Remnant of binary black-hole mergers: New simulations and peak luminosity studies

We present the results of 61 new simulations of nonprecessing spinning black hole binaries with mass ratios $q=m_1/m_2$ in the range $1/3\le q\le 1$ and individual spins covering the parameter space $-0.85\le {\alpha }_{1,2}\le 0.85$. We additionally perform ten new simulations of nonspinning black hole binaries with mass ratios covering the range $1/6\le q<1$. We follow the evolution for typically the last ten orbits before merger down to the formation of the final remnant black hole. This allows for assessment of the accuracy of our previous empirical formulas for relating the binary parameters to the remnant final black hole mass, spin and recoil. We use the new simulation to improve the fit to the above remnant formulas and add a formula for the peak luminosity of gravitational waves, produced around the merger of the two horizons into one. We find excellent agreement (typical errors $\sim 0.1\%–0.2\%$) for the mass and spin, and within $\sim 5\%$ for the recoil and peak luminosity. These formulas have direct application to parameter estimation techniques applied to LIGO observations of gravitational waves from binary black hole mergers.

Figure 1

Initial configuration of the simulated binaries. The black dots represent the previous simulations reported in [20] and those in blue are the new simulations of this paper. Those points in light gray are obtained by the symmetry $1\leftrightarrow 2$ of the case $q=1$.

Figure 2

Counts of the number of runs whose residual (data fit) falls within a particular bin. Both cases have 25 bins over the visible range with the final mass shown in the top panel, and final spin in the bottom panel. V1 labels the fitting from Ref. [20] and V2 labels the fitting from this paper.

Figure 3

Predicted values and residuals of the runs compared to the new fitting for the final mass.

Figure 4

Predicted values and residuals of the runs compared to the new fitting for the final spin.

Figure 5

Counts of the number of runs whose residual (data fit) falls within a particular bin. Both cases have 25 bins over the visible range with the recoil velocity shown in the top panel, and recoil velocity in the bottom panel. V1 labels the fitting from Ref. [20] and V2 labels the fitting from this paper.

Figure 6

Predicted values and residuals of the runs compared to the new fitting for the peak luminosity.

Figure 7

Predicted values and residuals (in km/s) of the runs compared to the new fitting for the recoil velocity.

Figure 8

Plots of the convergence of the recoil velocity (top left), peak luminosity (top right), energy radiated (bottom left), and angular momentum radiated (bottom right) as a function of $m/r_{\mathrm{obs}}$ for case 80—Q1.0000_-0.8000_0.8000. Horizontal green solid lines in the bottom row indicate the energy and angular momentum radiated calculated from the isolated horizon. The dark gray lines in each plot shows the extrapolation to infinite observer location using only up to $r=113\mathrm{m}$.

Figure 9

Plots of the convergence of the recoil velocity (top left), peak luminosity (top right), energy radiated (bottom left), and angular momentum radiated (bottom right) as a function of $m/r_{\mathrm{obs}}$ for case 47—Q0.7500_-0.8000_0.8000. Horizontal green solid lines in the bottom row indicate the energy and angular momentum radiated calculated from the isolated horizon.

Figure 10

Plots of the convergence of the recoil velocity (top left), peak luminosity (top right), energy radiated (bottom left), and angular momentum radiated (bottom right) as a function of $m/r_{\mathrm{obs}}$ for case 67—Q0.5000_0.0000_0.0000. Horizontal green solid lines in the bottom row indicate the energy and angular momentum radiated calculated from the isolated horizon.

Figure 11

Plots of the convergence of the recoil velocity (top left), peak luminosity (top right), energy radiated (bottom left), and angular momentum radiated (bottom right) as a function of $m/r_{\mathrm{obs}}$ for case 65—Q0.3333_0.0000_0.0000. Horizontal green solid lines in the bottom row indicate the energy and angular momentum radiated calculated from the isolated horizon.