**Authors**: Enrico Barausse (UMD), Luciano Rezzolla (AEI)

**Date**: 16 Apr 2009

**Abstract**: The knowledge of the spin of the black hole resulting from the merger of a generic binary system of black holes 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. While these expressions are in good agreement with the simulations, they are intrinsically imprecise when predicting the final spin direction, especially if applied to binaries with separations of hundred or thousands of gravitational radii. This is due to neglecting the precession of the orbital plane of the binary, and is a clear drawback 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 thousands of gravitational radii. We remove this problem by proposing an expression which is built on improved assumptions and that 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 total angular momentum of the binary at large separation. Hence, observations of the final spin direction (e.g. via a jet) can provide information on the orbital plane of the binary at large separations and could be relevant, for instance, to study X-shaped radio sources.

0904.2577
(/preprints)

2009-04-25, 16:02
**[edit]**

© M. Vallisneri 2012 — last modified on 2010/01/29

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