The final mass and spin of black hole mergers

TL;DR

This paper develops analytic formulas to predict the final mass and spin of black holes after mergers, valid for various initial conditions, and explores their implications in different astrophysical scenarios.

Contribution

It introduces new analytic formulas for the final mass and spin of merging black holes, fitting numerical data across arbitrary initial spins and mass ratios.

Findings

Formulas agree well with numerical simulations.

Final spin distributions depend on initial spin orientations.

Mean final spin varies with merger scenario and initial conditions.

Abstract

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.