arXiv subjects

Frank Herrmann

Publications and source records attributed to Frank Herrmann.

At least 19 recordsLinked to original sources

arXiv2013

Hidden Momentum and Black Hole Kicks

A stationary magnetic dipole immersed in an electric field carries "hidden" mechanical momentum. However, the fate of this momentum if the fields are turned off is unclear. We consider a charge-and-dipole hidden momentum configuration, and turn off the fields by collapsing a null shell onto the system, forming a black hole. In numerical calculations we find that the black hole receives a kick corresponding to 0.1% of the initial stored momentum. When extrapolated to apply to purely gravitational phenomena, this efficiency suggests a role for the hidden momentum kick mechanism in generating the binary black hole "superkicks" observed in numerical simulations of Einstein's equation.

gr-qc↗

arXiv2012

Two-step greedy algorithm for reduced order quadratures

We present an algorithm to generate application-specific, global reduced order quadratures (ROQ) for multiple fast evaluations of weighted inner products between parameterized functions. If a reduced basis (RB) or any other projection-based model reduction technique is applied, the dimensionality of integrands is reduced dramatically; however, the cost of approximating the integrands by projection still scales as the size of the original problem. In contrast, using discrete empirical interpolation (DEIM) points as ROQ nodes leads to a computational cost which depends linearly on the dimension of the reduced space. Generation of a reduced basis via a greedy procedure requires a training set, which for products of functions can be very large. Since this direct approach can be impractical in many applications, we propose instead a two-step greedy targeted towards approximation of such products. We present numerical experiments demonstrating the accuracy and the efficiency of the two-step approach. The presented ROQ are expected to display very fast convergence whenever there is regularity with respect to parameter variation. We find that for the particular application here considered, one driven by gravitational wave physics, the two-step approach speeds up the offline computations to build the ROQ by more than two orders of magnitude. Furthermore, the resulting ROQ rule is found to converge exponentially with the number of nodes, and a factor of ~50 savings, without loss of accuracy, is observed in evaluations of inner products when ROQ are used as a downsampling strategy for equidistant samples using the trapezoidal rule. While the primary focus of this paper is on quadrature rules for inner products of parameterized functions, our method can be easily adapted to integrations of single parameterized functions, and some examples of this type are considered.

math.NA↗

arXiv2012

Towards beating the curse of dimensionality for gravitational waves using Reduced Basis

Using the Reduced Basis approach, we efficiently compress and accurately represent the space of waveforms for non-precessing binary black hole inspirals, which constitutes a four dimensional parameter space (two masses, two spin magnitudes). Compared to the non-spinning case, we find that only a {\it marginal} increase in the (already relatively small) number of reduced basis elements is required to represent any non-precessing waveform to nearly numerical round-off precision. Most parameters selected by the algorithm are near the boundary of the parameter space, leaving the bulk of its volume sparse. Our results suggest that the full eight dimensional space (two masses, two spin magnitudes, four spin orientation angles on the unit sphere) may be highly compressible and represented with very high accuracy by a remarkably small number of waveforms, thus providing some hope that the number of numerical relativity simulations of binary black hole coalescences needed to represent the entire space of configurations is not intractable. Finally, we find that the {\it distribution} of selected parameters is robust to different choices of seed values starting the algorithm, a property which should be useful for indicating parameters for numerical relativity simulations of binary black holes. In particular, we find that the mass ratios $m_1/m_2$ of non-spinning binaries selected by the algorithm are mostly in the interval $[1,3]$ and that the median of the distribution follows a power-law behavior $\sim (m_1/m_2)^{-5.25}$.

gr-qc↗

arXiv2012

Numerical simulations with a first order BSSN formulation of Einstein's field equations

We present a new fully first order strongly hyperbolic representation of the BSSN formulation of Einstein's equations with optional constraint damping terms. We describe the characteristic fields of the system, discuss its hyperbolicity properties, and present two numerical implementations and simulations: one using finite differences, adaptive mesh refinement and in particular binary black holes, and another one using the discontinuous Galerkin method in spherical symmetry. The results of this paper constitute a first step in an effort to combine the robustness of BSSN evolutions with very high accuracy numerical techniques, such as spectral collocation multi-domain or discontinuous Galerkin methods.

gr-qc↗

arXiv2011

Reduced Basis representations of multi-mode black hole ringdown gravitational waves

We construct compact and high accuracy Reduced Basis (RB) representations of single and multiple quasinormal modes (QNMs). The RB method determines a hierarchical and relatively small set of the most relevant waveforms. We find that the exponential convergence of the method allows for a dramatic compression of template banks used for ringdown searches. Compressing a catalog with a minimal match $\MMm=0.99$, we find that the selected RB waveforms are able to represent {\em any} QNM, including those not in the original bank, with extremely high accuracy, typically less than $10^{-13}$. We then extend our studies to two-mode QNMs. Inclusion of a second mode is expected to help with detection, and might make it possible to infer details of the progenitor of the final black hole. We find that the number of RB waveforms needed to represent any two-mode ringdown waveform with the above high accuracy is {\em smaller} than the number of metric-based, one-mode templates with $\MMm=0.99$. For unconstrained two-modes, which would allow for consistency tests of General Relativity, our high accuracy RB has around $10^4$ {\em fewer} waveforms than the number of metric-based templates for $\MMm=0.99$. The number of RB elements grows only linearly with the number of multipole modes versus exponentially with the standard approach, resulting in very compact representations even for many multiple modes. The results of this paper open the possibility of searches of multi-mode ringdown gravitational waves.

gr-qc↗

arXiv2011

Reduced basis catalogs for gravitational wave templates

We introduce a reduced basis approach as a new paradigm for modeling, representing and searching for gravitational waves. We construct waveform catalogs for non-spinning compact binary coalescences, and we find that for accuracies of 99% and 99.999% the method generates a factor of about $10-10^5$ fewer templates than standard placement methods. The continuum of gravitational waves can be represented by a finite and comparatively compact basis. The method is robust under variations in the noise of detectors, implying that only a single catalog needs to be generated.

gr-qc↗

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.

gr-qc↗

arXiv2010

Statistical constraints on binary black hole inspiral dynamics

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.

gr-qc↗

arXiv2009

Integrating Post-Newtonian Equations on Graphics Processing Units

We report on early results of a numerical and statistical study of binary black hole inspirals. The two black holes are evolved using post-Newtonian approximations starting with initially randomly distributed spin vectors. We characterize certain aspects of the distribution shortly before merger. In particular we note the uniform distribution of black hole spin vector dot products shortly before merger and a high correlation between the initial and final black hole spin vector dot products in the equal-mass, maximally spinning case. These simulations were performed on Graphics Processing Units, and we demonstrate a speed-up of a factor 50 over a more conventional CPU implementation.

gr-qc↗

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.

gr-qc↗

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.

gr-qc↗

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.

gr-qc↗

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.

gr-qc↗

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.

gr-qc↗

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.

gr-qc↗

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.

gr-qc↗

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.

gr-qc↗

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.

gr-qc↗