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Binary black-hole systems with spins aligned with the orbital angular momentum are of special interest, as studies indicate that this configuration is preferred in nature due to non-vacuum environmental interactions, as well as post-Newtonian (PN) spin-orbit couplings. If the spins of the two bodies differ, there can be a prominent beaming of the gravitational radiation during the late plunge, causing a recoil of the final merged black hole. In this paper we perform an accurate and systematic study of recoil velocities from a sequence of equal-mass black holes whose spins are aligned with the orbital angular momentum, and whose individual spins range from a=+0.584 to -0.584. In this way we extend and refine the results of a previous study which concentrated on the antialigned portion of this sequence, to arrive at a consistent maximum recoil of 448±5km/s for antialigned models as well as to a phenomenological expression for the recoil velocity as a function of spin ratio. Quite surprisingly, this relation highlights a nonlinear behavior, not predicted by the PN estimates, and can be readily employed in astrophysical studies on the evolution of binary black holes in massive galaxies. An essential result of our analysis, without which no systematic behavior can be found, is the identification of different stages in the waveform, including a transient due to lack of an initial linear momentum in the initial data. Furthermore, by decomposing the recoil computation into coupled modes, we are able to identify a pair of terms which are largely responsible for the kick, indicating that an accurate computation can be obtained from modes up to ℓ=3. Finally, we provide accurate measures of the radiated energy and angular momentum, finding these to increase linearly with the spin ratio, and derive simple expressions for the final spin and the radiated angular momentum which can be easily implemented in N-body simulations of compact stellar systems. Our code is calibrated with strict convergence tests and we verify the correctness of our measurements by using multiple independent methods whenever possible. © 2007 The American Physical Society.

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Physical Review D - Particles, Fields, Gravitation and Cosmology