Massive black hole binary inspiral and spin evolution in a cosmological
  framework
  Massive black hole (MBH) binary inspiral time scales are uncertain, and their
spins are even more poorly constrained. Spin misalignment, along with unequal
mass ratios and spin magnitudes, introduces asymmetry in the gravitational
radiation, which imparts a recoil kick to the merged MBH. Understanding how MBH
binary spins evolve is crucial for determining their recoil velocities, their
gravitational wave (GW) waveforms detectable with LISA, as well as their
post-merger retention rate in galaxies and thus their subsequent merger rate.
Here we present a novel study that introduces a sub-resolution model for gas-
and GW-driven MBH binary spin evolution using a population of accreting MBHs
from the Illustris cosmological hydrodynamics simulations. We also model
sub-resolution binary inspiral via dynamical friction, stellar scattering,
viscous gas drag, and GW emission. Our model assumes differential accretion,
which causes greater alignment of the secondary MBH spin in unequal-mass
mergers. We find that 47% of the MBHs in our population merge by $z=0$. Of
these, 19% have misaligned primaries and 10% have misaligned secondaries at the
time of merger in our (conservative) fiducial model. The MBH misalignment
fraction depends strongly on the accretion disc parameters, however. Reducing
accretion rates by a factor of 100, in a thicker disc, yields 79% and 42%
misalignment for primaries and secondaries, respectively. Even in the fiducial
model, more than 12% of binaries experience recoils of $>500$ km s$^{-1}$,
which could displace them at least temporarily from galactic nuclei. We
additionally find that a significant number of systems experience strong
precession.
