A Tale of Two Black Holes: Multiband Gravitational-wave Measurement of Recoil Kicks

Abstract The nonlinear dynamics of General Relativity leave their imprint on remnants of black hole mergers in the form of a recoil “kick.” The kick has profound astrophysical implications across the black hole mass spectrum, from stellar-mass to supermassive black holes. However, a direct measurement of the kick would require observing the binary from different orientations. Therefore, the kick is primarily inferred by constraining the premerger parameters, mainly the spin orientations and mass ratio of the black holes and fitting them with postmerger parameters. In this study, we demonstrate the prospects for such measurements of black hole kicks in a multiband gravitational-wave network consisting of space mission LISA, the current Earth-based detector network, and a third-generation detector. For two distinct cases of remnant black hole kick (68, 1006 km s −1 ) emerging from near identical premerger configuration of GW190521—the first confirmed intermediate-mass black hole—we find that the multiband network will recover with a 90% credible level of the projection of the kick vector relative to the orbital plane within tens of km s −1 accuracy. Such precise measurement of the kick offers a new set of multimessenger follow-ups and unprecedented tests of astrophysical formation channels.