by Haas, Roland and Shcherbakov, Roman V. and Bode, Tanja and Laguna, Pablo
15 pages, 17 figures, submitted to Astrophysical Journal

We present numerical relativity results of tidal disruptions of white dwarfs from ultra-close encounters with a spinning, intermediate mass black hole. These encounters require a full general relativistic treatment of gravity. We show that the disruption process and prompt accretion of the debris strongly depend on the magnitude and orientation of the black hole spin. However, the late-time accretion onto the black hole follows the same decay, $latex \dot{M}$ ~ t^{-5/3}, estimated from Newtonian gravity disruption studies. We compute the spectrum of the disk formed from the fallback material using a slim disk model. The disk spectrum peaks in the soft X-rays and sustains Eddington luminosity for 1-3 yrs after the disruption. For arbitrary black hole spin orientations, the disrupted material is scattered away from the orbital plane by relativistic frame dragging, which often leads to obscuration of the inner fallback disk by the outflowing debris. The disruption events also yield bursts of gravitational radiation with characteristic frequencies of ~3.2 Hz and strain amplitudes of ~10^{-18} for galactic intermediate mass black holes. The optimistic rate of considered ultra-close disruptions is consistent with no sources found in ROSAT all-sky survey. The future missions like Wide-Field X-ray Telescope (WFXT) could observe dozens of events.

by Harko, Tiberiu and Mocanu, Gabriela
10 pages, 8 figures, accepted for publication in MNRAS

We analyze the general relativistic oscillations of thin accretion disks around compact astrophysical objects interacting with the surrounding medium through non-gravitational forces. The interaction with the external medium (a thermal bath) is modeled via a friction force, and a random force, respectively. The general equations describing the stochastically perturbed disks are derived by considering the perturbations of trajectories of the test particles in equatorial orbits, assumed to move along the geodesic lines. By taking into account the presence of a viscous dissipation and of a stochastic force we show that the dynamics of the stochastically perturbed disks can be formulated in terms of a general relativistic Langevin equation. The stochastic energy transport equation is also obtained. The vertical oscillations of the disks in the Schwarzschild and Kerr geometries are considered in detail, and they are analyzed by numerically integrating the corresponding Langevin equations. The vertical displacements, velocities and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases.

by Lousto, Carlos O. and Zlochower, Yosef and Dotti, Massimo and Volonteri, Marta
17 pages, 10 tables, 14 figures, revtex 4

We explore the newly discovered “hangup-kick” effect, which greatly amplifies the recoil for configuration with partial spin- orbital-angular momentum alignment, by studying a set of 48 new simulations of equal-mass, spinning black-hole binaries. We propose a phenomenological model for the recoil that takes this new effect into account and then use this model, in conjunction with statistical distributions for the spin magnitude and orientations, based on accretion simulations, to find the probabilities for observing recoils of several thousand km/s. In addition, we provide initial parameters, eccentricities, radiated linear and angular momentum, precession rates and remnant mass, spin, and recoils for all 48 configurations. Our results indicate that surveys exploring peculiar (redshifted or blueshifted) differential line-of-sight velocities should observe at least one case above 2000 km/s out of four thousand merged galaxies. The probability that a remnant BH receives a total recoil exceeding the ~2000 km/s escape velocity of large elliptical galaxies is ten times larger. Probabilities of recoils exceeding the escape velocity quickly rise to 5% for galaxies with escape velocities of 1000 km/s and nearly 20% for galaxies with escape velocities of 500 km/s. In addition the direction of these large recoils is strongly peaked toward the angular momentum axis, with very low probabilities of recoils exceeding 350 km/s for angles larger than 45 deg. with respect to the orbital angular momentum axis.

by Healy, James and Bode, Tanja and Haas, Roland and Pazos, Enrique and Laguna, Pablo and Shoemaker, Deirdre M. and Yunes, Nicolás
4 pages, 5 figures, 1 table

Gravitational wave observations will probe non-linear gravitational interactions and thus enable strong tests of Einstein’s theory of general relativity. We present a numerical relativity study of the late inspiral and merger of binary black holes in scalar-tensor theories of gravity. We consider black hole binaries in an inhomogeneous scalar field, specifically binaries inside a scalar field bubble, in some cases with a potential. We calculate the emission of dipole radiation. We also show how these configurations trigger detectable differences between gravitational waves in scalar-tensor gravity and the corresponding waves in general relativity. We conclude that, barring an external mechanism to induce dynamics in the scalar field, scalar-tensor gravity binary black holes alone are not capable of awaking a dormant scalar field, and are thus observationally indistinguishable from their general relativistic counterparts.

by Marx, Jay and Danzmann, Karsten and Hough, James and Kuroda, Kazuaki and McClelland, David and Mours, Benoit and Phinney, Sterl and Rowan, Sheila and Sathyaprakash, B. and Vetrano, Flavio and Vitale, Stefano and Whitcomb, Stan and Will, Clifford
116 pages. Original document in higher resolution can be found at https://gwic.ligo.org/roadmap/

Gravitational wave science is on the verge of direct observation of the waves predicted by Einstein’s General Theory of Relativity and opening the exciting new field of gravitational wave astronomy. In the coming decades, ultra-sensitive arrays of ground-based instruments and complementary spaced-based instruments will observe the gravitational wave sky, inevitably discovering entirely unexpected phenomena while providing new insight into many of the most profound astrophysical phenomena known. in July 2007 the Gravitational Wave International Committee (GWIC) initiated the development of a strategic roadmap for the field of gravitational wave science with a 30-year horizon. The goal of this roadmap is to serve the international gravitational wave community and its stakeholders as a tool for the development of capabilities and facilities needed to address the exciting scientific opportunities on the intermediate and long-term horizons.

by Ohme, Frank
12 pages, 2 figures, 1 table, NRDA2011/Amaldi 9 proceedings

Models of gravitational waveforms from coalescing black-hole binaries play a crucial role in the efforts to detect and interpret those signatures in the data of large-scale interferometers. Here we summarize recent models that combine information both from analytical approximations and numerical relativity. We briefly lay out and compare the strategies employed to build such complete models and we recapitulate the errors associated with various aspects of the modelling process.

by Aranha, R. F. and Soares, I. Damião and Tonini, E. V.
18 pages, 12 Figures

We examine numerically the post-merger regime of two Schwarzschild black holes in non head-on collision. Our treatment is made in the realm of non-axisymmetric Robinson-Trautman spacetimes which are appropriate for the description of the system. Characteristic initial data for the system are constructed and the Robinson-Trautman equation is integrated using a numerical code based on the Galerkin spectral method. The collision is planar, restricted to the plane determined by the directions of the two initial colliding black holes, with the net momentum fluxes of gravitational waves confined to this plane. We evaluate the efficiency of mass-energy extraction, the total energy and momentum carried out by gravitational waves and the momentum distribution of the remnant black hole. Our analysis is based on the Bondi-Sachs four momentum conservation laws. Head-on collisions and orthogonal collisions constitute, respectively, upper and lower bounds to the power emission and to the efficiency of mass-energy extraction by gravitational waves. The momentum extraction and the pattern of the momentum fluxes, as a function of the incidence angle, are examined. The momentum extraction characterizes a regime of strong deceleration of the system. The angular pattern of gravitational wave signals is also examined. They are typically bremsstrahlung for early times emission. Gravitational waves are also emitted outside the plane of collision but this component has a zero net momentum flux. The relation between the incidence angle of collision and the exit angle of the remnant closely approximates a relation for inelastic collisions of classical particles in Newtonian dynamics.

by Damour, Thibault and Nagar, Alessandro and Pollney, Denis and Reisswig, Christian
4 pages, 2 figures

Using accurate numerical relativity simulations of (nonspinning) black-hole binaries with mass ratios 1:1, 2:1 and 3:1 we compute the gauge invariant relation between the (reduced) binding energy $latex E$ and the (reduced) angular momentum $latex j$ of the system. We show that the relation $latex E(j)$ is an accurate diagnostic of the dynamics of a black-hole binary in a highly relativistic regime. By comparing the numerical-relativity $latex E^{\rm NR} (j)$ curve with the predictions of several analytic approximation schemes, we find that, while the usual, non-resummed post-Newtonian-expanded $latex E^{\rm PN} (j)$ relation exhibits large and growing deviations from $latex E^{\rm NR} (j)$, the prediction of the effective one-body formalism, based purely on known analytical results (without any calibration to numerical relativity), agrees strikingly well with the numerical-relativity results.

by Moesta, Philipp and Alic, Daniela and Rezzolla, Luciano and Zanotti, Olindo and Palenzuela, Carlos
4 pages, 3 figures

We revisit the suggestion that dual jets can be produced during the inspiral and merger of supermassive black holes when these are immersed in a force-free plasma threaded by a uniform magnetic field. By performing independent calculations and by computing the electromagnetic emission in a way which is consistent with estimates using the Poynting flux, we show that a dual-jet structure is present but energetically subdominant with respect to a non-collimated and predominantly quadrupolar emission, which is similar to the one computed when the binary is in electrovacuum. While our findings set serious restrictions on the detectability of dual jets from coalescing binaries, they also increase the chances of detecting an EM counterpart from these systems.

by Nakano, Hiroyuki and Zlochower, Yosef and Lousto, Carlos O. and Campanelli, Manuela
23 pages, 35 figures, revtex4

We revisit the scenario of small-mass-ratio (q) black-hole binaries; performing new, more accurate, simulations of mass ratios 10:1 and 100:1 for initially nonspinning black holes. We propose fitting functions for the trajectories of the two black holes as a function of time and mass ratio (in the range 1/100 < q < 1/10$) that combine aspects of post-Newtonian trajectories at smaller orbital frequencies and plunging geodesics at larger frequencies. We then use these trajectories to compute waveforms via black hole perturbation theory. Using the advanced LIGO noise curve, we see a match of ~99.5% for the leading (l,m)=(2,2) mode between the numerical relativity and perturbative waveforms. Nonleading modes have similarly high matches. We thus prove the feasibility of efficiently generating a bank of gravitational waveforms in the intermediate-mass-ratio regime using only a sparse set of full numerical simulations.

by Zanotti, Olindo
6 pages, 4 figures. Accepted by New Astronomy

We show the results of two dimensional general relativistic inviscid and isothermal hydrodynamical simulations comparing the behavior of co-rotating (with respect to the black hole rotation) and counter-rotating circumbinary quasi-Keplerian discs in the post merger phase of a supermassive binary black hole system. While confirming the spiral shock generation within the disc due to the combined effects of mass loss and recoil velocity of the black hole, we find that the maximum luminosity of counter-rotating discs is a factor ~(2-12) higher than in the co-rotating case, depending on the spin of the black hole. On the other hand, the luminosity peak happens ~10 days later with respect to the co-rotating case, for a binary with a total mass M~10^6 M_\odot. Although the global dynamics of counter-rotating discs in the post merger phase of a merging event is very similar to that for co-rotating discs, an important difference has been found. In fact, increasing the spin of the central black hole produces more luminous co-rotating discs while less luminous counter-rotating ones.

by Tchekhovskoy, Alexander and Narayan, Ramesh and McKinney, Jonathan C.
5 pages, 2 figures, MNRAS, submitted

We describe global, 3D, time-dependent, non-radiative, general-relativistic, magnetohydrodynamic simulations of accreting black holes (BHs). The simulations are designed to transport a large amount of magnetic flux to the center, more than the BH can swallow. The excess magnetic flux remains outside the BH, impedes accretion, and leads to a magnetically arrested disc. We find powerful outflows. For a BH with spin parameter a = 0.5, the efficiency with which the accretion system generates outflowing energy in jets and winds is eta ~ 30%. For a = 0.99, we find eta ~ 140%, which means that more energy flows out of the BH than flows in. Thus, the gravitational mass of the BH decreases with time. This simulation represents an unambiguous demonstration, within an astrophysically plausible scenario, of the extraction of net energy from a spinning BH via the Penrose-Blandford-Znajek mechanism. We suggest that magnetically arrested accretion might explain observations of AGN with apparent eta ~ few x 100%.

by Lousto, Carlos O. and Zlochower, Yosef
4 pages, 3 figures, revtex 4

We revisit the scenario of the gravitational radiation recoil acquired by the final remnant of a black-hole-binary merger by studying a set of configurations that have components of the spin both aligned with the orbital angular momentum and in the orbital plane. We perform a series of 24 new full numerical simulations for equal-mass and equal-spin-magnitude binaries, but with different spin orientations.

We extend previous recoil fitting formulas to include nonlinear terms in the spins and successfully include both the new and known results. For this new formula the predicted maximum velocity approaches 5000km/s. More importantly, from the astrophysical point of view, it reaches this maximum for spins partially aligned with the orbital angular momentum. The optimal configuration is near an equipartition of the hangup and superkick contributions. This newly discovered contribution to the recoil leads to an important increase of the probabilities of large recoils in generic astrophysical mergers. We measure these probabilities for the case of accretion-aligned spins and find non-negligible probabilities for supermassive black hole encounters leading to recoil velocities of several thousand km/s.

by Tonita, Aaryn
Code available at https://github.com/SwampWalker/LeapingMonkey

Black hole initial data is usually produced using Bowen-York type puncture initial data or by applying an excision boundary condition. The benefits of the Bowen-York initial data are the ability to specify the spin and momentum of the system as parameters of the initial data. In an attempt to extend these benefits to other formulations of the Einstein constraints, the puncture method is reformulated using distributions as source terms. It is shown how the Bowen-York puncture black hole initial data and the trumpet variation is generated by distributional sources. A heuristic argument is presented to argue that these sources are the general sources of spin and momentum. In order to clarify the meaning of other distributional sources, an exact family of initial data with generalized sources to the Hamiltonian constraint are studied; spinning trumpet black hole initial data and black hole initial data with higher order momentum sources are also studied.

by Kelly, Bernard J. and Baker, John G. and Boggs, William D. and McWilliams, Sean T. and Centrella, Joan
19 pages, 17 figures

We conduct a descriptive analysis of the multipolar structure of gravitational-radiation waveforms from equal-mass aligned-spin mergers, following an approach first presented in the complementary context of nonspinning black holes of varying mass ratio [Baker et al., Phys. Rev. D 78:044046 (2008)]. We find that, as with the nonspinning mergers, the dominant waveform mode phases evolve together in lock-step through inspiral and merger, supporting the previous waveform description in terms of an adiabatically rigid rotator driving gravitational-wave emission — an implicit rotating source (IRS). We further apply the late-time merger-ringdown model for the rotational frequency introduced in Baker et al. (2008), along with an improved amplitude model appropriate for the dominant (2,+/- 2) modes. This provides a quantitative description of the merger-ringdown waveforms, and suggests that the major features of these waveforms can be described with reference only to the intrinsic parameters associated with the state of the final black hole formed in the merger. We provide an explicit model for the merger-ringdown radiation, and demonstrate that this model agrees to fitting factors better than 95% with the original numerical waveforms for system masses above ~ 150 MSun. This model may be directly applicable to gravitational-wave detection of intermediate-mass black hole mergers.

by Ohme, Frank and Hannam, Mark and Husa, Sascha
15 pages, 9 figures, PDFLaTeX

With recent advances in post-Newtonian (PN) theory and numerical relativity (NR) it has become possible to construct inspiral-merger-ringdown gravitational waveforms from coalescing compact binaries by combining both descriptions into one complete hybrid signal. It is important to estimate the error of such waveforms. Previous studies have identified the PN contribution as the dominant source of error, which can be reduced by incorporating longer NR simulations. There are two outstanding issues that make it difficult to determine the minimum simulation length necessary to produce suitably accurate hybrids: (1) the relevant criteria for a signal search is the mismatch between the true waveform and a set of model waveforms, optimized over all waveforms in the model. For discrete hybrids this optimization is not possible. (2) these calculations require that NR waveforms already exist, while ideally we would like to know the necessary length before performing the simulation. Here we overcome these difficulties by developing a general procedure that allows us to estimate hybrid mismatch errors without numerical data, and to optimize them over all physical parameters. Using this procedure we find that, contrary to some earlier studies, ~10 NR orbits before merger allow for the construction of waveform families that are accurate enough for detection in a broad range of parameters, only excluding highly spinning, unequal-mass systems. Nonspinning binaries, even with high mass-ratio (>20) are well modeled for astrophysically reasonable component masses. In addition, the parameter bias is only of the order of 1% for total mass and symmetric mass-ratio and less than 0.1 for the dimensionless spin magnitude. We take the view that similar NR waveform lengths will remain the state of the art in the Advanced detector era, and begin to assess the limits of the science that can be done with them.

by Tiec, Alexandre Le and Mroué, Abdul H. and Barack, Leor and Buonanno, Alessandra and Pfeiffer, Harald P. and Sago, Norichika and Taracchini, Andrea
5 pages, 3 figures

The general relativistic periastron advance of non-spinning black hole binaries on quasi-circular orbits has been computed using black hole perturbation theory, post-Newtonian expansions, and the effective-one-body formalism. We compare these approximations with accurate numerical relativity simulations of mass ratios 1/8 < m1/m2 m1m2/(m1+m2)^2. The effective-one-body prediction also agrees very well over the entire mass-ratio range considered.

by Kiuchi, Kenta and Shibata, Masaru and Montero, Pedro J. and Font, José A.
4 pages, 4 figure, to be published in PRL

Black hole (BH)–torus systems are promising candidates for the central engine of gamma-ray bursts (GRBs), and also possible outcomes of the collapse of supermassive stars to supermassive black holes (SMBHs). By three-dimensional general relativistic numerical simulations, we show that an $latex m=1$ nonaxisymmetric instability grows for a wide range of self-gravitating tori orbiting BHs. The resulting nonaxisymmetric structure persists for a timescale much longer than the dynamical one, becoming a strong emitter of large amplitude, quasiperiodic gravitational waves. Our results indicate that both, the central engine of GRBs and newly formed SMBHs, can be strong gravitational wave sources observable by forthcoming ground-based and spacecraft detectors.

by Farris, Brian D. and Liu, Yuk Tung and Shapiro, Stuart L.
submitted to PRD

Simultaneous gravitational and electromagnetic wave observations of merging black hole binaries (BHBHs) can provide unique opportunities to study gravitation physics, accretion and cosmology. Here we perform fully general relativistic, hydrodynamic simulations of equal-mass, nonspinning BHBHs coalescing in a circumbinary disk. We evolve the metric using the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of Einstein’s field equations with standard moving puncture gauge conditions. We handle the hydrodynamics via a high-resolution shock-capturing (HRSC) scheme. We track the inspiral starting from a binary separation of 10M, where M is the total binary mass. We take the disks to have an inner radius at R_in~15M to account for the hollow created by the binary torques. Our disks extend to R=65M and have an initial scale height of H/R=0.03-0.11. The gas is governed by a Gamma-law EOS, with Gamma equal to 5/3, 4/3, and 1.1. Disks are allowed to relax in the “early inspiral” epoch to provide quasistationary realistic initial data. We then evolve the metric and matter during the “late inspiral and merger” epoch. The later simulations are designed to track BHBH inspiral following disk-binary decoupling, through merger and ringdown, terminating before viscosity has time to fill the hollow about the remnant. We compute the gas flow and accretion rate and estimate the electromagnetic luminosity due to bremsstrahlung and synchrotron emission as a perturbation for optically thin disks. The synchrotron component of the luminosity peaks in the infrared band and should be detectable by WFIRST and possibly the LSST for a 10^8 M_sun binary embedded in a disk with a density n~10^12/cm^3 at z=1, beginning with a maximum value of $L~10^46 n_12^2 M_8^3 erg/s at decoupling, and decreasing steadily over a timescale of ~100 M_8 hours to a value of L~10^45 n_12^2 M_8^3 erg/s at merger.

by Bishop, Nigel and Pollney, Denis and Reisswig, Christian
18 pages, 4 figures

We describe a method for initializing characteristic evolutions of the Einstein equations using a linearized solution corresponding to purely outgoing radiation. This allows for a more consistent application of the characteristic (null cone) techniques for invariantly determining the gravitational radiation content of numerical simulations. In addition, we are able to identify the {\em ingoing} radiation contained in the characteristic initial data, as well as in the initial data of the 3+1 simulation. We find that each component leads to a small but long lasting (several hundred mass scales) transient in the measured outgoing gravitational waves.

by Bode, Tanja and Bogdanovic, Tamara and Haas, Roland and Healy, James and Laguna, Pablo and Shoemaker, Deirdre
5 pages, 4 figures, 1 table

Modeling the late inspiral and merger of supermassive black holes is central to understanding accretion processes and the conditions under which electromagnetic emission accompanies gravitational waves. We use fully general relativistic, hydrodynamics simulations to investigate how electromagnetic signatures correlate with black hole spins, mass ratios, and the gaseous environment in this final phase of binary evolution. In all scenarios, we find some form of characteristic electromagnetic variability whose pattern depends on the spins and binary mass ratios. Binaries in hot accretion flows exhibit a flare followed by a sudden drop in luminosity associated with the plunge and merger, as well as quasi-periodic oscillations correlated with the gravitational waves during the inspiral. Conversely, circumbinary disk systems are characterized by a low luminosity of variable emission, suggesting challenging prospects for their detection.

by McWilliams, Sean T.
Invited review for NRDA/CAPRA 2010, CQG special issue – 7 pages, 1 figure, 1 table

The advent of long-term stability in numerical relativity has yielded a windfall of answers to long-standing questions regarding the dynamics of space-time, matter, and electromagnetic fields in the strong-field regime of black-hole binary mergers. In this review, we will briefly summarize the methodology currently applied to these problems, emphasizing the most recent advancements. We will discuss recent results of astrophysical relevance, and present some novel interpretation. Though we primarily present a review, we also present a simple analytical model for the time-dependent Poynting flux from two orbiting black holes immersed in a magnetic field, which compares favorably with recent numerical results. Finally, we will discuss recent advancements in our theoretical understanding of merger dynamics and gravitational waveforms that have resulted from interpreting the ever-growing body of numerical relativity results.

by Bernuzzi, Sebastiano and Nagar, Alessandro and Zenginoglu, Anil

We discuss the properties of the effective-one-body (EOB) multipolar gravitational waveform emitted by nonspinning black-hole binaries of masses $latex \mu$ and $latex M$ in the extreme-mass-ratio limit, $latex \mu/M=\nu\ll 1$. We focus on the transition from quasicircular inspiral to plunge, merger and ringdown.We compare the EOB waveform to a Regge-Wheeler-Zerilli (RWZ) waveform computed using the hyperboloidal layer method and extracted at null infinity. Because the EOB waveform keeps track analytically of most phase differences in the early inspiral, we do not allow for any arbitrary time or phase shift between the waveforms. The dynamics of the particle, common to both wave-generation formalisms, is driven by leading-order $latex {\cal O}(\nu)$ analytically–resummed radiation reaction. The EOB and the RWZ waveforms have an initial dephasing of about $latex 5\times 10^{-4}$ rad and maintain then a remarkably accurate phase coherence during the long inspiral ($latex \sim 33$ orbits), accumulating only about $latex -2\times 10^{-3}$ rad until the last stable orbit, i.e. $latex \Delta\phi/\phi\sim -5.95\times 10^{-6}$. We obtain such accuracy without calibrating the analytically-resummed EOB waveform to numerical data, which indicates the aptitude of the EOB waveform for LISA-oriented studies. We then improve the behavior of the EOB waveform around merger by introducing and tuning next-to-quasi-circular corrections both in the gravitational wave amplitude and phase. For each multipole we tune only four next-to-quasi-circular parameters by requiring compatibility between EOB and RWZ waveforms at the light-ring. The resulting phase difference around merger time is as small as $latex \pm 0.015$ rad, with a fractional amplitude agreement of $latex 2.5%$. This suggest that next-to-quasi-circular corrections to the phase can be a useful ingredient in comparisons between EOB and numerical relativity waveforms.

by Nakano, Hiroyuki and Campanelli, Manuela and Lousto, Carlos O. and Zlochower, Yosef
Proceedings of Theory Meets Data Analysis at Comparable and Extreme Mass Ratios (NRDA/Capra 2010), Perimeter Institute, June 2010 – 12 pages

Recently, we proposed an enhancement of the Regge-Wheeler-Zerilli formalism for first-order perturbations about a Schwarzschild background that includes first-order corrections due to the background black-hole spin. Using this formalism, we investigate gravitational wave recoil effects from a spinning black-hole binary system analytically. This allows us to better understand the origin of the large recoils observed in full numerical simulation of spinning black hole binaries.

by Lousto, Carlos O. and Zlochower, Yosef
8 pages, 7 figures, revtex4

We measure the recoil velocity as a function of spin for equal-mass, highly-spinning black-hole binaries, with spins in the orbital plane, equal in magnitude and opposite in direction. We confirm that the leading-order effect is linear in the spin and the cosine of angle between the spin direction and the infall direction at merger. We find higher-order corrections that are proportional to the odd powers in both the spin and cosine of this angle. Taking these corrections into account, we predict that the maximum recoil will be 3680+-130 km/s.

by Centrella, Joan M. and Baker, John G. and Kelly, Bernard J. and van Meter, James R.
53 pages, 42 figures. Review article submitted to Reviews of Modern Physics

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 waveforms can only be calculated through numerical simulations of Einstein’s 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, for the first time, allowed stable, robust black hole merger simulations. We chronicle this remarkable progress in the rapidly maturing field of numerical relativity, and the new understanding of black-hole binary dynamics that is emerging. We also discuss important applications of these fundamental physics results to astrophysics, to gravitational-wave astronomy, and in other areas.

by Lovelace, Geoffrey and Scheel, Mark. A. and Szilagyi, Bela
4 pages, 2 figures, submitted to Phys. Rev. Lett

Astrophysically realistic black holes may have spins that are nearly extremal (i.e., close to 1 in dimensionless units). Numerical simulations of binary black holes—important tools both for calibrating analytical templates for gravitational-wave detection and for exploring the nonlinear dynamics of curved spacetime—are particularly challenging when the holes’ spins are nearly extremal. Typical initial data methods cannot yield simulations with nearly extremal spins; e.g., Bowen-York data cannot produce simulations with spins larger than about 0.93. In this paper, we present the first binary black hole inspiral, merger, and ringdown with initial spins larger than the Bowen-York limit. Specifically, using the Spectral Einstein Code (SpEC), we simulate the inspiral (through 12.5 orbits), merger and ringdown of two equal-mass black holes with equal spins of magnitude 0.95 antialigned with the orbital angular momentum.

by Bogdanovic, Tamara and Bode, Tanja and Haas, Roland and Laguna, Pablo and Shoemaker, Deirdre
15 pages, 3 figures, submitted to Class. Quantum Grav. for proceedings of 8th LISA Symposium

What are the properties of accretion flows in the vicinity of coalescing supermassive black holes (SBHs)? The answer to this question has direct implications for the feasibility of coincident detections of electromagnetic (EM) and gravitational wave (GW) signals from coalescences. Such detections are considered to be the next observational grand challenge that will enable testing general relativity in the strong, nonlinear regime and improve our understanding of evolution and growth of these massive compact objects. In this paper we review the properties of the environment of coalescing binaries in the context of the circumbinary disk and hot, radiatively inefficient accretion flow models and use them to mark the extent of the parameter space spanned by this problem. We report the results from an initial, general relativistic, hydrodynamical study of the inspiral and merger of equal-mass, spinning black holes, motivated by the latter scenario. We find that correlated EM+GW oscillations can arise during the inspiral phase followed by the gradual rise and subsequent drop-off in the light curve at the time of coalescence. While there are indications that the latter EM signature is a more robust one, a detection of either signal coincidentally with GWs would be a convincing evidence for an impending SBH binary coalescence. The observability of an EM counterpart in the hot accretion flow scenario depends on the details of a model. In the case of the most massive binaries observable by the Laser Interferometer Space Antenna, upper limits on luminosity imply that they may be identified by EM searches out to z~0.1-1. However, given the radiatively inefficient nature of the gas flow, we speculate that a majority of massive binaries may appear as low luminosity AGN in the local universe.

by Centrella, Joan M. and Baker, John G. and Kelly, Bernard J. and van Meter, James R.
56 pages; 9 figures. Review article in press with Annual Review of Nuclear and Particle Physics, vol. 60

Recent breakthroughs in the field of numerical relativity have led to dramatic progress in understanding the predictions of General Relativity for the dynamical interactions of two black holes in the regime of very strong gravitational fields. Such black-hole binaries are important astrophysical systems and are a key target of current and developing gravitational-wave detectors. The waveform signature of strong gravitational radiation emitted as the black holes fall together and merge provides a clear observable record of the process. After decades of slow progress, these mergers and the gravitational-wave signals they generate can now be routinely calculated using the methods of numerical relativity. We review recent advances in understanding the predicted physics of events and the consequent radiation, and discuss some of the impacts this new knowledge is having in various areas of astrophysics.

by Lousto, Carlos O. and Zlochower, Yosef
4 pages, 4 figures, 3 tables

We perform the first fully nonlinear numerical simulations of black-hole binaries with mass ratios 100:1. Our technique for evolving such extreme mass ratios is based on the moving puncture approach with a new gauge condition and an optimal choice of the mesh refinement (plus large computational resources). We achieve a convergent set of results for simulations starting with a small nonspinning black hole just outside the ISCO that then performs over two orbits before plunging into the 100 times more massive black hole. We compute the gravitational energy and momenta radiated as well as the final remnant parameters and compare these quantities with the corresponding perturbative estimates. The results show a close agreement. We briefly discuss the relevance of this simulations for Advanced LIGO, third-generation ground based detectors, and LISA observations, and self-force computations.

by Lousto, Carlos O. and Nakano, Hiroyuki and Zlochower, Yosef and Campanelli, Manuela
31 pages, 33 figures revtex 4

We describe in detail full numerical and perturbative techniques to compute the gravitational radiation from intermediate mass ratio (IMR) black-hole-binary (BHB) inspirals and mergers. We perform a series of full numerical simulations of nonspinning black holes with mass ratios q=1/10 and q=1/15 from different initial separations and for different finite difference resolutions. The highest resolution runs reach phase accuracies with errors <0.05 radians when the gravitational wave frequency is 0.2/M. In order to perform those full numerical runs, we adapted the gauge of the moving punctures approach with a variable damping term for the shift. We also derive an extrapolation (to infinite radius) formula for the waveform extracted at finite radius. For the perturbative evolutions we use the full numerical tracks, transformed into the Schwarzschild gauge, in the source terms of the Regge-Wheller-Zerilli Schwarzschild perturbations formalism. We then extend this perturbative formalism to take into account small intrinsic spins of the large black hole, and validate it by computing the quasinormal mode (QNM) frequencies, where we find good agreement for spins |a/M|<0.3. Including the final spins improves the overlap functions when comparing full numerical and perturbative waveforms, reaching 99.5% for the leading (l,m)=(2,2) and (3,3) modes, and 98.3% for the nonleading (2,1) mode in the q=1/10 case, which includes 8 orbits before merger. For the q=1/15 case, we obtain overlaps near 99.7% for all three modes. We discuss the modeling of the full inspiral and merger based on a combined matching of Post-Newtonian, Full Numerical, and Geodesic trajectories.

by Hannam, Mark and Husa, Sascha and Ohme, Frank and Ajith, P.
13 pages, 11 figures, 2 tables

One way to produce complete inspiral-merger-ringdown gravitational waveforms from black-hole-binary systems is to connect post-Newtonian (PN) and numerical-relativity (NR) results to create “hybrid” waveforms. Hybrid waveforms are central to the construction of some phenomenological models for GW search templates, and for tests of GW search pipelines. The dominant error source in hybrid waveforms arises from the PN contribution, and can be reduced by increasing the number of NR GW cycles that are included in the hybrid. Hybrid waveforms are considered sufficiently accurate for GW detection if their mismatch error is below 3% (i.e., a fitting factor about 0.97). We address the question of the length requirements of NR waveforms such that the final hybrid waveforms meet this requirement, considering nonspinning binaries with q = M_2/M_1 \in [1,4] and equal-mass binaries with \chi = S_i/M_i^2 \in [-0.5,0.5]. We conclude that for the cases we study simulations must contain between three (in the equal-mass nonspinning case) and ten (the \chi = 0.5 case) orbits before merger, but there is also evidence that these are the regions of parameter space for which the least number of cycles will be needed.

by Alic, Daniela and Rezzolla, Luciano and Hinder, Ian and Mösta, Philipp
11 pages, 8 figures

Suitable gauge conditions are fundamental for stable and accurate numerical-relativity simulations of inspiralling compact binaries. A number of well-studied conditions have been developed over the last decade for both the lapse and the shift and these have been successfully used both in vacuum and non-vacuum spacetimes when simulating binaries with comparable masses. At the same time, recent evidence has emerged that the standard “Gamma-driver” shift condition requires a careful and non-trivial tuning of its parameters to ensure long-term stable evolutions of unequal-mass binaries. We present a novel gauge condition in which the damping constant is promoted to be a dynamical variable and the solution of an evolution equation. We show that this choice removes the need for special tuning and provides a shift damping term which is free of instabilities in our simulations and dynamically adapts to the individual positions and masses of the binary black-hole system. Our gauge condition also reduces the variations in the coordinate size of the apparent horizon of the larger black hole and could therefore be useful when simulating binaries with very small mass ratios.

by Jaramillo, Gabriela and Lousto, Carlos O.
31 pages, 21 figures

We study critical black hole separations for the formation of a common apparent horizon in systems of $latex N$ – black holes in a time symmetric configuration. We study in detail the aligned equal mass cases for $latex N=2,3,4,5$, and relate them to the unequal mass binary black hole case. We then study the apparent horizon of the time symmetric initial geometry of a ring singularity of different radii. The apparent horizon is used as indicative of the location of the event horizon in an effort to predict a critical ring radius that would generate an event horizon of toroidal topology. We found that a good estimate for this ring critical radius is $latex 20/(3\pi) M$. We briefly discuss the connection of this two cases through a discrete black hole ‘necklace’ configuration.

by Hannam, Mark and Husa, Sascha and Ohme, Frank and Mueller, Doreen and Bruegmann, Bernd
20 pages, 9 figures, 6 tables

We present gravitational waveforms for the last orbits and merger of black-hole-binary (BBH) systems along two branches of the BBH parameter space: equal-mass binaries with equal non-precessing spins, and nonspinning unequal-mass binaries. The waveforms are calculated from numerical solutions of Einstein’s equations for black-hole binaries that complete between six and ten orbits before merger. Along the equal-mass spinning branch, the spin parameter of each BH is $latex \chi_i = S_i/M_i^2 \in [-0.85,0.85]$, and along the unequal-mass branch the mass ratio is $latex q =M_2/M_1 \in [1,4]$. We discuss the construction of low-eccentricity puncture initial data for these cases, the properties of the final merged BH, and compare the last 8-10 GW cycles up to $latex M\omega = 0.1$ with the phase and amplitude predicted by standard post-Newtonian (PN) approximants. As in previous studies, we find that the phase from the 3.5PN TaylorT4 approximant is most accurate for nonspinning binaries. For equal-mass spinning binaries the 3.5PN TaylorT1 approximant (including spin terms up to only 2.5PN order) gives the most robust performance, but it is possible to treat TaylorT4 in such a way that it gives the best accuracy for spins $latex \chi_i > -0.75$. When high-order amplitude corrections are included, the PN amplitude of the $latex (\ell=2,m=\pm2)$ modes is larger than the NR amplitude by between 2-4%.

by Galley, Chad R. and Herrmann, Frank and Silberholz, John and Tiglio, Manuel and Guerberoff, Gustavo

We perform a statistical analysis of the binary black hole problem in the post-Newtonian approximation by systematically sampling and evolving the parameter space of initial configurations for quasi-circular inspirals. Through a principal component analysis of spin and orbital angular momentum variables we systematically look for uncorrelated quantities and find three of them which are highly conserved in a statistical sense, both as functions of time and with respect to variations in initial spin orientations. We also look for and find the variables that account for the largest variations in the problem. We present binary black hole simulations of the full Einstein equations analyzing to what extent these results might carry over to the full theory in the inspiral and merger regimes. Among other applications these results should be useful both in semi-analytical and numerical building of templates of gravitational waves for gravitational wave detectors.

by Kesden, Michael and Sperhake, Ulrich and Berti, Emanuele
7 pages, 4 figures, submitted to ApJL

Numerical-relativity simulations indicate that the black hole produced in a binary merger can recoil with a velocity up to v_max ~ 4,000 km/s with respect to the center of mass of the initial binary. This challenges the paradigm that most galaxies form through hierarchical mergers, yet retain supermassive black holes at their centers despite having escape velocities much less than v_max. Interaction with a circumbinary disk can align the binary black hole spins with their orbital angular momentum, reducing the recoil velocity of the final black hole produced in the subsequent merger. However, the effectiveness of this alignment depends on highly uncertain accretion flows near the binary black holes. In this Letter, we show that if the spin S_1 of the more massive binary black hole is even partially aligned with the orbital angular momentum L, relativistic spin precession on sub-parsec scales can align the binary black hole spins with each other. This alignment significantly reduces the recoil velocity even in the absence of gas. For example, if the angle between S_1 and L at large separations is 10 degrees while the second spin S_2 is isotropically distributed, the spin alignment discussed in this paper reduces the median recoil from 864 km/s to 273 km/s for maximally spinning black holes with a mass ratio of 9/11. This reduction will greatly increase the fraction of galaxies retaining their supermassive black holes.

by Lubich, Christian and Walther, Benny and Bruegmann, Bernd
9 pages, 6 figures

We present a non-canonically symplectic integration scheme tailored to numerically computing the post-Newtonian motion of a spinning black-hole binary. Using a splitting approach we combine the flows of orbital and spin contributions. In the context of the splitting, it is possible to integrate the individual terms of the spin-orbit and spin-spin Hamiltonians analytically, exploiting the special structure of the underlying equations of motion. The outcome is a symplectic, time-reversible integrator, which can be raised to arbitrary order by composition. A fourth-order version is shown to give excellent behavior concerning error growth and conservation of energy and angular momentum in long-term simulations. Favorable properties of the integrator are retained in the presence of weak dissipative forces due to radiation damping in the full post-Newtonian equations.

by Mueller, Doreen and Grigsby, Jason and Bruegmann, Bernd
10 pages, 14 figures

Certain numerical frameworks used for the evolution of binary black holes make use of a gamma driver, which includes a damping factor. Such simulations typically use a constant value for damping. However, it has been found that very specific values of the damping factor are needed for the calculation of unequal mass binaries. We examine carefully the role this damping plays, and provide two explicit, non-constant forms for the damping to be used with mass-ratios further from one. Our analysis of the resultant waveforms compares well against the constant damping case.

by van Meter, James R. and Miller, M. Coleman and Baker, John G. and Boggs, William D. and Kelly, Bernard J.
14 pages.

Although the gravitational wave kick velocity in the orbital plane of coalescing black holes has been understood for some time, apparently conflicting formulae have been proposed for the dominant out-of-plane kick, each a good fit to different data sets. This is important to resolve because it is only the out-of-plane kicks that can reach more than 500 km/s and can thus eject merged remnants from galaxies. Using a different ansatz for the out-of-plane kick, we show that we can fit almost all existing data to better than 5 %. This is good enough for any astrophysical calculation, and shows that the previous apparent conflict was only because the two data sets explored different aspects of the kick parameter space.

by Rezzolla, Luciano and Macedo, Rodrigo P. and Jaramillo, José Luis
4 pages

The generation of a large recoil velocity from the inspiral and merger of binary black holes represents one of the most exciting results of numerical-relativity calculations. While many aspects of this process have been investigated and explained, the “anti-kick”, namely the sudden deceleration after the merger, has not yet found a simple explanation. We show that the anti-kick can be easily understood in terms of the radiation from a deformed black hole where the intrinsically anisotropic curvature distribution on the horizon determines the direction and intensity of the recoil. Our analysis is focussed on the properties of Robinson-Trautman spacetimes and allows us to measure both the energies and momenta radiated in a gauge-invariant manner. At the same time, this simpler setup provides all the qualitative but also quantitative features of inspiralling black hole binaries, thus opening the way to a deeper understanding of the nonlinear dynamics of black-hole spacetimes.

by Berti, Emanuele and Cardoso, Vitor and Hinderer, Tanja and Lemos, Madalena and Pretorius, Frans and Sperhake, Ulrich and Yunes, Nicolas
29 pages, 19 figure, 6 tables

Ultrarelativistic collisions of black holes are ideal gedanken experiments to study the nonlinearities of general relativity. In this paper we use semianalytical tools to better understand the nature of these collisions and the emitted gravitational radiation. We explain many features of the energy spectra extracted from numerical relativity simulations using two complementary semianalytical calculations. In the first calculation we estimate the radiation by a “zero-frequency limit” analysis of the collision of two point particles with finite impact parameter. In the second calculation we replace one of the black holes by a point particle plunging with arbitrary energy and impact parameter into a Schwarzschild black hole, and we explore the multipolar structure of the radiation paying particular attention to the near-critical regime. We also use a geodesic analogy to provide qualitative estimates of the dependence of the scattering threshold on the black hole spin and on the dimensionality of the spacetime.

by Zanotti, Olindo and Rezzolla, Luciano and Del Zanna, Luca and Palenzuela, Carlos
17 pages, 11 figures, submitted to MNRAS, movies available at http://numrel.aei.mpg.de/Visualisations/Archive/BinaryBlackHoles/EMCounterparts/EMCounterparts.html

We investigate the dynamics of a circumbinary disc that responds to the loss of mass and to the recoil velocity of the black hole produced by the merger of a binary system of supermassive black holes. More specifically, we perform the first two-dimensional general relativistic hydrodynamics simulations of \textit{extended} non-Keplerian discs and employ a new technique to construct a “shock detector”, thus determining the precise location of the shocks produced in the accreting disc by the recoiling black hole. In this way we can study how the properties of the system, such as the spin, mass and recoil velocity of the black hole, affect the mass accretion rate and are imprinted on the electromagnetic emission from these sources. In contrast with what done in similar works, we here question the estimates of the bremsstrahlung luminosity when computed without properly taking into account the radiation transfer, thus yielding cooling times that are unrealistically short. At the same time we show, through an approximation based on the relativistic analogue of the isothermal evolution of \citet{Corrales2009}, that the luminosity produced can reach a peak value above $latex L \simeq 10^{43} {\rm erg/s} $ at about $latex \sim 20 {\rm d}$ after the merger of a binary with total mass $latex M\simeq 10^6 M_\odot$ and persist for several days at values which are a factor of a few smaller. If confirmed by more sophisticated calculations such a signal could indeed lead to an electromagnetic counterpart of the merger of binary black-hole system.

by Kesden, Michael and Sperhake, Ulrich and Berti, Emanuele
20 pages, 16 figures, revtex

The inspiral of binary black holes is governed by gravitational radiation reaction at binary separations r 10 M. Fortunately, binary evolution between these separations is well described by post-Newtonian equations of motion. We examine how this post-Newtonian evolution affects the distribution of spin orientations at separations r near 10 M where numerical-relativity simulations typically begin. Although isotropic spin distributions at r =1000 M remain isotropic at r = 10 M, distributions that are initially partially aligned with the orbital angular momentum can be significantly distorted during the post-Newtonian inspiral. Spin-orbit resonances tend to align (anti-align) the binary black hole spins with each other if the spins were initially partially aligned (anti-aligned) with respect to the orbital angular momentum, thus increasing (decreasing) the average final spin. Resonant effects are stronger for comparable-mass binaries, and they could produce significant spin alignment in massive black hole mergers at high redshifts and in stellar-mass black hole binaries. We also point out that precession induces an intrinsic accuracy limitation of 0.03 in the dimensionless spin magnitude, and about 20 degrees in the direction in predicting the final spin resulting from widely separated binary configurations.

by Hinder, Ian
14 pages; submitted to the Classical and Quantum Gravity special issue for NRDA2009

Since the breakthroughs in 2005 which have led to long term stable solutions of the binary black hole problem in numerical relativity, much progress has been made. I present here a short summary of the state of the field, including the capabilities of numerical relativity codes, recent physical results obtained from simulations, and improvements to the methods used to evolve and analyse binary black hole spacetimes.

by Campanelli, Manuela and Lousto, Carlos O. and Mundim, Bruno C. and Nakano, Hiroyuki and Zlochower, Yosef and Bischof, Hans-Peter
12 pages, 5 figures, Prepared for 8th Edoardo Amaldi Conference on Gravitational Waves (Amaldi8)

We review some of the recent dramatic developments in the fully nonlinear simulation of generic, highly-precessing, black-hole binaries, and introduce a new approach for generating hybrid post-Newtonian / Numerical waveforms for these challenging systems.

by Field, Scott E. and Hesthaven, Jan S. and Lau, Stephen R.
Uses revtex4, 23 pages, 9 figures, 3 tables

In the context of metric perturbation theory for non-spinning black holes, extreme mass ratio binary (EMRB) systems are described by distributionally forced master wave equations. Numerical solution of a master wave equation as an initial boundary value problem requires initial data. However, because the correct initial data for generic-orbit systems is unknown, specification of trivial initial data is a common choice, despite being inconsistent and resulting in a solution which is initially discontinuous in time. As is well known, this choice leads to a “burst” of junk radiation which eventually propagates off the computational domain. We observe another unintended consequence of trivial initial data: development of a persistent spurious solution, here referred to as the Jost junk solution, which contaminates the physical solution for long times. This work studies the influence of both types of junk on metric perturbations, waveforms, and self-force measurements, and it demonstrates that smooth modified source terms mollify the Jost solution and reduce junk radiation.

by Lousto, Carlos O. and Nakano, Hiroyuki and Zlochower, Yosef and Campanelli, Manuela
4 pages, 5 figures, revtex4

We study black-hole binaries in the intermediate-mass-ratio regime 0.01 < q < 0.1 with a new technique that makes use of nonlinear numerical trajectories and efficient perturbative evolutions to compute waveforms at large radii for the leading and nonleading modes. As a proof-of-concept, we compute waveforms for q=1/10. We discuss applications of these techniques for LIGO/VIRGO data analysis and the possibility that our technique can be extended to produce accurate waveform templates from a modest number of fully-nonlinear numerical simulations.

by Barausse, Enrico and Buonanno, Alessandra
22 pages, 9 figures

Building on a recent paper in which we computed the canonical Hamiltonian of a spinning test particle in curved spacetime, at linear order in the particle’s spin, we work out an improved effective-one-body (EOB) Hamiltonian for spinning black-hole binaries. As in previous descriptions, we endow the effective particle not only with a mass m, but also with a spin S*. Thus, the effective particle interacts with the effective Kerr background (having spin S_Kerr) through a geodesic-type interaction and an additional spin-dependent interaction proportional to S*. When expanded in post-Newtonian (PN) orders, the EOB Hamiltonian reproduces the leading order spin-spin coupling and the spin-orbit coupling through 2.5PN order, for any mass-ratio. Also, it reproduces all spin-orbit couplings in the test-particle limit. Similarly to the test-particle limit case, when we restrict the EOB dynamics to spins aligned or antialigned with the orbital angular momentum, for which circular orbits exist, the EOB dynamics has several interesting features, such as the existence of an innermost stable circular orbit, a photon circular orbit, and a maximum in the orbital frequency during the plunge subsequent to the inspiral. These properties are crucial for reproducing the dynamics and gravitational-wave emission of spinning black-hole binaries, as calculated in numerical relativity simulations.

by Mueller, Doreen and Bruegmann, Bernd
15 pages, submitted to CQG for NRDA 2009 conference proceedings

Moving puncture simulations of black hole binaries rely on a specific gauge choice that leads to approximately stationary coordinates near each black hole. Part of the shift condition is a damping parameter, which has to be properly chosen for stable evolutions. However, a constant damping parameter does not account for the difference in mass in unequal mass binaries. We introduce a position dependent shift damping that addresses this problem. Although the coordinates change, the changes in the extracted gravitational waves are small.