The importance of precession in modelling the direction of the final spin from a black-hole merger

TL;DR

This paper reviews and analyzes a formula for predicting the final spin of black holes after mergers, emphasizing the importance of precession effects for accurate modeling in cosmological simulations.

Contribution

It revisits and explains the physical basis of a formula that accurately predicts black hole merger spins, highlighting the role of spin precession in the model's success.

Findings

The formula accurately predicts final spin magnitude and direction.

Precession effects are crucial for modeling black hole mergers.

The formula is suitable for large-separation binary systems in cosmological contexts.

Abstract

The prediction of the spin of the black hole resulting from the merger of a generic black-hole binary system is of great importance to study the cosmological evolution of supermassive black holes. Several attempts have been recently made to model the spin via simple expressions exploiting the results of numerical-relativity simulations. Here, I first review the derivation of a formula, proposed in Barausse & Rezzolla, Apj 704 L40, which accurately predicts the final spin magnitude and direction when applied to binaries with separations of hundred or thousands of gravitational radii. This makes my formula particularly suitable for cosmological merger-trees and N-body simulations, which provide the spins and angular momentum of the two black holes when their separation is of thousands of gravitational radii. More importantly, I investigate the physical reason behind the good agreement between my formula and numerical relativity simulations, and nail it down to the fact that my formula takes into account the post-Newtonian precession of the spins and angular momentum in a consistent manner.