On the final spin from the coalescence of two black holes

Abstract

We provide a compact analytic formula to compute the spin of the black hole produced by the coalescence of two black holes. The expression, which uses an analytic fit of numerical-relativity data and relies on four assumptions, aims at modelling generic initial spin configurations and mass ratios. A comparison with numerical-relativity simulations already shows very accurate agreements with all of the numerical data available to date, but we also suggest a number of ways in which our predictions can be further improved.

Figures (2)

• Figure 1: Left panel: Rescaled residual for aligned binaries. The circles refer to equal-mass, equal-spin binaries presented in refs. Rezzolla-etal-2007Marronetti07tbgsBerti:2007snbBerti:2007sbBuonanno:2007ftRezzolla-etal-2007b, triangles to equal-mass, unequal-spin binaries presented in ref. Rezzolla-etal-2007Berti:2007sb, and squares to unequal-mass, equal-spin binaries presented in refs. Berti:2007snbBuonanno:2007ftRezzolla-etal-2007bBerti:2007sb. Here and in the right panel the "binary order number" is just a dummy index labelling the different configurations. Right panel: The top part reports with asterisks the final spin computed for misaligned binaries. Hexagons refer to data from ref. Campanelli:2006vp (labelled "RIT"), squares to the data Table \ref{['tableone']} (labelled "AEI"), circles to data from ref. Tichy:2007gso (labelled "FAU"), and triangles to data from ref. Herrmann:2007ex (labelled "PSU-UTA"). Note that these latter data points refer to the aligned component $a_{\rm fin}^{\parallel}$ since this is the only component available from ref. Herrmann:2007ex. The bottom part of this panel shows instead the rescaled residuals for these misaligned binaries.
• Figure 2: Using the same data (and convention for the symbols) as in the right panel of Fig. \ref{['fig:align_res']}, we here report the angle between the final spin vector and the initial orbital angular momentum $\theta_{\rm fin}$. Shown instead with asterisks and circles are the values predicted for the numerical data (as taken from refs. Campanelli:2006vpTichy:2007gsoHerrmann:2007ex and from Table \ref{['tableone']}) by our analytic fit (asterisks) and by the point-particle approach suggested in ref. Buonanno:07b (circles).