  Massive black hole binaries (MBHBs) produce gravitational waves (GWs) that
are detectable with pulsar timing arrays. We determine the properties of the
host galaxies of simulated MBHBs at the time they are producing detectable GW
signals. The population of MBHB systems we evaluate is from the Illustris
cosmological simulations taken in tandem with post processing semi-analytic
models of environmental factors in the evolution of binaries. Upon evolving to
the GW frequency regime accessible by pulsar timing arrays, we calculate the
detection probability of each system using a variety of different values for
pulsar noise characteristics in a plausible near-future International Pulsar
Timing Array dataset. We find that detectable systems have host galaxies that
are clearly distinct from the overall binary population and from most galaxies
in general. With conservative noise factors, we find that host stellar
metallicity, for example, peaks at twice solar metallicity as opposed to the
total population of galaxies which peaks at ~0.6 solar metallicity.
Additionally, the most detectable systems are much brighter in magnitude and
more red in color than the overall population, indicating their likely identity
as large ellipticals with diminished star formation. These results can be used
to develop effective search strategies for identifying host galaxies and
electromagnetic counterparts following GW detection by pulsar timing arrays.
