Revisiting the relationship of black-hole kicks and multipole asymmetries

Precession in black-hole binaries is caused by a misalignment between the total spin and the orbital angular momentum. The gravitational-wave emission of such systems is anisotropic, which leads to an asymmetry in the $\pm m$ multipoles when decomposed into a spherical harmonic basis. This asymmetric emission can impart a kick to the merger remnant black hole as a consequence of linear momentum conservation. Despite the astrophysical importance of kicks, multipole asymmetries contribute very little to the overall signal strength and, therefore, the majority of current gravitational-wave models do not include them. Recent efforts have been made to include asymmetries in waveform models. However, those efforts focus on capturing finer features of precessing waveforms without making explicit considerations of remnant kick velocities. Here we close that gap and present a comprehensive analysis of the linear momentum flux expressed in terms of multipole asymmetries. As expected, large asymmetries are needed to achieve the largest kick velocities. Interestingly, the same large asymmetries may lead to negligible kick velocities if the antisymmetric and symmetric waveform parts are perpendicular to each other around merger. We also present a phenomenological tool for testing the performance of waveform models with multipole asymmetries. This tool helped us to fix an inconsistency in the phase definition of the IMRPhenomXO4a waveform model.