  With projects such as Laser Interferometer Space Antenna (LISA) and Pulsar
Timing Arrays expected to detect gravitational waves from supermassive black
hole mergers in the near future, it is key that we understand what we expect
those detections to be, and maximize what we can learn from them. To address
this, we study the mergers of supermassive black holes in the Illustris
simulation, the overall rate of mergers, and the correlation between merging
black holes and their host galaxies. We find that these mergers occur in
typical galaxies along the $M_{\rm{BH}}-M_*$ relation, and that between LISA
and PTAs we expect to probe the full range of galaxy masses. As galaxy mergers
can trigger increased star formation, we find that galaxies hosting low-mass
black hole mergers tend to show a slight increase in star formation rates
compared to a mass-matched sample. However, high-mass merger hosts have typical
star formation rates, due to a combination of low gas fractions and powerful
AGN feedback. Although minor black hole mergers do not correlate with disturbed
morphologies, major mergers (especially at high-masses) tend to show
morphological evidence of recent galaxy mergers which survives for ~500 Myr.
This is on the same scale as the infall/hardening time of the merging black
holes, suggesting that electromagnetic followups to gravitational wave signals
may not be able to observe this correlation. We further find that incorporating
a realistic timescale delay for the black hole mergers could shift the
distribution of merger masses toward higher-masses, decreasing the rate of LISA
detections while increasing the rate of PTA detections.
