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

TL;DR

This paper demonstrates that a multiband gravitational-wave network can accurately measure black hole recoil kicks, providing new insights into black hole merger dynamics and formation channels.

Contribution

It shows the feasibility of measuring black hole recoil velocities using combined space and ground-based gravitational-wave detectors for the first time.

Findings

Multiband network recovers kick vectors within tens of km/s accuracy.

Measurement is feasible for kicks of 68 km/s and 1006 km/s.

Enables new multi-messenger follow-ups and tests of formation models.

Abstract

The non-linear 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 range from stellar to super-massive. However, a robust measurement of the kick for generic binaries from gravitational-wave observations has proved so far to be extremely challenging. In this \emph{letter}, we demonstrate the prospects of measuring black hole kicks through 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 km/s, 1006 km/s) emerging from near identical pre-merger configuration of GW190521 -- the first confirmed intermediate-mass black hole -- we find that the multiband network will recover with 90\% credible level the projection of the kick vector relative to the orbital plane within tens of km/s accuracy. Such precise measurement of the kick offer a new set of multi-messenger follow-ups and unprecedented tests of astrophysical formation channels.