tokens: We include only neighboring galaxies with stellar masses greater than M * = 10 9 M ⊙ h −1 . We define the observable Δ r as the ratio of density within 0.6 Mpc h −1 , as compared to the density within 5 Mpc h −1 . The smaller scale is chosen to represent a galaxy’s local environment, sensitive to whether or not it exists as a part of a group or a cluster of galaxies, while the larger radius is representative of its large-scale environment or neighborhood beyond its own parent halo. In the following sections, we study the properties of the host galaxies in relation to BNS mergers, as a function of the time-delay model. We then estimate the number of events required in order to make inferences about the evolutionary history of merging binaries. 3. Results 3.1. Weighted Distributions The underlying population of BNS systems is drawn from the distribution of stars in the universe. Among the first questions to be posed is whether BNS host galaxies are biased tracers of the underlying population of galaxies in the universe. For example, we may ask whether BNS mergers trace stellar mass, in which case they would occur preferentially in high M * galaxies (Artale et al. 2020 ; Ducoin et al. 2020 ; Toffano et al. 2019 ). Alternatively, BNS mergers may trace star formation rate (Phinney 1991 ) or halo mass, or they may be randomly distributed in galaxies with equal probability. We ask how large a sample of host galaxies would be required in order to distinguish these simple models, where mergers trace either the stellar mass of a galaxy, the star formation rate, or the virial mass of the parent halo in which they reside. The arguments in this section are not specific to BNS systems, and can be extrapolated to black hole binaries, or black hole–neutron star mergers, assuming that their host galaxies can be identified. Physically, we can associate a model in which BNS mergers trace the star formation rate with a zero delay time model, where binaries merge as soon as they are born. In this scenario, the merger rate would simply trace the rate at which new stars are forming in a galaxy. At the other extreme, for very long time delays on the order of 10 Gyr, we expect low-redshift BNS mergers to trace the stellar mass, as high stellar mass galaxies reached the peak of their star formation at early redshifts. Alternatively, it has been proposed that, rather than forming from isolated stellar binaries in the galactic field (Tauris et al. 2017 ; Vigna-Gómez et al. 2018 ), a significant fraction of BNSs may form via dynamical interactions in dense globular clusters (Grindlay et al. 2006 ; Andrews Mandel 2019 ). Recent studies indicate that globular cluster abundance is a good tracer of a galaxy’s host halo mass (Hudson et al. 2014 ; Harris et al. 2013 ). In this way, a BNS merger rate that traces dark matter halo mass, rather than galaxy stellar mass, could be an indication that BNS systems are preferentially formed in globular clusters. We also note that some
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