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 _ { max } = 526 \pm 23 km s ^ { -1 } , which occurs when the progenitor spins are maximal , the mass ratio is q _ { max } = m _ { 1 } / m _ { 2 } = 0.623 \pm 0.038 , the smaller black-hole spin is aligned with the orbital angular momentum , and the larger black-hole spin is counteraligned ( \alpha _ { 1 } = - \alpha _ { 2 } = 1 ) .
This maximum recoil is about 80 km s ^ { -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 km s ^ { -1 } can be as large as 17 \% , while the probability for recoils faster than 250 km s ^ { -1 } can be as large as 45 % .
We provide explicit phenomenological formulas for the final mass , spin , and recoil as a function of the individual BH 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 _ { rad } / m \approx 11.3 \% and final spin \alpha _ { rem } ^ { max } \approx 0.952 for equal mass , aligned maximally spinning binaries .