Formation and Evolution of Binary Neutron Stars: Mergers and Their Host
  Galaxies
  In this paper, we investigate the properties of binary neutron stars (BNSs)
and their mergers by combining population synthesis models for binary stellar
evolution (BSE) with cosmological galaxy formation and evolution models. We
obtain constraints on BSE model parameters by using the observed Galactic BNSs
and local BNS merger rate density ($R_0$) inferred from Gravitational Wave (GW)
observations, and consequently estimate the host galaxy distributions of BNS
mergers. We find that the Galactic BNS observations imply efficient energy
depletion in the common envelope (CE) phase, a bimodal kick velocity
distribution, and low mass ejection during the secondary supernova explosion.
However, the inferred $R_0$ does not necessarily require an extremely high CE
ejection efficiency and low kick velocities, different from the previous
claims, mainly because the latest inferred $R_0$ is narrowed to a lower value
($320_{-240}^{+490}\,{\rm Gpc^{-3}\,yr^{-1}}$). The BNS merger rate density
resulting from the preferred model can be described by $R(z)\sim
R_0(1+z)^{\zeta}$ at low redshift ($z\lesssim0.5$), with
$R_0\sim316$-$784\,{\rm Gpc^{-3}\,yr^{-1}}$ and $\zeta\sim1.34$-$2.03$,
respectively. Our results also show that $R_{0}$ and $\zeta$ depend on settings
of BSE model parameters, and thus accurate estimates of these parameters by
future GW detections will put strong constraints on BSE models. We further
estimate that the fractions of BNS mergers hosted in spiral and elliptical
galaxies at $z\sim0$ are $\sim81$%-$84$% and $\sim16$%-$19$%, respectively. The
BNS merger rate per galaxy can be well determined by the host galaxy stellar
mass, star formation rate, and metallicity, which provides a guidance in search
for most probable candidates of BNS host galaxies.
