Modeling the remnant mass, spin, and recoil from unequal-mass, precessing black-hole binaries: The intermediate mass ratio regime

We revisit the modeling of the properties of the remnant black hole resulting from the merger of a black-hole binary as a function of the parameters of the binary. We provide a set of empirical formulas for the final mass, spin, and recoil velocity of the final black hole as a function of the mass ratio and individual spins of the progenitor. In order to determine the fitting coefficients for these formulas, we perform a set of 128 new numerical evolutions of precessing, unequal-mass black-hole binaries, and fit to the resulting remnant mass, spin, and recoil. In order to reduce the complexity of the analysis, we chose configurations that have one of the black holes spinning, with dimensionless spin α =0.8 , at different angles with respect to the orbital angular momentum, and the other nonspinning. In addition to evolving families of binaries with different spin-inclination angles, we also evolved binaries with mass ratios as small as q =M₁/M₂=1 /6 . We use the resulting empirical formulas to predict the probabilities of black hole mergers leading to a given recoil velocity, total radiated gravitational energy, and final black hole spin.