Observing binary neutron star subpopulations with the Einstein Telescope

TL;DR

The paper addresses how future gravitational-wave detectors, notably the Einstein Telescope, can identify and characterize multiple binary neutron star subpopulations with distinct formation channels. It develops a two-component population model (heavy and light) with different delay-time distributions, and uses hierarchical Bayesian inference on mock ET catalogs to assess the detectability of bimodal mass distributions and redshift evolution. The results indicate that hundreds to thousands of detections are sufficient to establish bimodality in the total mass and to disentangle the redshift distributions for moderate delay indices, with larger samples needed for steeper delays. This work demonstrates the potential of ET to illuminate BNS formation pathways (e.g., short-delay case BB channels) and emphasizes practical limits related to computational resources and model assumptions.

Abstract

The formation channels of binary neutron stars (BNSs) remain uncertain. The detection of GW190425 by LIGO/Virgo/KAGRA (LVK) suggests a subpopulation 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 identify and characterise such subpopulations. Using the latest LVK constraints on the BNS merger rate, we generate mock ET catalogues containing a mixture of light and heavy subpopulations. The redshift distribution of each subpopulation is modeled as the convolution of the cosmic star formation rate with a time-delay distribution: heavy BNSs have fixed short delays, while light BNSs follow power-law delays with indices -0.5,-1,-1.5. Hierarchical Bayesian analyses are then performed on catalogues of 100-5,000 events. 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 subpopulations for moderate time-delay indices (-0.5 or -1). For steeper indices (-1.5), the differences are more subtle, requiring larger catalogues, beyond what we could explore given our computational resources. Next-generation detectors should enable the detection of multiple BNS subpopulations and their redshift evolution, providing valuable insight into their formation pathways.

Figures (8)

• Figure 1: Merger rate of the long delays population (dashed lines), short delays population (dotted lines) and total population (full line) for three different hypothesis of the time-delays distribution. The rate is normalised at $z=0$ to the mean of the interval reported by the LVK following GWTC-4 LIGOScientific:2025pvj. The gray band at $z=0$ shows the $90\%$ credible interval reported by the LVK.
• Figure 2: Number of events above a given SNR threshold per year in the three scenarios considered for the time-delay distribution.
• Figure 3: Credible intervals on the confidence that the mass distribution is bimodal as a function of the number of events and for the different values of $\alpha_{\rm L}$. The red horizontal line corresponds to a probability of 0.95.
• Figure 4: Upper panel: reconstructions of the redshift distributions for increasing catalogue sizes. Coloured bands show the $90\%$ credible intervals for the light (red) and heavy (golden) populations. Solid lines indicate the median reconstructions, while dashed lines mark the true distributions. For the heavy population, the dashed and full lines superimpose almost perfectly. Lower panel: distribution of within-population and between-populations KS statistics. The value on top shows the probability that the two heavy and light population have different redshift distributions.
• Figure 5: Credible intervals on the confidence with which we can determine that the redshift distribution of the light and of the heavy population are different as a function of the number of events and for the different values of $\alpha_{\rm L}$. The red horizontal line corresponds to a probability of 0.95.