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The behavior of merging black holes (including the emitted gravitationalwaves and the properties of the remnant) can currently be computed only bynumerical simulations. This paper introduces ten numerical relativitysimulations of binary black holes with equal masses and equal spins aligned oranti-aligned with the orbital angular momentum. The initial spin magnitudeshave $|\chi_i| \lesssim 0.95$ and are more concentrated in the aligneddirection because of the greater astrophysical interest of this case. Wecombine this data with five previously reported simulations of the sameconfiguration, but with different spin magnitudes, including the highest spinsimulated to date, $\chi_i \approx 0.97$. This data set is sufficientlyaccurate to enable us to offer improved analytic fitting formulae for the finalspin and for the energy radiated by gravitational waves as a function ofinitial spin. The improved fitting formulae can help to improve ourunderstanding of the properties of binary black hole merger remnants and can beused to enhance future approximate waveforms for gravitational wave searches,such as Effective-One-Body waveforms.

Final spin and radiated energy in numerical simulations of binary black holes with equal masses and equal, aligned or anti-aligned spins