Implementation of standard testbeds for numerical relativity

We discuss results that have been obtained from the implementation of the initial round of testbeds for numerical relativity which was proposed in the first paper of the Apples with Apples Alliance. We present benchmark results for various codes which provide templates for analyzing the testbeds and to draw conclusions about various features of the codes. This allows us to sharpen the initial test specifications, design a new test and add theoretical insight.Comment: Corrected versio

Beyond the Bowen-York extrinsic curvature for spinning black holes

It is well-known that Bowen-York initial data contain spurious radiation. Although this ``junk'' radiation has been seen to be small for non-spinning black-hole binaries in circular orbit, its magnitude increases when the black holes are given spin. It is possible to reduce the spurious radiation by applying the puncture approach to multiple Kerr black holes, as we demonstrate for examples of head-on collisions of equal-mass black-hole binaries.Comment: 10 pages, 2 figures, submitted to special "New Frontiers in Numerical Relativity" issue of Classical and Quantum Gravit

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.Comment: 20 pages, 8 figures. Final version, to appear in a special issue of Class. Quantum Grav. based on the New Frontiers in Numerical Relativity Conference, Golm, July 200

Method to estimate ISCO and ring-down frequencies in binary systems and consequences for gravitational wave data analysis

Recent advances in the description of compact binary systems have produced gravitational waveforms that include inspiral, merger and ring-down phases. Comparing results from numerical simulations with those of post-Newtonian (PN), and related, expansions has provided motivation for employing PN waveforms in near merger epochs when searching for gravitational waves and has encouraged the development of analytic fits to full numerical waveforms. The models and simulations do not yet cover the full binary coalescence parameter space. For these yet un-simulated regions, data analysts can still conduct separate inspiral, merger and ring-down searches. Improved knowledge about the end of the inspiral phase, the beginning of the merger, and the ring-down frequencies could increase the efficiency of both coherent inspiral-merger-ring-down (IMR) searches and searches over each phase separately. Insight can be gained for all three cases through a recently presented theoretical calculation, which, corroborated by the numerical results, provides an implicit formula for the final spin of the merged black holes, accurate to within 10% over a large parameter space. Knowledge of the final spin allows one to predict the end of the inspiral phase and the quasinormal mode ring-down frequencies, and in turn provides information about the bandwidth and duration of the merger. In this work we will discuss a few of the implications of this calculation for data analysis.Comment: Added references to section 3 14 pages 5 figures. Submitted to Classical and Quantum Gravit

Radiation from low-momentum zoom-whirl orbits

We study zoom-whirl behaviour of equal mass, non-spinning black hole binaries in full general relativity. The magnitude of the linear momentum of the initial data is fixed to that of a quasi-circular orbit, and its direction is varied. We find a global maximum in radiated energy for a configuration which completes roughly one orbit. The radiated energy in this case exceeds the value of a quasi-circular binary with the same momentum by 15%. The direction parameter only requires minor tuning for the localization of the maximum. There is non-trivial dependence of the energy radiated on eccentricity (several local maxima and minima). Correlations with orbital dynamics shortly before merger are discussed. While being strongly gauge dependent, these findings are intuitive from a physical point of view and support basic ideas about the efficiency of gravitational radiation from a binary system.Comment: 9 pages, 6 figures, Amaldi8 conference proceedings as publishe

Ninja data analysis with a detection pipeline based on the Hilbert-Huang Transform

The Ninja data analysis challenge allowed the study of the sensitivity of data analysis pipelines to binary black hole numerical relativity waveforms in simulated Gaussian noise at the design level of the LIGO observatory and the VIRGO observatory. We analyzed NINJA data with a pipeline based on the Hilbert Huang Transform, utilizing a detection stage and a characterization stage: detection is performed by triggering on excess instantaneous power, characterization is performed by displaying the kernel density enhanced (KD) time-frequency trace of the signal. Using the simulated data based on the two LIGO detectors, we were able to detect 77 signals out of 126 above SNR 5 in coincidence, with 43 missed events characterized by signal to noise ratio SNR less than 10. Characterization of the detected signals revealed the merger part of the waveform in high time and frequency resolution, free from time-frequency uncertainty. We estimated the timelag of the signals between the detectors based on the optimal overlap of the individual KD time-frequency maps, yielding estimates accurate within a fraction of a millisecond for half of the events. A coherent addition of the data sets according to the estimated timelag eventually was used in a characterization of the event.Comment: Accepted for publication in CQG, special issue NRDA proceedings 200

Matching post-Newtonian and numerical relativity waveforms: systematic errors and a new phenomenological model for non-precessing black hole binaries

We present a new phenomenological gravitational waveform model for the inspiral and coalescence of non-precessing spinning black hole binaries. Our approach is based on a frequency domain matching of post-Newtonian inspiral waveforms with numerical relativity based binary black hole coalescence waveforms. We quantify the various possible sources of systematic errors that arise in matching post-Newtonian and numerical relativity waveforms, and we use a matching criteria based on minimizing these errors; we find that the dominant source of errors are those in the post-Newtonian waveforms near the merger. An analytical formula for the dominant mode of the gravitational radiation of non-precessing black hole binaries is presented that captures the phenomenology of the hybrid waveforms. Its implementation in the current searches for gravitational waves should allow cross-checks of other inspiral-merger-ringdown waveform families and improve the reach of gravitational wave searches.Comment: 22 pages, 11 figure

Toward a dynamical shift condition for unequal mass black hole binary simulations

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.Comment: 15 pages, submitted to CQG for NRDA 2009 conference proceeding

Merger of black hole-neutron star binaries in full general relativity

We present our latest results for simulation for merger of black hole (BH)-neutron star (NS) binaries in full general relativity which is performed preparing a quasicircular state as initial condition. The BH is modeled by a moving puncture with no spin and the NS by the $\Gamma$-law equation of state with $\Gamma=2$ and corotating velocity field as a first step. The mass of the BH is chosen to be $\approx 3.2 M_{\odot}$ or $4.0M_{\odot}$, and the rest-mass of the NS $\approx 1.4 M_{\odot}$ with relatively large radius of the NS $\approx 13$--14 km. The NS is tidally disrupted near the innermost stable orbit but $\sim 80$--90% of the material is swallowed into the BH and resulting disk mass is not very large as $\sim 0.3M_{\odot}$ even for small BH mass $\sim 3.2M_{\odot}$. The result indicates that the system of a BH and a massive disk of $\sim M_{\odot}$ is not formed from nonspinning BH-NS binaries irrespective of BH mass, although a disk of mass $\sim 0.1M_{\odot}$ is a possible outcome for this relatively small BH mass range as $\sim 3$--4$M_{\odot}$. Our results indicate that the merger of low-mass BH and NS may form a central engine of short-gamma-ray bursts.Comment: 14 pages. To appear in a special issue of Classical and Quantum Gravity: New Frontiers in Numerical Relativit