Binary black hole mergers: What causes the final kick?

Decoding the physics of asymmetric gravitational-wave radiation and its connection to black-hole kicks

In some binaries, the spins of the black holes are not aligned with the system’s orbital angular momentum. These binaries are unlikely to emit gravitational waves symmetrically. Merger remnants of such systems receive a recoil, also called a “kick”, with velocities of up to 5000 km/s. This happens because gravitational waves carry away linear momentum, but the total (including the black hole's) momentum is conserved. While the relationship between asymmetric gravitational-wave emission and kicks is well known, most waveform models used by the LIGO-Virgo-KAGRA collaboration do not contain the multipole asymmetries that describe asymmetric emission. Moreover, they certainly do not include the physics this relationship encodes. Now, a team of researchers from the Max Planck Independent Research Group “Binary Merger Observations and Numerical Relativity” at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) has taken a closer look at this and found something seemingly counterintuitive: A large amplitude of the antisymmetric waveform part does not necessarily correlate with a large kick. Rather, the phase at the merger relative to the symmetric part determines the kick velocity. The team also presents a new tool for testing the performance of multipole asymmetry models.

Paper abstract

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 -m and +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.