Remnant masses, spins and recoils from the merger of generic black hole binaries

Abstract

We obtain empirical formulae for the final remnant black hole mass, spin, and recoil velocity from merging black hole binaries (BHBs) with arbitrary mass ratios and spins. Our formulae are based on the mass ratio and spin dependence of the post-Newtonian expressions for the instantaneous radiated energy, linear momentum, and angular momentum, as well as the ISCO binding energy and angular momentum. The relative weight between the different terms is fixed by amplitude parameters chosen through a least-squares fit of recently available fully nonlinear numerical simulations. These formulae can be used for statistical studies of N-body simulations of galaxy cores and clusters, and the cosmological growth of supermassive black holes. As an example, we use these formulae to obtain a universal spin magnitude distribution of merged black holes and recoil velocity distributions for dry and hot/cold wet mergers. We also revisit the long-term orbital precession and resonances and discuss how they affect spin distributions before the merging regime.