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Authors: Luciano Rezzolla, Ernst Nils Dorband, Christian Reisswig, Peter Diener, Denis Pollney, Erik Schnetter, Bela Szilagyi

Date: 29 Aug 2007

Abstract: 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 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 |v_kick| and the final black-hole spin a_fin in terms of the dimensionless spins a_1 and a_2 of the two initial black holes. The analytic expressions used to construct the spin diagrams could be easily implemented in N-body simulations of compact stellar systems or in statistical studies on the evolution of binary black holes in massive galaxies, and suggest a maximum recoil velocity of |v_kick| = 441.94 +- 1.56 km/s for systems with a_1=-a_2=1 and maximum final spin a_fin =0.9591 +- 0.0022 for systems with a_1=a_2=1.

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