Measuring the delay time distribution of binary neutron stars. II. Using
the redshift distribution from third-generation gravitational wave detectors
network
We investigate the ability of current and third-generation gravitational wave
(GW) detectors to determine the delay time distribution (DTD) of binary neutron
stars (BNS) through a direct measurement of the BNS merger rate as a function
of redshift. We assume that the DTD follows a power law distribution with a
slope Γ and a minimum merger time tmin​, and also allow the
overall BNS formation efficiency per unit stellar mass to vary. By convolving
the DTD and mass efficiency with the cosmic star formation history, and then
with the GW detector capabilities, we explore two relevant regimes. First, for
the current generation of GW detectors, which are only sensitive to the local
universe, but can lead to precise redshift determinations via the
identification of electromagnetic counterparts and host galaxies, we show that
the DTD parameters are strongly degenerate with the unknown mass efficiency and
therefore cannot be determined uniquely. Second, for third-generation detectors
such as Einstein Telescope (ET) and Cosmic Explorer (CE), which will detect BNS
mergers at cosmological distances, but with a redshift uncertainty inherent to
GW-only detections (δ(z)/z≈0.1z), we show that the DTD and mass
efficiency can be well-constrained to better than 10\% with a year of
observations. This long-term approach to determining the DTD through a direct
mapping of the BNS merger redshift distribution will be supplemented by more
near term studies of the DTD through the properties of BNS merger host galaxies
at z≈0 (Safarzadeh & Berger 2019).Comment: 10 pages, Accepted to ApJ Letter