2021ApJ...909..207R

The rate and location of binary neutron star (BNS) mergers are determined by a combination of the star formation history and the delay-time distribution (DTD) function. In this paper, we couple the star formation rate histories from the IllustrisTNG model to a series of varied assumptions for the BNS DTD to make predictions for the BNS merger host galaxy mass function. These predictions offer two outcomes: (i) in the near term they influence the BNS merger event follow-up strategy by scrutinizing where most BNS merger events are expected to occur, and (ii) in the long term they constrain the DTD for BNS merger events once the host galaxy mass function is observationally well determined. From our fiducial model analysis, we predict that 50% of BNS mergers will occur in host galaxies with stellar mass between 10¹⁰ and 10¹¹ M_☉, 68% between 4 x 10⁹ and 3 x 10¹¹ M_☉, and 95% between 4 x 10⁸ and 2 x 10¹² M_☉. We find that the details of the DTD employed do not have a strong effect on the peak of the host mass function. However, varying the DTD provides enough spread that the true DTD can be determined from enough electromagnetic observations of BNS mergers. Knowing the true DTD can help us determine the prevalence of BNS systems formed through highly eccentric and short-separation fast-merging channels and can constrain the dominant source of r-process material.