A catalog of 171 high-quality binary black-hole simulations for gravitational-wave astronomy Abdul H. Mrou´ e, 1 Mark A. Scheel, 2 B´ ela Szil´ agyi, 2 Harald P. Pfeiffer, 1 Michael Boyle, 3 Daniel A. Hemberger, 3 Lawrence E. Kidder, 3 Geoffrey Lovelace, 4, 2 Sergei Ossokine, 1, 5 Nicholas W. Taylor, 2 Anıl Zengino˘ glu, 2 Luisa T. Buchman, 2 Tony Chu, 1 Evan Foley, 4 Matthew Giesler, 4 Robert Owen, 6 and Saul A. Teukolsky 3 1 Canadian Institute for Theoretical Astrophysics, 60 St. George Street, University of Toronto, Toronto, ON M5S 3H8, Canada 2 Theoretical Astrophysics 350-17, California Institute of Technology, Pasadena, CA 91125, USA 3 Center for Radiophysics and Space Research, Cornell University, Ithaca, New York 14853, USA 4 Gravitational Wave Physics and Astronomy Center, California State University Fullerton, Fullerton, California 92834, USA 5 Department of Astronomy and Astrophysics, 50 St. George Street, University of Toronto, Toronto, ON M5S 3H4, Canada 6 Department of Physics and Astronomy, Oberlin College, Oberlin, Ohio 44074, USA (Dated: December 26, 2013) Coalescing binary black holes are a primary science target of ground-based gravitational-wave detectors, which require detailed knowledge of the expected waveforms to maximize detections and our understanding of the waves’ sources. This paper presents a catalog of numerical binary black- hole simulations that represents a major advance toward the application of numerical relativity to gravitational-wave data analysis. Specifically, the catalog contains 171 numerical simulations that maintain the high accuracy required for matched filtering while following more orbits (up to 33) than previous simulations. A larger number of orbits allows a more reliable connection to approximate analytical waveforms, which are used to extend numerical waveforms to span the entire frequency range of a detector. The catalog contains 91 precessing binaries, providing the most comprehensive survey of precessing systems to date, and includes waveforms with black-hole spins up to 0.97, mass ratios up to 8, and orbital eccentricities from a few percent to ∼10 -4 . With this combination of length, accuracy, and parameter-space coverage, the catalog can be used to significantly improve existing gravitational-wave templates (including precessing binaries), to study detection efficiency of gravitational-wave searches, and to quantify systematic biases of parameter estimation of detected gravitational waves. Formidable challenges remain; for example, precession complicates the connection of numerical and approximate analytical waveforms, and vast regions of the parameter space remain unexplored. PACS numbers: 04.25.D-, 04.25.dg, 04.25.Nx, 04.30.-w, 04.30.Db INTRODUCTION Gravitational waves (GW) from coalescing compact object binaries —black holes (BH) or neutron stars (NS)— are the primary targets for the next generation of GW detectors, such as advanced LIGO, Virgo and KA- GRA [1–4]. The ability to detect compact object bina- ries depends on the quality and accuracy of the theoret- ical waveform models used in template banks for GW searches. Similarly, parameter estimation of detected candidate signals relies on theoretical waveform models used in Markov-Chain-Monte Carlo algorithms [5]. For widely separated binaries, post-Newtonian (PN) calculations [6] provide the gravitational waveforms to good accuracy. However, as the binary tightens and be- comes more relativistic, the accuracy of the PN expansion deteriorates. The failure of PN expansions particularly concerns binaries containing BHs because their higher to- tal mass places the merger portion of the waveform close to the most sensitive frequency region of the GW detec- tors. Moreover, black holes may carry large spins (up to the maximum allowed dimensionless spin of the Kerr solution, χ = S/M 2 = 1), but PN spin contributions have been known to lower expansion order than the non- spinning terms [7–26]. Direct numerical simulations of the full Einstein equations are therefore needed to cover the late inspiral, merger, and ringdown portions of the binary evolution. This paper focuses on binary black holes (BBH). Di- rect numerical simulations of BBHs became possible eight years ago [27], with tremendous progress since (e.g., [28, 29]). Such simulations must satisfy several conditions: (i) sufficient accuracy; (ii) astrophysical rel- evance, particularly low orbital eccentricity [30, 31]; (iii) sufficient length (i.e., number of orbits) to connect reli- ably to PN waveforms; (iv) sufficiently dense coverage of relevant regions of parameter space. The meaning of “sufficient” is determined by the ap- plication. Regarding simulation length, for instance, 10 orbits suffices for signal detection at modestly challenging BH parameters (mass ratio q < ∼ 4, aligned spins χ < ∼ 0.7) [32]. For parameter estimation, the number of orbits is well above 100 [32–35]. Requirements become more strin- gent with increasing black hole spin and mass ratio [34]. For precessing binaries, analogous studies have not even been performed. Satisfying all conditions (i) to (iv) is so difficult that, despite the advances in numerical methods, simulations arXiv:1304.6077v1 [gr-qc] 22 Apr 2013