科研之友
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摘要
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, to study precession effects. We vary the initial direction of the total spin (S) over right arrow with respect to the orbital angular momentum (L) over right arrow, covering the two-dimensional space of orientation angles with 38 configurations consisting of 36 configurations distributed in the azimuthal angle phi and polar angle mu = cos theta, and two configurations on the poles. In all cases, we set the initial dimensionless black hole spins to 0.8. We observe that during the late-inspiral stage, the total angular momentum of the system (J) over right arrow remains within 5 degrees of its original direction, with the largest changes in direction occurring when the spins are nearly (but not exactly) counteraligned with the orbital angular momentum. We also observe that the angle between (S) over right arrow and (L) over right arrow 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) using a least-squared fit to the results of this new set of 38 runs, an additional set of five new configurations with spins aligned or counteraligned with the orbital angular momentum, and more than a hundred recent simulations. We find that our formulas reproduce the remnant mass and spin of these simulations to within a relative error of 2.5%. We discuss the region of validity of this dynamical picture for precessing unequalmass 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.
- 出版日期2014-5-23
