http://arxiv.org/abs/1312.5775
We perform a set of 38 fully-nonlinear numerical simulations of equal-mass black-hole binaries in a configuration where the two black-hole spins in the binary are equal in both magnitude and direction, which maximizes precession effects. We vary the initial direction of the total spin S with respect to the orbital angular momentum L, covering the 2 dimensional space of orientation angles with 36 configurations equally distributed in the azimuthal angle phi and polar angle mu=cos theta, plus one configuration on each of the two poles. We observe that during the late inspiral stage, the total angular momentum of the system J remains within 5 deg. of its original direction, with the largest changes in direction occurring when the spins are nearly counter-aligned with the orbital angular momentum. We also observe that the angle between S and L is nearly conserved during the inspiral phase. These two dynamical properties allow us to propose a new phenomenological formula for the final mass and spin of merged black holes in terms of the individual masses and spins of the progenitor binary at far separations. We determine coefficients of this formula (in the equal-mass limit) by fitting to this new set of 38 runs, an additional set of five configurations with spins aligned/counteraligned with the orbital angular momentum, and over a hundred recent simulations. We discuss the region of validity of this dynamical picture for precessing unequal-mass binaries. Finally, we perform a statistical study to see the consequence of this new formula for distributions of spin-magnitudes and remnant masses with applications to black-hole-spin distributions and gravitational radiation in cosmological scenarios involving several mergers.
Mon, 23 Dec 13
42/48
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