The final spin from binary black holes in quasi-circular orbits
  We revisit the problem of predicting the spin magnitude and direction of the
black hole resulting from the merger of two black holes with arbitrary masses
and spins inspiralling in quasi-circular orbits. We do this by analyzing a
catalog of 619 recent numerical-relativity simulations collected from the
literature and spanning a large variety of initial conditions. By combining
information from the post-Newtonian approximation, the extreme mass-ratio limit
and perturbative calculations, we improve our previously proposed
phenomenological formulae for the final remnant spin. In contrast with
alternative suggestions in the literature, and in analogy with our previous
expressions, the new formula is a simple algebraic function of the initial
system parameters and is not restricted to binaries with spins
aligned/anti-aligned with the orbital angular momentum, but can be employed for
fully generic binaries. The accuracy of the new expression is significantly
improved, especially for almost extremal progenitor spins and for small mass
ratios, yielding a root-mean-square error $\sigma\approx0.002$ for
aligned/anti-aligned binaries and $\sigma\approx0.006$ for generic binaries.
Our new formula is suitable for cosmological applications and can be employed
robustly in the analysis of the gravitational waveforms from advanced
interferometric detectors.
