Remnant mass, spin, and recoil from spin aligned black-hole binaries
We perform a set of 36 nonprecessing black-hole binary simulations with spins either aligned or counteraligned with the orbital angular momentum in order to model the final mass, spin, and recoil of the merged black hole as a function of the individual black-hole spin magnitudes and the mass ratio of the progenitors. We find that the maximum recoil for these configurations is ${V}_{\mathrm{max}}=526\ifmmode\pm\else\textpm\fi{}23\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$, which occurs when the progenitor spins are maximal, the mass ratio is ${q}_{\mathrm{max}}={m}_{1}/{m}_{2}=0.623\ifmmode\pm\else\textpm\fi{}0.038$, the smaller black-hole spin is aligned with the orbital angular momentum, and the larger black-hole spin is counteraligned (${\ensuremath{\alpha}}_{1}=\ensuremath{-}{\ensuremath{\alpha}}_{2}=1$). This maximum recoil is about $80\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ larger than previous estimates, but most importantly, because the maximum occurs for smaller mass ratios, the probability for a merging binary to recoil faster than $400\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ can be as large as 17%, while the probability for recoils faster than $250\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ can be as large as 45% when the spins are aligned or counteraligned by accretion. We provide explicit phenomenological formulas for the final mass, spin, and recoil as a function of the individual black-hole spins and the mass difference between the two black holes. Here we include terms up through fourth order in the initial spins and mass difference and find excellent agreement (within a few percent) with independent results available in the literature. The maximum radiated energy is ${E}_{\text{rad}}/m\ensuremath{\approx}11.3%$ and final spin ${\ensuremath{\alpha}}_{\text{rem}}^{\mathrm{max}}\ensuremath{\approx}0.952$ for equal-mass, aligned, maximally spinning binaries.