Final mass and spin of black-hole mergers

We consider black holes resulting from binary black-hole mergers. By fitting to numerical results we construct analytic formulas that predict the mass and spin of the final black hole. Our formulas are valid for arbitrary initial spins and mass ratios and agree well with available numerical simulations. We use our spin formula in the context of two common merger scenarios for supermassive galactic black holes. We consider the case of isotropically distributed initial spin orientations (when no surrounding matter is present) and also the case when matter closely aligns the spins with the orbital angular momentum. The spin magnitude of black holes resulting from successive generations of mergers (with symmetric mass ratio $\eta$) has a mean of $1.73\eta +0.28$ in the isotropic case and 0.94 for the closely aligned case.

Figure 1

Probability density (for different mass ratios) of the final BH spin magnitude after 4 generations of dry mergers (top) and wet mergers (bottom).

Figure 2

Mean value of the final spin magnitude as a function of the symmetric mass ratio $\eta$. The vertical bars are the corresponding standard deviations.