Constraining Delay Time Distribution of Binary Neutron Star Mergers from
  Host Galaxy Properties
  Gravitational wave (GW) observatories are discovering binary neutron star
mergers (BNSMs), and in at least one event we were able to track it down in
multiple wavelengths of light, which allowed us to identify the host galaxy.
Using a catalogue of local galaxies with inferred star formation histories and
adopting a BNSM delay time distribution (DTD) model, we investigate the
dependence of BNSM rate on an array of galaxy properties. Compared to the
intrinsic property distribution of galaxies, that of BNSM host galaxies is
skewed toward galaxies with redder colour, lower specific star formation rate,
higher luminosity, and higher stellar mass, reflecting the tendency of higher
BNSM rates in more massive galaxies. We introduce a formalism to efficiently
make forecast on using host galaxy properties to constrain DTD models. We find
comparable constraints from the dependence of BNSM occurrence distribution on
galaxy colour, specific star formation rate, and stellar mass, all better than
those from dependence on $r$-band luminosity. The tightest constraints come
from using individual star formation histories of host galaxies, which reduces
the uncertainties on DTD parameters by a factor of three or more. Substantially
different DTD models can be differentiated with about 10 BNSM detections. To
constrain DTD parameters at 10\% precision level requires about one hundred
detections, achievable with GW observations on a decade time scale.
