The final spin from the coalescence of aligned-spin black hole binaries

Determining the final spin of a black hole (BH) binary is a question of key importance in astrophysics. Modeling this quantity in general is made difficult by the fact that it depends on the seven-dimensional space of parameters characterizing the two initial black holes. However, in special cases, when symmetries can be exploited, the description can become simpler. For BH binaries with unequal masses but with equal spins which are aligned with the orbital angular momentum, we show that the use of recent simulations and basic but exact constraints derived from the extreme mass-ratio limit allow us to model this quantity with a simple analytic expression. Despite the simple dependence, the expression models very accurately all of the available estimates, with errors of a couple of percent at most. We also discuss how to use the fit to predict when a Schwarzschild BH is produced by the merger of two spinning BHs, when the total angular momentum of the spacetime "flips" sign, or under what conditions the final BH is "spun up" by the merger. Finally, we suggest an extension of the fit to include unequal-spin binaries, thus potentially providing a complete description of the final spin from the coalescence of generic BH binaries with spins aligned to the orbital angular momentum.