Second RIT binary black hole simulations catalog and its application to gravitational waves parameter estimation

The RIT numerical relativity group is releasing the second public catalog of black-hole-binary waveforms http://ccrg.rit.edu/~RITCatalog. This release consists of 320 accurate simulations that include 46 precessing and 274 nonprecessing binary systems with mass ratios $q=m_1/m_2$ in the range $1/7\le q\le 1$ and individual spins up to $s/m^2=0.95$. The new catalog contains search and ordering tools for the waveforms based on initial parameters of the binary, trajectory information, peak radiation, and final remnant black hole properties. The final black hole remnant properties provided here can be used to model the merger of black-hole binaries from its initial configurations. The waveforms are extrapolated to future null infinity and can be used to independently interpret gravitational wave signals from laser interferometric detectors. As an application of this waveform catalog we reanalyze the signal of GW150914 implementing parameter estimation techniques that make use of only numerical waveforms without any reference to information from phenomenological waveforms models.

Figure 1

Initial parameters in the $(q,{\chi }_1,{\chi }_2)$ space for the 274 nonprecessing binaries. Note that ${\chi }_i$ denotes the component of the dimensionless spin of BH $i$ along the orbital angular momentum. Each panel corresponds to a given mass ratio that covers the comparable masses binary range from $q=1$ to $q=1/5$. The dots in black denote the simulations of the catalog first release, and the dots in red are those of this second release.

Figure 2

Counting simulations in the $(q,{\chi }_1,{\chi }_2)$ planes (faces of the cube) for the 274 nonprecessing binaries. The 120 release 1 simulations are black and the 154 release 2 simulations are red.

Figure 3

Top: Distributions of the total mass of BHB systems in the RIT catalog corresponding to a starting gravitational wave frequency of 20 Hz (blue) and 30 Hz (red) in bins of $5M_{\odot }$. Bottom: The cumulative version of the above plot also in bins of $5M_{\odot }$ for the 320 simulations in this catalog.

Figure 4

Heat maps of the GW150914 likelihood for each of the eight mass ratio panels covering form $q=1$ to $q=1/5$ and aligned/antialigned individual spins. The individual panel with $q=0.85$ contains the highest likelihood. Contour lines are in increments of 5. The interpolated $\ln \mathcal{L}$ maximum at its location in $(q,{\chi }_1,{\chi }_2)$ space is given in each panel’s title and denoted by the * in the plots.

Figure 5

90% confidence interval heat maps of the GW150914 likelihood for the aligned binary mass ratio and individual spin parameters. The dark grey region constitutes the 99.7% ($3\sigma$) confidence interval range, and the light grey is the 95% ($2\sigma$) range. The colored region shows the $\ln \mathcal{L}$ of the values within the 90% confidence interval. The black points indicate the placement of the numerical simulations.

Figure 6

Heat maps of the GW150914 likelihood for the aligned binary with effective variables $S_{hu}$ and ${\chi }_{\mathrm{eff}}$ versus mass ratios using linear interpolation. In black the 90% confidence contours and the interpolated $\ln \mathcal{L}$ maximum is given in each panel’s title and denoted by the * in the plots.

Figure 7

Final parameter space heatmaps for simulations that fall within the 90% confidence interval for the final mass, spin, recoil, peak luminosity, and orbital frequency and strain amplitude at peak strain. A maximum $\ln \mathcal{L}$ is reached for $m_f/m=0.952$, ${\chi }_f=0.683$, $V=44\mathrm{km}/\mathrm{s}$, $L^{\text{peak}}=1.01e-3$, $m{\mathrm{\Omega }}_{22}^{\text{peak}}=0.358$, and $(r/m)A_{22}^{\text{peak}}=0.391$.

Figure 8

Heat maps of the GW150914 likelihood for each of the six mass ratio panels covering form $q=2$ to $q=1/3$ (labeled from NQ200 to NQ33, respectively) and large black hole spin oriented over the sphere (interpolated using multiquadric radial basis functions between simulations). The individual panel with $q=1$ contains the highest likelihood (near the orbital plane orientation), and it is bracketed by the $q=1.4$ and $q=0.66$ panels ($q>1$ here means the smaller black hole is the one spinning). We have used Hammer-Aitoff coordinates $X_{HA},Y_{HA}$, to represent the map and level curves. The interpolated $\ln \mathcal{L}$ maximum location is denoted by the an x in the plots, the black points are simulations, and the gray points are extrapolated simulations using the sinusoidal dependence of the azimuthal angle.

Figure 9

We use the results of the Monte-Carlo intrinsic log-likelihood calculations (100 samples in $M_{\text{total}}$ for each simulation in the catalog) to estimate the extrinsic parameters of GW150914. The gray boundary denotes the public LIGO GWTC-1 data and the colored points indicate simulations which fell within the $\ln \mathcal{L}>\max \ln \mathcal{L}-3.125$, or roughly the 90% confidence interval. The dark blue background points denote simulations outside of the 90% confidence interval.

Figure 10

Direct comparison of the highest $\ln \mathcal{L}$ nonprecessing simulation (RIT:BBH:0113 in red) and precessing simulation (RIT:BBH:0126 in blue) to the Hanford (top) and Livingston (bottom) GW150914 signals. The bottom panel in each figure shows the residual between the whitened NR waveform and detector signal.

Figure 11

Panels showing different combinations of the 7 binary parameters of the precessing parameter space $(q,|{\chi }_1|,{\theta }_1,{\phi }_1,|{\chi }_2|,{\theta }_2,{\phi }_2)$ for the 46 precessing simulations in this catalog.