Predicting the direction of the final spin from the coalescence of two black holes

TL;DR

This paper introduces an improved formula to accurately predict the final spin's magnitude and direction of merging black holes at any separation, accounting for precession effects neglected in previous models.

Contribution

The authors develop a new predictive formula for black hole merger spins that remains accurate at large separations, unlike previous models that neglect precession effects.

Findings

The new formula accurately predicts the final spin magnitude and direction.

Final spin direction aligns closely with the binary's total angular momentum at large separation.

Observations of the final spin can reveal the binary's orbital plane at large distances.

Abstract

Knowledge of the spin of the black hole resulting from the merger of a generic black-hole binary is of great importance for studying the cosmological evolution of supermassive black holes. Several attempts have been made to model the spin via simple expressions exploiting the results of numerical-relativity simulations. While these expressions are in reasonable agreement with the simulations, they neglect the precession of the binary's orbital plane, and cannot therefore be applied directly -- i.e., without evolving the system to small separations using post-Newtonian theory -- to binaries with separations larger than a few hundred gravitational radii. While not a problem in principle, this may be impractical if the formulas are employed in cosmological merger-trees or N-body simulations, which provide the spins and angular momentum of the two black holes when their separation is of hundreds or thousands of gravitational radii. The formula that we propose is instead built on improved assumptions and gives, for any separation, a very accurate prediction both for the norm of the final spin and for its direction. By comparing with the numerical data, we also show that the final-spin direction is very accurately aligned with the binary's total angular momentum at large separation. Hence, observations of the final-spin direction (e.g. via a jet) can provide information on the binary's orbital plane at large separations and could be relevant, for instance, for studying X-shaped radio sources.