arXiv subjects

Wolfgang Tichy

Publications and source records attributed to Wolfgang Tichy.

At least 55 records · Page 3Linked to original sources

arXiv2012

The NINJA-2 catalog of hybrid post-Newtonian/numerical-relativity waveforms for non-precessing black-hole binaries

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 and parameter-estimation algorithms using numerically generated waveforms, and to foster closer collaboration between the numerical relativity and data analysis communities. The first NINJA project used only a small number of injections of short numerical-relativity waveforms, which limited its ability to draw quantitative conclusions. The goal of the NINJA-2 project is to overcome these limitations with long post-Newtonian - numerical relativity hybrid waveforms, large numbers of injections, and the use of real detector data. We report on the submission requirements for the NINJA-2 project and the construction of the waveform catalog. Eight numerical relativity groups have contributed 63 hybrid waveforms consisting of a numerical portion modelling the late inspiral, merger, and ringdown stitched to a post-Newtonian portion modelling the early inspiral. We summarize the techniques used by each group in constructing their submissions. We also report on the procedures used to validate these submissions, including examination in the time and frequency domains and comparisons of waveforms from different groups against each other. These procedures have so far considered only the $(\ell,m)=(2,2)$ mode. Based on these studies we judge that the hybrid waveforms are suitable for NINJA-2 studies. We note some of the plans for these investigations.

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arXiv2011

Covariant formulation of the post-1-Newtonian approximation to General Relativity

We derive a coordinate-independent formulation of the post-1-Newtonian approximation to general relativity. This formulation is a generalization of the Newton-Cartan geometric formulation of Newtonian gravity. It involves several fields and a connection, but no spacetime metric at the fundamental level. We show that the usual coordinate-dependent equations of post-Newtonian gravity are recovered when one specializes to asymptotically flat spacetimes and to appropriate classes of coordinates.

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arXiv2011

Recent Advances in the Numerical Simulations of Binary Black Holes

Since the breakthrough papers from 2005/2006, the field of numerical relativity has experienced a growth spurt that took the two-body problem in general relativity from the category of "really-hard-problems" to the realm of "things-we-know-how-to-do". Simulations of binary black holes in circular orbits, the holy grail of numerical relativity, are now tractable problems that lead to some of the most spectacular results in general relativity in recent years. We cover here some of the latest achievements and highlight the field's next challenges.

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arXiv2011

Initial data for binary neutron stars with arbitrary spins

In general neutron stars in binaries are spinning. Due to the existence of millisecond pulsars we know that these spins can be substantial. We argue that spins with periods on the order a few dozen milliseconds could influence the late inspiral and merger dynamics. Thus numerical simulations of the last few orbits and the merger should start from initial conditions that allow for arbitrary spins. We discuss quasi-equilibrium approximations one can make in the construction of binary neutron star initial data with spins. Using these approximations we are able to derive two new matter equations. As in the case of irrotational neutron star binaries one of these equations is algebraic and the other elliptic. If these new matter equations are solved together with the equations for the metric variables following the Wilson-Mathews or conformal thin sandwich approach one can construct neutron star initial data. The spin of each star is described by a rotational velocity that can be chosen freely so that one can create stars in arbitrary rotation states. Our new matter equations reduce to the well known limits of both corotating and irrotational neutron star binaries.

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arXiv2011

A Simple method to set up low eccentricity initial data for moving puncture simulations

We introduce two new eccentricity measures to analyze numerical simulations. Unlike earlier definitions these eccentricity measures do not involve any free parameters which makes them easy to use. We show how relatively inexpensive grid setups can be used to estimate the eccentricity during the early inspiral phase. Furthermore, we compare standard puncture data and post-Newtonian data in ADMTT gauge. We find that both use different coordinates. Thus low eccentricity initial momentum parameters for a certain separation measured in ADMTT coordinates are hard to use in puncture data, because it is not known how the separation in puncture coordinates is related to the separation in ADMTT coordinates. As a remedy we provide a simple approach which allows us to iterate the momentum parameters until our numerical simulations result in acceptably low eccentricities.

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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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arXiv2009

Long term black hole evolution with the BSSN system by pseudospectral methods

We present long term evolutions of a single black hole of mass $M$ with the BSSN system using pseudospectral methods. For our simulations we use the SGRID code where the BSSN system is implemented in its standard second order in space form. Previously we found that such simulations are quite unstable. The main goal of this paper is to present two improvements which now allow us to evolve for longer times. The first improvement is related to the boundary conditions at the excised black hole interior. We now use a gauge condition that ensures that all modes are going into the black hole, so that no boundary conditions are needed at the excision surface. The second more significant improvement has to do with our particular numerical method and involves filters based on projecting the double Fourier expansions used for the angular dependence onto Spherical Harmonics. With these two improvements it is now easily possible to evolve for several thousand $M$. The only remaining limitation seems to be the radiative outer boundary conditions used here. Yet this problem can be ameliorated by pushing out the location of the outer boundary, which leads to even longer run-times.

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arXiv2009

Self-force with (3+1) codes: a primer for numerical relativists

Prescriptions for numerical self-force calculations have traditionally been designed for frequency-domain or (1+1) time-domain codes which employ a mode decomposition to facilitate in carrying out a delicate regularization scheme. This has prevented self-force analyses from benefiting from the powerful suite of tools developed and used by numerical relativists for simulations of the evolution of comparable-mass black hole binaries. In this work, we revisit a previously-introduced (3+1) method for self-force calculations, and demonstrate its viability by applying it to the test case of a scalar charge moving in a circular orbit around a Schwarzschild black hole. Two (3+1) codes originally developed for numerical relativity applications were independently employed, and in each we were able to compute the two independent components of the self-force and the energy flux correctly to within $< 1%$. We also demonstrate consistency between $t$-component of the self-force and the scalar energy flux. Our results constitute the first successful calculation of a self-force in a (3+1) framework, and thus open opportunities for the numerical relativity community in self-force analyses and the perturbative modeling of extreme-mass-ratio inspirals.

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arXiv2009

A new numerical method to construct binary neutron star initial data

We present a new numerical method for the generation of binary neutron star initial data using a method along the lines of the the Wilson-Mathews or the closely related conformal thin sandwich approach. Our method uses six different computational domains, which include spatial infinity. Each domain has its own coordinates which are chosen such that the star surfaces always coincide with domain boundaries. These properties facilitate the imposition of boundary conditions. Since all our fields are smooth inside each domain, we are able to use an efficient pseudospectral method to solve the elliptic equations associated with the conformal thin sandwich approach. Currently we have implemented corotating configurations with arbitrary mass ratios, but an extension to arbitrary spins is possible. The main purpose of this paper is to introduce our new method and to test our code for several different configurations.

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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

Conformally curved binary black hole initial data including tidal deformations and outgoing radiation

(Abridged) By asymptotically matching a post-Newtonian (PN) metric to two tidally perturbed Schwarzschild metrics, we generate approximate initial data (in the form of a 4-metric) for a nonspinning black hole binary in a circular orbit. We carry out this matching through O(v^4) in the binary's orbital velocity v, so the resulting data are conformally curved. Far from the holes, we use the appropriate PN metric that accounts for retardation, which we construct using the highest-order PN expressions available to compute the binary's past history. The data set's uncontrolled remainders are thus O(v^5) throughout the timeslice; we also generate an extension to the data set that has uncontrolled remainders of O(v^6) in the purely PN portion of the timeslice (i.e., not too close to the holes). The resulting data are smooth, since we join all the metrics together by smoothly interpolating between them. We perform this interpolation using transition functions constructed to avoid introducing excessive additional constraint violations. Due to their inclusion of tidal deformations and outgoing radiation, these data should substantially reduce the initial spurious ("junk") radiation observed in current simulations that use conformally flat initial data. Such reductions in the nonphysical components of the initial data will be necessary for simulations to achieve the accuracy required to supply Advanced LIGO and LISA with the templates necessary for parameter estimation.

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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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arXiv2008

The final mass and spin of black hole mergers

We consider black holes resulting from binary black hole mergers. By fitting to numerical results we construct analytic formulas that predict the mass and spin of the final black hole. Our formulas are valid for arbitrary initial spins and mass ratios and agree well with available numerical simulations. We use our spin formula in the context of two common merger scenarios for supermassive galactic black holes. We consider the case of isotropically distributed initial spin orientations (when no surrounding matter is present) and also the case when matter closely aligns the spins with the orbital angular momentum. The spin magnitude of black holes resulting from successive generations of mergers (with symmetric mass ratio $η$) has a mean of $1.73η+ 0.28$ in the isotropic case and 0.94 for the closely aligned case.

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arXiv2008

High-spin binary black hole mergers

We study identical mass black hole binaries with spins perpendicular to the binary's orbital plane. These binaries have individual spins ranging from $s/m^2=-0.90$ to 0.90, ($s_1 = s_2$ in all cases) which is near the limit possible with standard Bowen-York puncture initial data. The extreme cases correspond to the largest initial spin simulations to date. Our results expand the parameter space covered by Rezzolla {\it et al.} and, when combining both data sets, we obtain estimations for the minimum and maximum values for the intrinsic angular momenta of the remnant of binary black hole mergers of $J/M^2=0.341 \pm 0.004$ and $0.951 \pm 0.004$ respectively. Note, however, that these values are reached through extrapolation to the singular cases $|s_1| = |s_2| = 1$ and thus remain as {\it estimates} until full-fledged numerical simulations provide confirmation.

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arXiv2007

Black hole puncture initial data with realistic gravitational wave content

We present improved post-Newtonian-inspired initial data for non-spinning black-hole binaries, suitable for numerical evolution with punctures. We revisit the work of Tichy et al. [W. Tichy, B. Bruegmann, M. Campanelli, and P. Diener, Phys. Rev. D 67, 064008 (2003)], explicitly calculating the remaining integral terms. These terms improve accuracy in the far zone and, for the first time, include realistic gravitational waves in the initial data. We investigate the behavior of these data both at the center of mass and in the far zone, demonstrating agreement of the transverse-traceless parts of the new metric with quadrupole-approximation waveforms. These data can be used for numerical evolutions, enabling a direct connection between the merger waveforms and the post-Newtonian inspiral waveforms.

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arXiv2007

Binary black holes on a budget: Simulations using workstations

Binary black hole simulations have traditionally been computationally very expensive: current simulations are performed in supercomputers involving dozens if not hundreds of processors, thus systematic studies of the parameter space of binary black hole encounters still seem prohibitive with current technology. Here we show how the multi-layered refinement level code BAM can be used on dual processor workstations to simulate certain binary black hole systems. BAM, based on the moving punctures method, provides grid structures composed of boxes of increasing resolution near the center of the grid. In the case of binaries, the highest resolution boxes are placed around each black hole and they track them in their orbits until the final merger when a single set of levels surrounds the black hole remnant. This is particularly useful when simulating spinning black holes since the gravitational fields gradients are larger. We present simulations of binaries with equal mass black holes with spins parallel to the binary axis and intrinsic magnitude of S/m^2= 0.75. Our results compare favorably to those of previous simulations of this particular system. We show that the moving punctures method produces stable simulations at maximum spatial resolutions up to M/160 and for durations of up to the equivalent of 20 orbital periods.

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arXiv2007

Binary black hole mergers: large kicks for generic spin orientations

We present results from several simulations of equal mass black holes with spin. The spin magnitudes are $S/m^2=0.8$ in all cases, but we vary the spin orientations arbitrarily, in and outside the orbital plane. We find that in all but one case the final merged black hole acquires a kick of more than 1000 km/s, indicating that kicks of this magnitude are likely to be generic and should be expected for mergers with general spin orientations. The maximum kick velocity we find is 2500 km/s and occurs for initial spins which are anti-aligned in the initial orbital plane.

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arXiv2006

Binary black hole initial data from matched asymptotic expansions

We present an approximate metric for a binary black hole spacetime to construct initial data for numerical relativity. This metric is obtained by asymptotically matching a post-Newtonian metric for a binary system to a perturbed Schwarzschild metric for each hole. In the inner zone near each hole, the metric is given by the Schwarzschild solution plus a quadrupolar perturbation corresponding to an external tidal gravitational field. In the near zone, well outside each black hole but less than a reduced wavelength from the center of mass of the binary, the metric is given by a post-Newtonian expansion including the lowest-order deviations from flat spacetime. When the near zone overlaps each inner zone in a buffer zone, the post-Newtonian and perturbed Schwarzschild metrics can be asymptotically matched to each other. By demanding matching (over a 4-volume in the buffer zone) rather than patching (choosing a particular 2-surface in the buffer zone), we guarantee that the errors are small in all zones. The resulting piecewise metric is made formally $C^\infty$ with smooth transition functions so as to obtain the finite extrinsic curvature of a 3-slice. In addition to the metric and extrinsic curvature, we present explicit results for the lapse and the shift, which can be used as initial data for numerical simulations. This initial data is not accurate all the way to the asymptotically flat ends inside each hole, and therefore must be used with evolution codes which employ black hole excision rather than puncture methods. This paper lays the foundations of a method that can be sraightforwardly iterated to obtain initial data to higher perturbative order.

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