  We investigate the properties of the host galaxies of compact binary mergers
across cosmic time. To this end, we combine population synthesis simulations
together with galaxy catalogues from the hydrodynamical cosmological simulation
EAGLE to derive the properties of the host galaxies of binary neutron star
(BNS), black hole-neutron star (BHNS) and binary black hole (BBH) mergers.
Within this framework, we derive the host galaxy probability, i.e., the
probability that a galaxy hosts a compact binary coalescence as a function of
its stellar mass, star formation rate, $K_s$ magnitude and $B$ magnitude. This
quantity is particularly important for low-latency searches of gravitational
wave (GW) sources as it provides a way to rank galaxies lying inside the
credible region in the sky of a given GW detection, hence reducing the number
of viable host candidates. Furthermore, even if no electromagnetic counterpart
is detected, the proposed ranking criterion can still be used to classify the
galaxies contained in the error box. Our results show that massive galaxies (or
equivalently galaxies with a high luminosity in $K_s$ band) have a higher
probability of hosting BNS, BHNS, and BBH mergers. We provide the probabilities
in a suitable format to be implemented in future low-latency searches.
