The SXS Collaboration catalog of binary black hole simulations

TL;DR

The study addresses the need for accurate gravitational-wave templates by expanding the SXS catalog of numerical-relativity BBH simulations to $2018$ configurations, including $1426$ precessing cases with mass ratios up to $10$ and spin magnitudes up to $0.998$, with a median waveform length of about $N_{ m cyc}\approx39$ for the dominant mode. It employs the Spectral Einstein Code (SpEC) with XCTS initial data, eccentricity-reduction loops, and a generalized harmonic evolution on a multi-domain spectral grid, accompanied by dual gravitational-wave extraction methods ($\Psi_4$ extrapolated to $\\mathscr{I}^+$ and RWZ perturbation theory) and comprehensive post-processing (extrapolation to infinity and center-of-mass corrections). The work provides detailed assessments of waveform quality (typical mismatches $\sim 10^{-4}$–$10^{-3}$) and remnant properties (mass/spin uncertainties $\sim 0.03\%$ and $0.1\%$ at $90^{\text{th}}$ percentile), demonstrates good agreement with existing remnant fits, and makes the full catalog publicly available, enabling improved GW data analysis, surrogate modeling, and NR-based validations. The authors also outline future directions to further expand the parameter space, lengthen simulations, reduce junk radiation, and pursue Cauchy-characteristic extraction for more accurate waveforms.

Abstract

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 .

Figures (13)

• Figure 1: Center of Mass (COM) corrected and uncorrected waveform mode amplitudes (left) and COM drift in simulation units (right) for spin-aligned system SXS:BBH:0314 (top) and precessing system SXS:BBH:0622 (bottom). For the waveform mode amplitude plots on the left, the thick translucent curves show the COM corrected amplitudes and the solid thin curves show the uncorrected amplitudes. Removing unphysical modulations with our COM correction allows for the physical amplitude modulations of precessing systems to become more apparent. For the COM drift plots on the right, the axes show the coordinate positions of the apparent-horizon centers, normalized by the initial total mass of the system $M_0$. The different colored lines correspond to the Newtonian COM, Eq. \ref{['COMdef']}, at different resolutions. Note that each resolution for a simulation uses the same initial conditions. The COM values are plotted for each system from start until a common horizon is found.
• Figure 2: Histograms showing the magnitude of the center-of-mass (COM) translations $\vec{\alpha}$ and boosts $\vec{\beta}$ as defined in Eq. \ref{['eq:COMsupertranslation_def']}, and total displacements $\vec{\alpha} + t_{{\textrm{\tiny{CAH}}}}\vec{\beta}$, for all simulations in our catalog. The top row shows values for non-precessing systems while the bottom row shows values for precessing systems. The blue bars denote the newer simulations that utilize the improved initial data procedure Ossokine:2015yla, whereas the orange bars denote earlier simulations.
• Figure 3: Coverage of the SXS Catalog parameter space. Each point is one simulation. Shown here are the mass ratio $q = m_{1}/m_{2}$ and the spin magnitudes $|\chi_1|$ and $|\chi_2|$ of the larger and smaller black hole, respectively. Orange points correspond to configurations that are not precessing (spins aligned with the orbital angular momentum), while blue points correspond to precessing configurations.
• Figure 4: Number of cycles of $\ell=m=2$ gravitational waves before merger for the simulations in the catalog, as determined by the coordinate trajectories of the black holes. Bin edges are multiples of 10 cycles.
• Figure 5: Initial eccentricities $e_{0}$ in the catalog. The main population is the result of eccentricity-reduction, and those intentionally exploring high $e_{0}$ constitute the tail.