Measuring the Delay Time Distribution of Binary Neutron Stars. III. Using the Individual Star Formation Histories of Gravitational-wave Event Host Galaxies in the Local Universe

In Paper I we studied the determination of the delay time distribution (DTD) of binary neutron stars (BNSs) through scaling relations between halo/stellar mass and the star formation history (SFH) of galaxies hosting gravitational-wave (GW) events in the local universe. Here we explore how a detailed reconstruction of the individual SFHs of BNS merger host galaxies can improve on the use of the scaling relations. We use galaxies from the Galaxy and Mass Assembly survey, which is mass complete at M* > 109 M⊙ in the redshift range 0.05 < z < 0.08. We use the reconstructed SFHs derived from the Prospector code for two distinct sets of priors (favoring continuous and bursty SFHs), and convolve those with power-law DTDs characterized by an index Γ and a minimum delay time tmin. We find that with this approach ${ \mathcal O }(100)-{ \mathcal O }(300)$ host galaxies are required to constrain the DTD parameters, with the number depending on the choice of SFH prior and on the parameters of the true DTD. We further show that using only the host galaxies of BNS mergers, as opposed to the full population of potential host galaxies in the relevant cosmic volume, leads to a minor bias in the recovered DTD parameters. The required host galaxy sample size is nearly an order of magnitude smaller relative to the approach of using scaling relations, and we expect such a host galaxy sample to be collected within a decade or two, prior to the advent of third-generation GW detectors.