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In Paper I (Safarzadeh & Berger 2019) we studied the determination of thedelay time distribution (DTD) of binary neutron stars (BNS) through scalingrelations between halo/stellar mass and the star formation history (SFH) ofgalaxies hosting gravitational wave (GW) events in the local universe. Here weexplore how a detailed reconstruction of the individual SFHs of BNS merger hostgalaxies can improve on the use of the scaling relations. We use galaxies fromthe Galaxy and Mass Assembly (GAMA) survey, which is mass complete at$M_*>10^9$ M$_\odot$ in the redshift range $0.05<z<0.08$. We use thereconstructed SFHs derived from the Prospector code, for two distinct sets ofpriors (favoring continuous and bursty SFHs), and convolve those with power lawDTDs characterized by an index $\Gamma$ and a minimum delay time $t_{\rm min}$.We find that with this approach $\mathcal{O}(100)-\mathcal{O}(300)$ hostgalaxies are required to constrain the DTD parameters, with the numberdepending on the choice of SFH prior and on the parameters of the true DTD. Wefurther show that using only the host galaxies of BNS mergers, as opposed tothe full population of potential host galaxies in the relevant cosmic volume,leads to a minor bias in the recovered DTD parameters. The required host galaxysample size is nearly an order of magnitude smaller relative to the approach ofusing scaling relations, and we expect such a host galaxy sample to becollected within a decade or two, prior to the advent of third-generation GWdetectors.

the astrophysical journal. letters

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