# Measuring the delay time distribution of binary neutron stars. II. Using the redshift distribution from third-generation gravitational wave detectors network

## TL;DR

This study assesses how current and future gravitational wave detectors can measure the delay time distribution of binary neutron star mergers by analyzing their redshift distribution, highlighting the potential for third-generation detectors to constrain DTD parameters accurately.

## Contribution

It demonstrates that third-generation GW detectors can precisely determine the BNS delay time distribution and formation efficiency, overcoming degeneracies present in current detector measurements.

## Key findings

- Current detectors cannot uniquely determine DTD due to degeneracies.
- Third-generation detectors can constrain DTD and efficiency to better than 10%.
- Redshift uncertainties at high z are manageable for DTD inference.

## Abstract

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 $\Gamma$ and a minimum merger time $t_{\rm min}$, 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 ($\delta(z)/z\approx 0.1z$), 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 $z\approx 0$ (Safarzadeh & Berger 2019).