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 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 Laser Interferometer Space Antenna, and their retention rate in galaxies. Here, we introduce a sub-resolution model for gas- and gravitational wave (GW)-driven MBH binary spin evolution using accreting MBHs from the Illustris cosmological hydrodynamic simulations. We also model binary inspiral via dynamical friction, stellar scattering, viscous gas drag, and GW emission. Our model assumes that the circumbinary disc always removes angular momentum from the binary. It also assumes differential accretion, which causes greater alignment of the secondary MBH spin in unequal-mass mergers. We find that 47 per cent of the MBHs in our population merge by z = 0. Of these, 19 per cent have misaligned primaries and 10 per cent have misaligned secondaries at the time of merger in our fiducial model with initial eccentricity of 0.6 and accretion rates from Illustris. 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 per cent misalignment for primaries and secondaries, respectively. Even in the more conservative fiducial model, more than 12 per cent 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.