arXiv subjects

Ian Hinder

Publications and source records attributed to Ian Hinder.

At least 37 records · Page 2Linked to original sources

arXiv2010

Dynamical damping terms for symmetry-seeking shift conditions

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.

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arXiv2010

Kranc: a Mathematica application to generate numerical codes for tensorial evolution equations

We present a suite of Mathematica-based computer-algebra packages, termed "Kranc", which comprise a toolbox to convert (tensorial) systems of partial differential evolution equations to parallelized C or Fortran code. Kranc can be used as a "rapid prototyping" system for physicists or mathematicians handling very complicated systems of partial differential equations, but through integration into the Cactus computational toolkit we can also produce efficient parallelized production codes. Our work is motivated by the field of numerical relativity, where Kranc is used as a research tool by the authors. In this paper we describe the design and implementation of both the Mathematica packages and the resulting code, we discuss some example applications, and provide results on the performance of an example numerical code for the Einstein equations.

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arXiv2010

Comparisons of eccentric binary black hole simulations with post-Newtonian models

We present the first comparison between numerical relativity (NR) simulations of an eccentric binary black hole system with corresponding post-Newtonian (PN) results. We evolve an equal-mass, non-spinning configuration with an initial eccentricity e ~ 0.1 for 21 gravitational wave cycles before merger, and find agreement in the gravitational wave phase with an adiabatic eccentric PN model with 2 PN radiation reaction within 0.1 radians for 10 cycles. The NR and PN phase difference grows to 0.7 radians by 5 cycles before merger. We find that these results can be obtained by expanding the eccentric PN expressions in terms of the frequency-related variable x = (omega M)^{2/3} with M the total mass of the binary. When using instead the mean motion n = 2 π/P, where P is the orbital period, the comparison leads to significant disagreements with NR.

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arXiv2010

The Current Status of Binary Black Hole Simulations in Numerical Relativity

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.

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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

The Samurai Project: verifying the consistency of black-hole-binary waveforms for gravitational-wave detection

We quantify the consistency of numerical-relativity black-hole-binary waveforms for use in gravitational-wave (GW) searches with current and planned ground-based detectors. We compare previously published results for the $(\ell=2,| m | =2)$ mode of the gravitational waves from an equal-mass nonspinning binary, calculated by five numerical codes. We focus on the 1000M (about six orbits, or 12 GW cycles) before the peak of the GW amplitude and the subsequent ringdown. We find that the phase and amplitude agree within each code's uncertainty estimates. The mismatch between the $(\ell=2,| m| =2)$ modes is better than $10^{-3}$ for binary masses above $60 M_{\odot}$ with respect to the Enhanced LIGO detector noise curve, and for masses above $180 M_{\odot}$ with respect to Advanced LIGO, Virgo and Advanced Virgo. Between the waveforms with the best agreement, the mismatch is below $2 \times 10^{-4}$. We find that the waveforms would be indistinguishable in all ground-based detectors (and for the masses we consider) if detected with a signal-to-noise ratio of less than $\approx14$, or less than $\approx25$ in the best cases.

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arXiv2009

Binary black hole evolutions of approximate puncture initial data

Approximate solutions to the Einstein field equations are a valuable tool to investigate gravitational phenomena. An important aspect of any approximation is to investigate and quantify its regime of validity. We present a study that evaluates the effects that approximate puncture initial data, based on "skeleton" solutions to the Einstein constraints as proposed by Faye et al. [PRD 69, 124029 (2004)], have on numerical evolutions. Using data analysis tools, we assess the effectiveness of these constraint-violating initial data and show that the matches of waveforms from skeleton data with the corresponding waveforms from constraint-satisfying initial data are > 0.97 when the total mass of the binary is > 40M(solar). In addition, we demonstrate that the differences between the skeleton and the constraint-satisfying initial data evolutions, and thus waveforms, are due to negative Hamiltonian constraint violations present in the skeleton initial data located in the vicinity of the punctures. During the evolution, the skeleton data develops both Hamiltonian and momentum constraint violations that decay with time, with the binary system relaxing to a constraint-satisfying solution with black holes of smaller mass and thus different dynamics.

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arXiv2008

Superkicks in Hyperbolic Encounters of Binary Black Holes

Generic inspirals and mergers of binary black holes produce beamed emission of gravitational radiation that can lead to a gravitational recoil or kick of the final black hole. The kick velocity depends on the mass ratio and spins of the binary as well as on the dynamics of the binary configuration. Studies have focused so far on the most astrophysically relevant configuration of quasi-circular inspirals, for which kicks as large as 3,300 km/s have been found. We present the first study of gravitational recoil in hyperbolic encounters. Contrary to quasi-circular configurations, in which the beamed radiation tends to average during the inspiral, radiation from hyperbolic encounters is plunge dominated, resulting in an enhancement of preferential beaming. As a consequence, it is possible to achieve kick velocities as large as 10,000 km/s.

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arXiv2008

Circularization and Final Spin in Eccentric Binary Black Hole Inspirals

We present results from numerical relativity simulations of equal mass, non-spinning binary black hole inspirals and mergers with initial eccentricities e <= 0.8 and coordinate separations D >= 12 M of up to 9 orbits (18 gravitational wave cycles). We extract the mass M_f and spin a_f of the final black hole and find, for eccentricities e < 0.4, that a_f/M_f = 0.69 and M_f/M_adm = 0.96 are independent of the initial eccentricity, suggesting that the binary has circularized by the merger time. For e > 0.5, the black holes plunge rather than orbit, and we obtain a maximum spin parameter a_f/M_f = 0.72 around e = 0.5.

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arXiv2008

Numerical Relativity meets Data Analysis: Spinning Binary Black Hole Case

We present a study of the gravitational waveforms from a series of spinning, equal-mass black hole binaries focusing on the harmonic content of the waves and the contribution of the individual harmonics to the signal-to-noise ratio. The gravitational waves were produced from two series of evolutions with black holes of initial spins equal in magnitude and anti-aligned with each other. In one series the magnitude of the spin is varied; while in the second, the initial angle between the black-hole spins and the orbital angular momentum varies. We also conduct a preliminary investigation into using these waveforms as templates for detecting spinning binary black holes. Since these runs are relativity short, containing about two to three orbits, merger and ringdown, we limit our study to systems of total mass greater than 50 solar masses. This choice ensures that our waveforms are present in the ground-based detector band without needing addition gravitational wave cycles. We find that while the mode contribution to the signal-to-noise ratio varies with the initial angle, the total mass of the system caused greater variations in the match.

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arXiv2008

Robustness of Binary Black Hole Mergers in the Presence of Spurious Radiation

We present an investigation into how sensitive the last orbits and merger of binary black hole systems are to the presence of spurious radiation in the initial data. Our numerical experiments consist of a binary black hole system starting the last couple of orbits before merger with additional spurious radiation centered at the origin and fixed initial angular momentum. As the energy in the added spurious radiation increases, the binary is invariably hardened for the cases we tested, i.e. the merger of the two black holes is hastened. The change in merger time becomes significant when the additional energy provided by the spurious radiation increases the Arnowitt-Deser-Misner (ADM) mass of the spacetime by about 1%. While the final masses of the black holes increase due to partial absorption of the radiation, the final spins remain constant to within our numerical accuracy. We conjecture that the spurious radiation is primarily increasing the eccentricity of the orbit and secondarily increasing the mass of the black holes while propagating out to infinity.

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arXiv2008

Probing the Binary Black Hole Merger Regime with Scalar Perturbations

We present results obtained by scattering a scalar field off the curved background of a coalescing binary black hole system. A massless scalar field is evolved on a set of fixed backgrounds, each provided by a spatial hypersurface generated numerically during a binary black hole merger. We show that the scalar field scattered from the merger region exhibits quasinormal ringing once a common apparent horizon surrounds the two black holes. This occurs earlier than the onset of the perturbative regime as measured by the start of the quasinormal ringing in the gravitational waveforms. We also use the scalar quasinormal frequencies to associate a mass and a spin with each hypersurface, and observe the compatibility of this measure with the horizon mass and spin computed from the dynamical horizon framework.

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arXiv2007

Binary Black Holes: Spin Dynamics and Gravitational Recoil

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

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arXiv2007

Matched Filtering of Numerical Relativity Templates of Spinning Binary Black Holes

Tremendous progress has been made towards the solution of the binary-black-hole problem in numerical relativity. The waveforms produced by numerical relativity will play a role in gravitational wave detection as either test-beds for analytic template banks or as template banks themselves. As the parameter space explored by numerical relativity expands, the importance of quantifying the effect that each parameter has on first the detection of gravitational waves and then the parameter estimation of their sources increases. In light of this, we present a study of equal-mass, spinning binary-black-hole evolutions through matched filtering techniques commonly used in data analysis. We study how the match between two numerical waveforms varies with numerical resolution, initial angular momentum of the black holes and the inclination angle between the source and the detector. This study is limited by the fact that the spinning black-hole-binaries are oriented axially and the waveforms only contain approximately two and a half orbits before merger. We find that for detection purposes, spinning black holes require the inclusion of the higher harmonics in addition to the dominant mode, a condition that becomes more important as the black-hole-spins increase. In addition, we conduct a preliminary investigation of how well a template of fixed spin and inclination angle can detect target templates of arbitrary spin and inclination for the axial case considered here.

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arXiv2007

Gravitational recoil from spinning binary black hole mergers

The inspiral and merger of binary black holes will likely involve black holes with both unequal masses and arbitrary spins. The gravitational radiation emitted by these binaries will carry angular as well as linear momentum. A net flux of emitted linear momentum implies that the black hole produced by the merger will experience a recoil or kick. Previous studies have focused on the recoil velocity from unequal mass, non-spinning binaries. We present results from simulations of equal mass but spinning black hole binaries and show how a significant gravitational recoil can also be obtained in these situations. We consider the case of black holes with opposite spins of magnitude $a$ aligned/anti-aligned with the orbital angular momentum, with $a$ the dimensionless spin parameters of the individual holes. For the initial setups under consideration, we find a recoil velocity of $V = 475 \KMS a$. Supermassive black hole mergers producing kicks of this magnitude could result in the ejection from the cores of dwarf galaxies of the final hole produced by the collision.

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arXiv2006

Numerical stability for finite difference approximations of Einstein's equations

We extend the notion of numerical stability of finite difference approximations to include hyperbolic systems that are first order in time and second order in space, such as those that appear in Numerical Relativity. By analyzing the symbol of the second order system, we obtain necessary and sufficient conditions for stability in a discrete norm containing one-sided difference operators. We prove stability for certain toy models and the linearized Nagy-Ortiz-Reula formulation of Einstein's equations. We also find that, unlike in the fully first order case, standard discretizations of some well-posed problems lead to unstable schemes and that the Courant limits are not always simply related to the characteristic speeds of the continuum problem. Finally, we propose methods for testing stability for second order in space hyperbolic systems.

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arXiv2005

Constraint damping in the Z4 formulation and harmonic gauge

We show that by adding suitable lower-order terms to the Z4 formulation of the Einstein equations, all constraint violations except constant modes are damped. This makes the Z4 formulation a particularly simple example of a lambda-system as suggested by Brodbeck et al. We also show that the Einstein equations in harmonic coordinates can be obtained from the Z4 formulation by a change of variables that leaves the implied constraint evolution system unchanged. Therefore the same method can be used to damp all constraints in the Einstein equations in harmonic gauge.

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