Precision tracking of massive black hole spin evolution with LISA

The Laser Interferometer Space Antenna (LISA) will play a vital role in constraining the origin and evolution of massive black holes throughout the Universe. In this study we use a waveform model (IMRPhenomXPHM) that includes both precession and higher multipoles, and full Bayesian inference to explore the accuracy to which LISA can constrain the binary parameters. We demonstrate that LISA will be able to track the evolution of the spins-magnitude and orientation-to percent accuracy, providing crucial information on the dynamics and evolution of massive black hole binaries and the galactic environment in which the merger takes place. Such accurate spin-tracking further allows LISA to measure the recoil velocity of the remnant black hole to better than 100 km s-1 (90% credibility) and its direction to a few degrees, which provides additional important astrophysical information on the postmerger association. Using a suite of binaries at z 1/4 3 broadly consistent with astrophysical predictions, we showcase that the component masses will be measurable at the subpercent level, the sky area can be constrained to within Delta omega 90 approximate to 0.01 deg2, and the binary redshift to less than 0.01.