Catalog of 174 Binary Black Hole Simulations for Gravitational Wave Astronomy

This Letter presents a publicly available catalog of 174 numerical binary black hole simulations following up to 35 orbits. The catalog includes 91 precessing binaries, mass ratios up to $8:1$, orbital eccentricities from a few percent to ${10}^{-5}$, black hole spins up to 98% of the theoretical maximum, and radiated energies up to 11.1% of the initial mass. We establish remarkably good agreement with post-Newtonian precession of orbital and spin directions for two new precessing simulations, and we discuss other applications of this catalog. Formidable challenges remain: e.g., precession complicates the connection of numerical and approximate analytical waveforms, and vast regions of the parameter space remain unexplored.

Figure 1

The parameter space covered by our catalog. Each point represents a simulation. The axes show the mass ratio and the spin magnitudes of the larger (blue arrows) and smaller (red arrows) BHs. Arrows indicate the magnitude and direction of the spins.

Figure 2

Properties of all simulations in the catalog. From top to bottom: Dimensionless initial spin magnitudes ${\chi }_{A,B}$, angles ${\theta }_{A,B}$ between the initial spin vectors and the initial orbital angular momentum, angles ${\varphi }_{A,B}$ between the line segment connecting the centers of the black holes and the initial spin vectors projected into the initial orbital plane, mass ratio $q=M_A/M_B$, number of orbits before merger, initial eccentricity $e$ (triangles indicate an upper bound on $e$), and final remnant spin ${\chi }_f$.

Figure 3

Waveform polarizations $(r/M)h_{+}$ (blue curves) and $(r/M)h_{\times }$ (orange curves) in a sky direction parallel to the initial orbital plane of each simulation. The unit of the time axis corresponds to $1000M=0.1\mathrm{s}$ for binaries with total mass $M=20M_{\odot }$.

Figure 4

Top: Waveforms $r{h}_{+}/M$ (blue curves) and $r{h}_{\times }/M$ (orange curves) for two detector directions ($\theta$, $\varphi$) relative to the initial orbital plane. Bottom: Cumulative phase differences between the $\ell =2$, $m=2$ spherical-harmonic mode of the waveform of numerical resolutions $L1$ through $L5$ compared to that of the highest resolution $L6$.

Figure 5

Precessing simulations 0035 and 0165. Top: Precession and nutation of the orbital angular momentum and the spin vectors of the BHs. The circles denote the initial location of the vectors. Bottom: Comparison of dynamical quantities with post-Newtonian theory: angle $\angle L$ between PN and NR Newtonian orbital angular momentum, angle $\angle {\chi }_{A,B}$ between PN and NR spins (${\chi }_B=0$ for 0035), and difference $\delta {\varphi }_{\mathrm{orb}}$ in orbital phase. All differences are in radians.

Figure 6

The radiated energy (as measured by the fractional difference between the initial and final Christodoulou masses, where the initial mass is the sum of the holes’ masses after the initial relaxation) for each simulation in the catalog.