Gravitational waves produced from the merger of binary neutron stars (BNSs) are accompanied by electromagnetic counterparts, making it possible to identify the associated host galaxy. We explore how properties of the host galaxies relate to the astrophysical processes leading to the mergers. It is thought that the BNS merger rate within a galaxy at a given epoch depends primarily on the galaxys star-formation history as well as the underlying merger time-delay distribution of the binary systems. The stellar history of a galaxy, meanwhile, depends on the cosmological evolution of the galaxy through time, and is tied to the growth of structure in the Universe. We study the hosts of BNS mergers in the context of structure formation by populating the Universe Machine simulations with gravitational-wave events~ according to a simple time-delay model. We find that different time-delay distributions predict different properties of the associated host galaxies, including the distributions of stellar mass, star-formation rate, halo mass, and local and large-scale clustering of hosts. BNSs that merge today with short delay times prefer to be in hosts that have high star-formation rates, while those with long delay times live in dense regions within massive halos that have low star formation. We show that with ${mathcal O}(10)$ events from current gravitational-wave detector networks, it is possible to make preliminary distinctions between formation channels which trace stellar mass, halo mass, or star-formation rate. We also find that strategies to follow up gravitational-wave events with electromagnetic telescopes can be significantly optimized using the clustering properties of their hosts.
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