  Observations of gravitational waves from binary black hole (BBH) mergers have
measured the redshift evolution of the BBH merger rate. The number density of
galaxies in the Universe evolves differently with redshift based on their
physical properties, such as their stellar masses and star formation rates. In
this work we show that the measured population-level redshift distribution of
BBHs sheds light on the properties of their probable host-galaxies. We first
assume that the hosts of BBHs can be described by a mixture model of galaxies
weighted by stellar mass or star formation rate, and find that we can place
upper limits on the fraction of mergers coming from a stellar mass weighted
sample of galaxies. We then constrain parameters of a physically motivated
power-law delay-time distribution using GWTC-3 data, and self-consistently
track galaxies in the \textsc{UniverseMachine} simulations with this delay-time
model to infer the probable host-galaxies of BBHs over a range of redshifts. We
find that the inferred host-galaxy distribution at redshift $z=0.21$ has a
median star formation rate $\sim 0.9\,M_\odot\mathrm{yr}^{-1}$ and a median
stellar mass of $\sim 1.9 \times 10^{10}\,M_\odot$. We also provide
distributions for the mean stellar age, halo mass, halo radius, peculiar
velocity, and large scale bias associated with the host-galaxies, as well as
their absolute magnitudes in the B- and ${ \rm K_s}$-bands. Our results can be
used to design optimal electromagnetic follow-up strategies for BBHs, and also
to aid the measurement of cosmological parameters using the statistical dark
siren method.
