arXiv subjects

Yosef Zlochower

Publications and source records attributed to Yosef Zlochower.

At least 73 records · Page 4Linked to original sources

arXiv2010

Perturbative effects of spinning black holes with applications to recoil velocities

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.

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arXiv2010

Modeling maximum astrophysical gravitational recoil velocities

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.

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arXiv2010

Post-Newtonian Initial Data with Waves: Progress in Evolution

In Kelly et al. [Phys. Rev. D, 76:024008, 2007], we presented new binary black-hole initial data adapted to puncture evolutions in numerical relativity. This data satisfies the constraint equations to 2.5 post-Newtonian order, and contains a transverse-traceless "wavy" metric contribution, violating the standard assumption of conformal flatness. We report on progress in evolving this data with a modern moving-puncture implementation of the BSSN equations in several numerical codes. We discuss the effect of the new metric terms on junk radiation and continuity of physical radiation extracted.

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arXiv2010

Remnant Masses, Spins and Recoils from the Merger of Generic Black-Hole Binaries

We obtain empirical formulae for the final remnant black hole mass, spin, and recoil velocity from merging black-hole binaries with arbitrary mass ratios and spins. Our formulae are based on the mass ratio and spin dependence of the post-Newtonian expressions for the instantaneous radiated energy, linear momentum, and angular momentum, as well as the ISCO binding energy and angular momentum. The relative weight between the different terms is fixed by amplitude parameters chosen through a least-squares fit of recently available fully nonlinear numerical simulations. These formulae can be used for statistical studies of N-body simulations of galaxy cores and clusters, and the cosmological growth of supermassive black holes. As an example, we use these formulae to obtain a universal spin magnitude distribution of merged black holes and recoil velocity distributions for dry and hot/cold wet mergers. We also revisit the long term orbital precession and resonances and discuss how they affect spin distributions before the merging regime.

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arXiv2010

Advances in Simulations of Generic Black-Hole Binaries

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.

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arXiv2010

Statistical studies of Spinning Black-Hole Binaries

We study the statistical distributions of the spins of generic black-hole binaries during the inspiral and merger, as well as the distributions of the remnant mass, spin, and recoil velocity. For the inspiral regime, we start with a random uniform distribution of spin directions S1 and S2 and magnitudes S1=S2=0.97 for different mass ratios. Starting from a fiducial initial separation of ri=50m, we perform 3.5PN evolutions down to rf=5m. At this final fiducial separation, we compute the angular distribution of the spins with respect to the final orbital angular momentum, L. We perform 16^4 simulations for six mass ratios between q=1 and q=1/16 and compute the distribution of the angles between L and Delta and L and S, directly related to recoil velocities and total angular momentum. We find a small but statistically significant bias of the distribution towards counter-alignment of both scalar products. To study the merger of black-hole binaries, we turn to full numerical techniques. We introduce empirical formulae to describe the final remnant black hole mass, spin, and recoil velocity for merging black-hole binaries with arbitrary mass ratios and spins. We then evaluate those formulae for randomly chosen directions of the individual spins and magnitudes as well as the binary's mass ratio. We found that the magnitude of the recoil velocity distribution decays as P(v) \exp(-v/2500km/s), =630km/s, and sqrt{ - ^2}= 534km/s, leading to a 23% probability of recoils larger than 1000km/s, and a highly peaked angular distribution along the final orbital axis. The final black-hole spin magnitude show a universal distribution highly peaked at Sf/mf^2=0.73 and a 25 degrees misalignment with respect to the final orbital angular momentum.

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arXiv2010

Intermediate Mass Ratio Black Hole Binaries: Numerical Relativity meets Perturbation Theory

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.

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arXiv2009

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.

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arXiv2009

Status of NINJA: the Numerical INJection Analysis project

The 2008 NRDA conference introduced the Numerical INJection Analysis project (NINJA), a new collaborative effort between the numerical relativity community and the data analysis community. NINJA focuses on modeling and searching for gravitational wave signatures from the coalescence of binary system of compact objects. We review the scope of this collaboration and the components of the first NINJA project, where numerical relativity groups shared waveforms and data analysis teams applied various techniques to detect them when embedded in colored Gaussian noise.

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arXiv2009

Algebraic Classification of Numerical Spacetimes and Black-Hole-Binary Remnants

In this paper we develop a technique for determining the algebraic classification of a numerical spacetime, possibly resulting from a generic black-hole-binary merger, using the Newman-Penrose Weyl scalars. We demonstrate these techniques for a test case involving a close binary with arbitrarily oriented spins and unequal masses. We find that, post merger, the spacetime quickly approaches Petrov type II, and only approaches type D on much longer timescales. These techniques allow us to begin to explore the validity of the "no-hair theorem" for generic merging-black-hole spacetimes.

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arXiv2009

Modeling gravitational recoil from precessing highly-spinning unequal-mass black-hole binaries

We measure the gravitational recoil for unequal-mass-black- hole-binary mergers, with the larger BH having spin a/m^H=0.8, and the smaller BH non-spinning. We choose our configurations such that, initially, the spins lie on the orbital plane. The spin and orbital plane precess significantly, and we find that the out-of plane recoil (i.e. the recoil perpendicular to the orbital plane around merger) varies as η^2 / (1+q), in agreement with our previous prediction, based on the post-Newtonian scaling.

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arXiv2009

Comparison of Post-Newtonian and Numerical Evolutions of Black-Hole Binaries

In this paper, we compare the waveforms from the post-Newtonian (PN) approach with the numerical simulations of generic black-hole binaries which have mass ratio $q\sim0.8$, arbitrarily oriented spins with magnitudes $S_1/m_1^2\sim0.6$ and $S_2/m_2^2\sim0.4$, and orbit 9 times from an initial orbital separation of $r\approx11M$ prior to merger. We observe a reasonably good agreement between the PN and numerical waveforms, with an overlap of over 98% for the first six cycles of the $(\ell=2,m=\pm2)$ mode and over 90% for the $(\ell=2,m=1)$ and $(\ell=3,m=3)$ modes.

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arXiv2009

Comparison of Numerical and Post-Newtonian Waveforms for Generic Precessing Black-Hole Binaries

We compare waveforms and orbital dynamics from the first long-term, fully non-linear, numerical simulations of a generic black-hole binary configuration with post-Newtonian predictions. The binary has mass ratio q~0.8 with arbitrarily oriented spins of magnitude S_1/m_1^2~0.6 and S_2/m_2^2~0.4 and orbits 9 times prior to merger. The numerical simulation starts with an initial separation of r~11M, with orbital parameters determined by initial 2.5PN and 3.5PN post-Newtonian evolutions of a quasi-circular binary with an initial separation of r=50M. The resulting binaries have very little eccentricity according to the 2.5PN and 3.5PN systems, but show significant eccentricities of e~0.01-0.02 and e~0.002-0.005 in the respective numerical simulations, thus demonstrating that 3.5PN significantly reduces the eccentricity of the binary compared to 2.5PN. We perform three numerical evolutions from r~11M with maximum resolutions of h=M/48,M/53.3,M/59.3, to verify numerical convergence. We observe a reasonably good agreement between the PN and numerical waveforms, with an overlap of nearly 99% for the first six cycles of the (l=2,m=+-2) modes, 91% for the (l=2,m=+-1) modes, and nearly 91% for the (l=3,m=+-3) modes. The phase differences between numerical and post-Newtonian approximations appear to be independent of the (l,m) modes considered and relatively small for the first 3-4 orbits. An advantage of the 3.5 PN model over the 2.5 PN one seems to be observed, which indicates that still higher PN order (perhaps even 4.0PN) may yield significantly better waveforms. In addition, we identify features in the waveforms likely related to precession and precession-induced eccentricity.

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arXiv2008

Extra-Large Remnant Recoil Velocities and Spins from Near-Extremal-Bowen-York-Spin Black-Hole Binaries

We evolve equal-mass, equal-spin black-hole binaries with specific spins of a/mH 0.925, the highest spins simulated thus far and nearly the largest possible for Bowen-York black holes, in a set of configurations with the spins counter-aligned and pointing in the orbital plane, which maximizes the recoil velocities of the merger remnant, as well as a configuration where the two spins point in the same direction as the orbital angular momentum, which maximizes the orbital hang-up effect and remnant spin. The coordinate radii of the individual apparent horizons in these cases are very small and the simulations require very high central resolutions (h ~ M/320). We find that these highly spinning holes reach a maximum recoil velocity of ~3300 km/s (the largest simulated so far) and, for the hangup configuration, a remnant spin of a/mH 0.922. These results are consistent with our previous predictions for the maximum recoil velocity of ~4000 km/s and remnant spin; the latter reinforcing the prediction that cosmic censorship is not violated by merging highly-spinning black-hole binaries. We also numerically solve the initial data for, and evolve, a single maximal-Bowen-York-spin black hole, and confirm that the 3-metric has an O(1/r^2) singularity at the puncture, rather than the usual O(1/r^4) singularity seen for non-maximal spins.

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arXiv2008

Close encounters of three black holes

We present the first fully relativistic longterm numerical evolutions of three equal-mass black holes in a system consisting of a third black hole in a close orbit about a black-hole binary. We find that these close-three-black-hole systems have very different merger dynamics from black-hole binaries. In particular, we see complex trajectories, a redistribution of energy that can impart substantial kicks to one of the holes, distinctive waveforms, and suppression of the emitted gravitational radiation. We evolve two such configurations and find very different behaviors. In one configuration the binary is quickly disrupted and the individual holes follow complicated trajectories and merge with the third hole in rapid succession, while in the other, the binary completes a half-orbit before the initial merger of one of the members with the third black hole, and the resulting two-black-hole system forms a highly elliptical, well separated binary that shows no significant inspiral for (at least) the first t~1000M of evolution.

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arXiv2008

Further insight into gravitational recoil

We test the accuracy of our recently proposed empirical formula to model the recoil velocity imparted to the merger remnant of spinning, unequal-mass black-hole binaries. We study three families of black-hole binary configurations, all with mass ratio q=3/8 (to maximize the unequal-mass contribution to the kick) and spins aligned (or counter aligned) with the orbital angular momentum, two with spin configurations chosen to minimize the spin-induced tangential and radial accelerations of the trajectories respectively, and a third family where the trajectories are significantly altered by spin-orbit coupling. We find good agreement between the measured and predicted recoil velocities for the first two families, and reasonable agreement for the third. We also re-examine our original generic binary configuration that led to the discovery of extremely large spin-driven recoil velocities and inspired our empirical formula, and find reasonable agreement between the predicted and measured recoil speeds.

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arXiv2008

Foundations of multiple black hole evolutions

We present techniques for long-term, stable, and accurate evolutions of multiple-black-hole spacetimes using the `moving puncture' approach with fourth- and eighth-order finite difference stencils. We use these techniques to explore configurations of three black holes in a hierarchical system consisting of a third black hole approaching a quasi-circular black-hole binary, and find that, depending on the size of the binary, the resulting encounter may lead to a prompt merger of all three black holes, production of a highly elliptical binary (with the third black hole remaining unbound), or disruption of the binary (leading to three free black holes). We also analyze the classical Burrau three-body problem using full numerical evolutions. In both cases, we find behaviors distinctly different from Newtonian predictions, which has important implications for N-body black-hole simulations. For our simulations we use analytic approximate data. We find that the eighth-order stencils significantly reduce the numerical errors for our choice of grid sizes, and that the approximate initial data produces the expected waveforms (after a rescaling of the puncture masses) for black-hole binaries with modest initial separations.

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arXiv2007

Quasi-Local Linear Momentum in Black-Hole Binaries

We propose a quasi-local formula for the linear momentum of black-hole horizons inspired by the formalism of quasi-local horizons. We test this formula using two complementary configurations: (i) by calculating the large orbital linear momentum of the two black holes in an unequal-mass, zero-spin, quasi-circular binary and (ii) by calculating the very small recoil momentum imparted to the remnant of the head-on collision of an equal-mass, anti-aligned-spin binary. We obtain results consistent with the horizon trajectory in the orbiting case, and consistent with the net radiated linear momentum for the much smaller head-on recoil velocity.

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