The final spin from the coalescence of aligned-spin black-hole binaries

TL;DR

This paper presents a simple, accurate analytic model for predicting the final spin of black holes resulting from the coalescence of aligned-spin binaries, based on recent simulations and theoretical constraints.

Contribution

It introduces a new analytic formula for the final spin in aligned-spin black-hole mergers, simplifying predictions and extending potential applicability to unequal-spin systems.

Findings

Model achieves a few percent accuracy across available data.

Predicts conditions for spin flip and spin-up during mergers.

Provides a foundation for extending to generic spin configurations.

Abstract

Determining the final spin of a black-hole (BH) binary is a question of key importance in astrophysics. Modelling this quantity in general is made difficult by the fact that it depends on the 7-dimensional space of parameters characterizing the two initial black holes. However, in special cases, when symmetries can be exploited, the description can become simpler. For black-hole binaries with unequal masses but with equal spins which are aligned with the orbital angular momentum, we show that the use of recent simulations and basic but exact constraints derived from the extreme mass-ratio limit allow to model this quantity with a simple analytic expression. Despite the simple dependence, the expression models very accurately all of the available estimates, with errors of a couple of percent at most. We also discuss how to use the fit to predict when a Schwarzschild BH is produced by the merger of two spinning BHs, when the total angular momentum of the spacetime ``flips'' sign, or under what conditions the final BH is ``spun-up'' by the merger. Finally, suggest an extension of the fit to include unequal-spin binaries, thus potentially providing a complete description of the final spin from the coalescence of generic black-hole binaries with spins aligned to the orbital angular momentum.