Spin Diagrams for Equal-mass Black Hole Binaries with Aligned Spins

Binary black hole systems with spins aligned with the orbital angular momentum are of special interest, as they may be the preferred end state of the inspiral of generic supermassive binary black hole systems. In view of this, we have computed the inspiral and merger of a large set of binary systems of equal-mass black holes with spins aligned with the orbital angular momentum but otherwise arbitrary. By least-square fitting the results of these simulations, we have constructed two ‘‘spin diagrams’’ which provide straightforward information about the recoil velocity jvkickj and the final black hole spin aBn in terms of the dimensionless spins a1 and a2 of the two initial black holes. Overall, they suggest a maximum recoil velocity of jvkickj ’ 441:94 km s , andminimum andmaximumfinal spins aBn ’ 0:3471 and aBn 1⁄4 0:9591, respectively. Subject headinggs: black hole physics — gravitational waves — relativity — stars: statistics Online material: color figures