Application of the third RIT binary black hole simulations catalog to parameter estimation of gravitational waves signals from the LIGO-Virgo O1/O2 observational runs James Healy, Carlos O. Lousto, Jacob Lange, and Richard O'Shaughnessy Center for Computational Relativity and Gravitation, School of Mathematical Sciences, Rochester Institute of Technology, 85 Lomb Memorial Drive, Rochester, New York 14623 (Dated: October 2, 2020) Using exclusively the 777 full numerical waveforms of the third Binary Black Holes RIT catalog, we reanalyze the ten black hole merger signals reported in LIGO/Virgo's O1/O2 observation runs. We obtain binary parameters, extrinsic parameters, and the remnant properties of these gravitational waves events which are consistent with, but not identical to previously presented results. We have also analyzed three additional events (GW170121, GW170304, GW170727) reported in [1] and found closely matching parameters. We finally assess the accuracy of our waveforms with convergence studies applied to O1/O2 events and found them adequate for current estimation of parameters. PACS numbers: 04.25.dg, 04.25.Nx, 04.30.Db, 04.70.Bw I. INTRODUCTION 46]. Previous comparisons of GW observations to banks of NR simulations have used heterogeneous sets of NR simulations, with differences in accuracy standards and The Advanced LIGO [2] and Virgo [3] ground-based choices for initial starting separation. Only the analysis gravitational wave (GW) detectors have identified sev- of GW190521 presented posteriors for all intrinsic param- eral coalescing compact binaries [4{9] and characterized eters of a generic quasicircular binary black hole, allowing their properties with Bayesian inference [4{13]. As obser- for precessing spins. vatories' sensitivities increase, many more observations are expected [14], and some will be even better resolved. In this work, we analyze all proposed candidate BBH With more and some very informative events, these GW observations reported before the latest observing run observations pose a challenge to source parameter infer- (O3) with a single, consistent set of numerical relativity ence: barring substantial improvements, systematic un- simulations: the simulations in the third release of the certainty in our models will increasingly limit our ability RIT public catalog [38]. These simulations adopt consis- to draw the sharpest possible conclusions from each ob- tent resolutions and initial conditions. We demonstrate servation. that direct comparisons to numerical relativity simula- tions can recover all astrophysically interesting proper- Our understanding of the gravitational waves from ties of merging binary black holes, including the effect of merging binary black holes follows from numerical solu- misaligned spin. tions to Einstein's equations. Numerical relativity break- throughs [15{17] led to detailed predictions of the grav- This paper is organized as follows. In Sec. II we re- itational waves from the late inspiral, plunge, merger, view the methods we use to infer the intrinsic and ex- and ringdown of black-hole-binary systems (BHB). These trinsic parameters of compact binary sources, via direct predictions helped to accurately identify the first direct comparison to our specific set of numerical relativity sim- detection [18] of gravitational waves with such binary ulations. Specifically, following [44], on the grid of sim- arXiv:2010.00108v1 [gr-qc] 30 Sep 2020 black hole systems [19{22] and match them to targeted ulations we evaluate the Bayesian likelihood maximized supercomputer simulations [23{25]. There have been over extrinsic parameters, using RIFT [47]. We gener- several significant efforts to coordinate numerical rela- ate posterior distributions by interpolating the resulting tivity simulations to support gravitational wave obser- (marginal) likelihood distribution. In Sec. III we use the vations. These include the numerical injection analysis waveform catalog to estimate the binary black hole pa- (NINJA) project [26{29], the numerical relativity and rameters that best match the ten BBH signals reported in analytical relativity (NRAR) collaboration [30], and the the first and second LIGO-Virgo observing runs [48]. We waveform catalogs released by the SXS collaboration [31{ find our method can produce posteriors quite consistent 34], Georgia Tech, [35], and RIT [36{38]. Numerical rel- with previously reported results. Our headline posterior ativity simulations have been directly compared to GW inferences differ principally because we adopt different observations to draw inferences about binary parame- prior distributions for the binary mass, mass ratio, and ters, starting with GW150914 [23, 25, 37] and contin- spin [49]. We conclude in Sec. IV with a discussion of uing through GW170104 [39, 40], GW170608 [41], the the future use of this catalog for parameter inference of analysis in GWTC-1 [10], and GW190521 [42, 43]. Fur- new gravitational waves events and the extensions of this ther discussion of these methods can be found in [44{ work to more generic precessing binaries. 2 R 1 ∗~ II. APPLICATION OF THE WAVEFORMS hajbik ≡ −∞ 2dfa~(f) b(f)=Sh;k(jfj) is an inner prod- CATALOG TO PARAMETER ESTIMATION OF uct implied by the kth detector's noise power spectrum BINARY BLACK HOLES Sh;k(f). In practice we adopt a low-frequency cutoff fmin so all inner products are modified to A. Simulations Z [~a(f)]∗~b(f) hajbi ≡ 2 df : (2) The third release of the RIT public catalog [38] of k jfj>fmin Sh;k(jfj) numerical relativity black-hole-binary waveforms http: //ccrg.rit.edu/~RITCatalog consists of 777 accurate For our analysis of GW150914, we adopt the same noise simulations that include 300 precessing and 477 non- power spectrum employed in previous work [23, 54]. For precessing binary systems with mass ratios q = m1=m2 each simulation and each detector-frame mass Mz = (1+ in the range 1=15 ≤ q ≤ 1 and individual spins up to z)M, we then compute the marginalized likelihood S =m2 = 0:95. The catalog also provides initial parame- i i Z ters of the binary, trajectory information, peak radiation, L (λ) = dθp(θ)L(λ; θ) (3) and final remnant black hole properties. The catalog in- marg cludes all waveform modes ` ≤ 4 of 4 and the strain h (both extrapolated to null-infinity) and is updated to cor- where λ denotes the simulation parameters and the red- rect for the center of mass displacement during inspiral shifted mass Mz and where p(θ) is a conventional prior and after merger [38]. on the extrinsic parameters. The third RIT public catalog has two families of simu- For each simulation, the marginalized likelihood in Eq. lations salient to our comparison. First, the RIT catalog (3) is a one-dimensional function of Mz. In practice, has many nonprecessing simulations, displayed in Fig. 5 we explore a small range of redshifted masses for each of Ref. [38]. The RIT catalog also has many precess- simulation, to be sure we cover the region near the peak ing simulations, performed with similar settings and to a values well; see [23, 45]. consistent standard. To simplify the large precessing pa- rameter space, we focus on systems where one black hole is nonspinning, and vary the spin orientation of the other. C. Intrinsic coordinate systems and priors for binaries Currently this set of simulations consists of nine different mass ratio families as displayed in Fig. 8 of Ref. [38] with up to 40 different spin orientations per family. We sup- We characterize the intrinsic parameters of BH bina- plement the new simulations in this catalog release with ries with the (redshifted) components masses m1;z; m2;z those reported in Ref. [50, 51] and dimensionless spins χi. However, we will also use several other coordinates to characterize binary proper- ties when performing parameter inference. We use the B. Direct comparison of NR to GW observations familiar total mass Mz = m1;z + m2;z and mass ratio q = m1;z=m2;z, where we require m2;z > m1;z. For We can directly compare any of our simulations to real binary spins, we principally characterize the effects of or synthetic gravitational wave observations by scaling aligned spin in the strong field with Shu, defined by that simulation and its predictions to a specific total red- 2 1 ~ 1 ~ ^ shifted mass Mz and then marginalizing the likelihood for M Shu = (1 + ) S1 + (1 + q) S2 · L; (4) the gravitational wave data over all extrinsic parameters 2q 2 [23, 45, 52{54]: the seven coordinates characterizing the to describe the leading effect of hangup on the full nu- spacetime coordinates and orientation of the binary rel- merical waveforms [55]. Motivated by work on post- ative to the earth. Specifically the likelihood of the data Newtonian inspiral, we also use the variable [56] given Gaussian noise has the form (up to normalization) 1 1 X M 2 χ = (1 + ) S~ + (1 + q) S~ · L^ ln L(λ; θ) = − hh (λ; θ)−d jh (λ; θ)−d i −hd jd i ; eff q 1 2 2 k k k k k k k k k (1) to characterize the effects of aligned spins. th where hk are the predicted response of the k detector We adopt four distinct joint prior distributions over due to a source with parameters (λ, θ) and dk are the these intrinsic parameters. For the first family, appropri- detector data in each instrument k; λ denotes the combi- ate to generic quasicircular binaries, we adopt the generic nation of redshifted mass Mz and the remaining intrinsic quasicircular priors used in previous work [10, 47]: jointly parameters (mass ratio and spins; with eccentricity ≈ 0) uniform in m1;z; m2;z; a uniformly isotropic spin orienta- needed to uniquely specify the binary's dynamics; θ rep- tion distribution for both spins; and magnitudes jχ1j, resents the seven extrinsic parameters (4 spacetime co- jχ2j both uniform from 0 to 1. For the second fam- ordinates for the coalescence event and 3 Euler angles ily, appropriate to nonprecessing binaries, we adopt a for the binary's orientation relative to the Earth); and familiar nonprecessing prior [10, 47]: jointly uniform in 3 m1;z; m2;z; both spin angular momenta aligned with L^ robustness of the algorithm.