Testing the Accuracy and Stability of Spectral Methods in Numerical Relativity

The accuracy and stability of the Caltech-Cornell pseudospectral code is evaluated using the KST representation of the Einstein evolution equations. The basic "Mexico City Tests" widely adopted by the numerical relativity community are adapted here for codes based on spectral methods. Exponential convergence of the spectral code is established, apparently limited only by numerical roundoff error. A general expression for the growth of errors due to finite machine precision is derived, and it is shown that this limit is achieved here for the linear plane-wave test. All of these tests are found to be stable, except for simulations of high amplitude gauge waves with nontrivial shift.Comment: Final version, as published in Phys. Rev. D; 13 pages, 16 figure

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.Comment: 17 pages, 9 figures. Version accepted by PR

The SXS Collaboration catalog of binary black hole simulations

Accurate models of gravitational waves from merging black holes are necessary for detectors to observe as many events as possible while extracting the maximum science. Near the time of merger, the gravitational waves from merging black holes can be computed only using numerical relativity. In this paper, we present a major update of the Simulating eXtreme Spacetimes (SXS) Collaboration catalog of numerical simulations for merging black holes. The catalog contains 2018 distinct configurations (a factor of 11 increase compared to the 2013 SXS catalog), including 1426 spin-precessing configurations, with mass ratios between 1 and 10, and spin magnitudes up to 0.998. The median length of a waveform in the catalog is 39 cycles of the dominant $\ell=m=2$ gravitational-wave mode, with the shortest waveform containing 7.0 cycles and the longest 351.3 cycles. We discuss improvements such as correcting for moving centers of mass and extended coverage of the parameter space. We also present a thorough analysis of numerical errors, finding typical truncation errors corresponding to a waveform mismatch of $\sim 10^{-4}$. The simulations provide remnant masses and spins with uncertainties of 0.03% and 0.1% ($90^{\text{th}}$ percentile), about an order of magnitude better than analytical models for remnant properties. The full catalog is publicly available at https://www.black-holes.org/waveforms .Comment: 33+18 pages, 13 figures, 4 tables, 2,018 binaries. Catalog metadata in ancillary JSON file. v2: Matches version accepted by CQG. Catalog available at https://www.black-holes.org/waveform

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.Comment: 56 pages, 25 figures; various clarifications; accepted to CQ

Zodiacal Exoplanets in Time (Zeit) Iii: A Short-Period Planet Orbiting a Pre-Main-Sequence Star in the Upper Scorpius Ob Association

We confirm and characterize a close-in (Porb = 5.425 days), super-Neptune sized (5.04+0.34 −0.37 R⊕) planet transiting K2-33 (2MASS J16101473-1919095), a late-type (M3) pre-main sequence (11 Myr-old) star in the Upper Scorpius subgroup of the Scorpius-Centaurus OB association. The host star has the kinematics of a member of the Upper Scorpius OB association, and its spectrum contains lithium absorption, an unambiguous sign of youth (< 20 Myr) in late-type dwarfs. We combine photometry from K2 and the ground-based MEarth project to refine the planet’s properties and constrain the host star’s density. We determine K2-33’s bolometric flux and effective temperature from moderate resolution spectra. By utilizing isochrones that include the effects of magnetic fields, we derive a precise radius (6-7%) and mass (16%) for the host star, and a stellar age consistent with the established value for Upper Scorpius. Follow-up high-resolution imaging and Doppler spectroscopy confirm that the transiting object is not a stellar companion or a background eclipsing binary blended with the target. The shape of the transit, the constancy of the transit depth and periodicity over 1.5 years, and the independence with wavelength rules out stellar variability, or a dust cloud or debris disk partially occulting the star as the source of the signal; we conclude it must instead be planetary in origin. The existence of K2-33b suggests close-in planets can form in situ or migrate within ∼ 10 Myr, e.g., via interactions with a disk, and that long-timescale dynamical migration such as by Lidov-Kozai or planet-planet scattering is not responsible for all short-period planets.Astronom

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. © 2009 IOP Publishing Ltd

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. © 2009 IOP Publishing Ltd