Multipole analysis of kicks in collision of spinning binary black holes (Q1016004)

Thorne and Kidder give expressions which allow for analytical estimates of the ``kick'', i.e. the recoil, produced from asymmetrical gravitational radiation during the interaction of black holes, or in fact any gravitating compact bodies (the Thorne-Kidder formula uses momentum flux calculations based on the linearized general relativity of gravitational radiation). The authors specifically treat kicks arising in the binary interaction of equal mass black holes, when at least one of the black holes has significant spin, \(a\). Such configurations can produce very large kicks in computational simulations. The authors consider both fly-by and quasicircular orbits. For fly-by orbits one finds substantial kicks from those Thorne-Kidder terms which are linear in \(a\). For the quasi-circular case, one considers in addition the nonlinear contribution (\(O(a^2)\)) to the kicks, and provides a dynamical explanation for such terms discovered and displayed by \textit{L. Boyle} and \textit{M. Kesden} [The spin expansion for binary black hole merger: new predictions and future directions, \url{arXiv:0712.2819} (2007)]. However in the cases of maximal kick velocities, the dependence on spin is largely linear reproduced in numerical results [see \textit{F. Herrmann, I. Hinder} et al., ApJ 661, 430 (2007; doi:10.1086/513603)].