The final spin from binary black holes in quasi-circular orbits

TL;DR

This paper presents an improved, simple algebraic formula for predicting the final spin of black holes resulting from binary mergers, applicable to generic initial spins and mass ratios, with high accuracy validated against extensive numerical simulations.

Contribution

The authors develop a new phenomenological formula for the final black hole spin that is more accurate and applicable to generic binary configurations, improving upon previous models.

Findings

Root-mean-square error of ~0.002 for aligned/anti-aligned spins.

Error of ~0.006 for generic spins and mass ratios.

Formula validated against 619 numerical relativity simulations.

Abstract

We revisit the problem of predicting the spin magnitude and direction of the black hole resulting from the merger of two black holes with arbitrary masses and spins inspiralling in quasi-circular orbits. We do this by analyzing a catalog of 619 recent numerical-relativity simulations collected from the literature and spanning a large variety of initial conditions. By combining information from the post-Newtonian approximation, the extreme mass-ratio limit and perturbative calculations, we improve our previously proposed phenomenological formulae for the final remnant spin. In contrast with alternative suggestions in the literature, and in analogy with our previous expressions, the new formula is a simple algebraic function of the initial system parameters and is not restricted to binaries with spins aligned/anti-aligned with the orbital angular momentum, but can be employed for fully generic binaries. The accuracy of the new expression is significantly improved, especially for almost extremal progenitor spins and for small mass ratios, yielding a root-mean-square error $\sigma\approx0.002$ for aligned/anti-aligned binaries and $\sigma\approx0.006$ for generic binaries. Our new formula is suitable for cosmological applications and can be employed robustly in the analysis of the gravitational waveforms from advanced interferometric detectors.