  In Paper I (Safarzadeh & Berger 2019) we studied the determination of the
delay time distribution (DTD) of binary neutron stars (BNS) 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 (GAMA) survey, which is mass complete at
$M_*>10^9$ M$_\odot$ 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 $\Gamma$ and a minimum delay time $t_{\rm min}$.
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.
