve the reach of gravitational-wave searches.

Calibration of moving puncture simulations

We present single and binary black-hole simulations that follow the “moving-puncture” paradigm of simulating black-hole spacetimes without excision, and use “moving boxes” mesh refinement. Focusing on binary black-hole configurations where the simulations cover roughly two orbits, we address five major issues determining the quality of our results: numerical discretization error, finite extraction radius of the radiation signal, physical appropriateness of initial data, gauge choice, and computational performance. We also compare results we have obtained with the BAM code described here with the independent LEAN code.

Frequency-domain gravitational waves from non-precessing black-hole binaries. II. A phenomenological model for the advanced detector era

We present a new frequency-domain phenomenological model of the gravitational-wave signal from the inspiral, merger and ringdown of nonprecessing (aligned-spin) black-hole binaries. The model is calibrated to 19 hybrid effective-one-body–numerical-relativity waveforms up to mass ratios of 1∶18 and black-hole spins of |a/m|∼0.85 (0.98 for equal-mass systems). The inspiral part of the model consists of an extension of frequency-domain post-Newtonian expressions, using higher-order terms fit to the hybrids. The merger ringdown is based on a phenomenological ansatz that has been significantly improved over previous models. The model exhibits mismatches of typically less than 1% against all 19 calibration hybrids and an additional 29 verification hybrids, which provide strong evidence that, over the calibration region, the model is sufficiently accurate for all relevant gravitational-wave astronomy applications with the Advanced LIGO and Virgo detectors. Beyond the calibration region the model produces physically reasonable results, although we recommend caution in assuming that any merger-ringdown waveform model is accurate outside its calibration region. As an example, we note that an alternative nonprecessing model, SEOBNRv2 (calibrated up to spins of only 0.5 for unequal-mass systems), exhibits mismatch errors of up to 10% for high spins outside its calibration region. We conclude that waveform models would benefit most from a larger number of numerical-relativity simulations of high-aligned-spin unequal-mass binaries.

Simple model of complete precessing black-hole-binary gravitational waveforms

The construction of a model of the gravitational-wave (GW) signal from generic configurations of spinning-black-hole binaries, through inspiral, merger, and ringdown, is one of the most pressing theoretical problems in the buildup to the era of GW astronomy. We present the first such model in the frequency domain, PhenomP, which captures the basic phenomenology of the seven-dimensional parameter space of binary configurations with only three key physical parameters. Two of these (the binarys mass ratio and an effective total spin parallel to the orbital angular momentum, which determines the inspiral rate) define an underlying nonprecessing-binary model. The nonprecessing-binary waveforms are then twisted up with approximate expressions for the precessional motion, which require only one additional physical parameter, an effective precession spin, χ(p). All other parameters (total mass, sky location, orientation and polarization, and initial phase) can be specified trivially. The model is constructed in the frequency domain, which will be essential for efficient GW searches and source measurements. We have tested the models fidelity for GW applications by comparison against hybrid post-Newtonian-numerical-relativity waveforms at a variety of configurations--although we did not use these numerical simulations in the construction of the model. Our model can be used to develop GW searches, to study the implications for astrophysical measurements, and as a simple conceptual framework to form the basis of generic-binary waveform modeling in the advanced-detector era.

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.

A phenomenological template family for black-hole coalescence waveforms

Recent progress in numerical relativity has enabled us to model the non-perturbative merger phase of the binary black-hole coalescence problem. Based on these results, we propose a phenomenological family of waveforms which can model the inspiral, merger and ring-down stages of black-hole coalescence. We also construct a template bank using this family of waveforms and discuss its implementation in the search for signatures of gravitational waves produced by black-hole coalescences in the data of ground-based interferometers. This template bank might enable us to extend the present inspiral searches to higher-mass binary black-hole systems, i.e., systems with total mass greater than about 80 solar masses, thereby increasing the reach of the current generation of ground-based detectors.