Probing the redshift evolution and sub-populations of binary neutron stars with the Einstein Telescope

¹ Dipartimento di Fisica “G. Occhialini”, Universitá degli Studi di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy
² INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy
³ Institut d’Astrophysique de Paris, UMR 7095, CNRS and Sorbonne Université, 98 bis boulevard Arago, 75014 Paris, France
⁴ Institut Universitaire de France, Ministère de l’Enseignement Supérieur et de la Recherche, 1 rue Descartes, 75231 Paris Cedex F-05, France

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 4 December 2025
Accepted: 14 May 2026

Abstract

Aims. The formation channels of binary neutron stars (BNSs) currently remain uncertain, but important information can be gathered by observing their mergers with gravitational-wave detectors. The processes that lead to BNS coalescence are encoded in the time-delay distribution between stellar binary formation and BNS coalescence, and therefore in the BNS merger rate. Moreover, the detection of GW190425 by LIGO/Virgo/KAGRA (LVK) suggests a sub-population of massive BNSs, possibly formed through unstable ‘case BB’ mass transfer with short merger delays. We investigate whether next-generation detectors such as the Einstein Telescope (ET) can constrain the time-delay distribution of BNSs and identify such sub-populations.

Methods. Using the latest LVK constraints, we generated mock ET catalogues that contain a mixture of light and heavy subpopulations. We modelled the redshift distribution of each sub-population as the convolution of the cosmic star formation rate with a time-delay distribution. We first considered a scenario where the time-delay distribution is common to all BNSs and follows a power law with indices α = −0.5, −1, −1.5. In the second scenario, heavy BNSs have fixed short delays, while light BNSs follow power-law delays with the same set of indices. Hierarchical Bayesian analyses were then performed on catalogues of 100-5000 events.

Results. With thousands of events, ET will be able to accurately characterise the time-delay distribution for the α = −0.5 and α = −1 cases. We find that with hundreds of detections from ET, we will be able to establish that the total mass distribution is bimodal. A few thousand events are sufficient to disentangle the redshift distributions of the two sub-populations for moderate time-delay indices (α_L = −0.5 or −1). For steeper indices (α_L = −1.5), the differences are more subtle and require larger catalogues, which was beyond what we could explore given our computational resources.

Conclusions. Next-generation detectors should enable the detection of multiple BNS sub-populations and their redshift evolution, and provide valuable insights into their formation pathways.