⚛️ nuclear theory

Binary neutron stars in the next-generation era: Multi-messenger detection prospects and constraints on the equation of state, mass distribution, and cosmology

This paper projects that next-generation gravitational-wave observatories like the Einstein Telescope and Cosmic Explorer will enable hundreds of multi-messenger binary neutron star detections annually, allowing for precise constraints on the neutron star equation of state, mass distribution, and cosmological parameters through joint hierarchical Bayesian inference.

Original authors: Hauke Koehn, Thibeau Wouters, Gilad Sadeh, Peter T. H. Pang, Mattia Bulla, Chris Van Den Broeck, Michael W. Coughlin, Tim Dietrich

Published 2026-07-31

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CC BY 4.0

Original authors: Hauke Koehn, Thibeau Wouters, Gilad Sadeh, Peter T. H. Pang, Mattia Bulla, Chris Van Den Broeck, Michael W. Coughlin, Tim Dietrich

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, cosmic orchestra. For decades, we've been listening to its music with our ears, catching the light from stars and galaxies. But recently, we've started listening with a new sense: touch. When massive objects like black holes or neutron stars crash into each other, they ripple the very fabric of space and time, creating "gravitational waves." These are like the bass notes of the universe, vibrating through everything. But sometimes, these crashes also scream in light—bursting into gamma rays, glowing in radio waves, and flashing in visible colors. This is "multi-messenger astronomy": listening to the bass while watching the lights.

The stars in this story are binary neutron stars. Think of a neutron star as a city-sized ball of matter so dense that a single teaspoon would weigh a billion tons. When two of these heavyweights dance together and merge, they create a spectacular explosion called a kilonova. This event is a cosmic laboratory. It tells us how matter behaves under extreme pressure (the "equation of state"), how heavy these stars usually are (the "mass distribution"), and even helps us measure how fast the universe is expanding (the "Hubble constant"). The big question is: how many of these cosmic concerts will we catch in the future, and what secrets will they reveal?

The Cosmic Crystal Ball: Predicting the Next-Gen Star Show

A team of scientists has built a super-smart computer simulation to peek into the future of astronomy. They are looking ahead to the "next-generation era," a time when we will have brand-new, super-sensitive detectors called the Einstein Telescope (ET) and Cosmic Explorer (CE). These machines will be like upgrading from a cheap radio to a high-definition surround-sound system, capable of hearing the faintest whispers of colliding stars from billions of light-years away.

The researchers wanted to know two main things: How many of these star crashes will we actually see with both our ears (gravitational waves) and our eyes (light)? And once we see them, how much can we learn about the universe?

The Great Cosmic Hunt: How Many Will We Catch?

To answer this, the team created two different "mock" universes in their computer. In one version, the neutron stars are all very similar in weight, clustering around a standard size (the "narrow" distribution). In the other version, the stars have a wild mix of weights, ranging from light to very heavy (the "wide" distribution). They then simulated a whole year of observations with different detector setups.

Here is what their crystal ball showed:

The Solo Act (Einstein Telescope only): If we only have the Einstein Telescope, they expect to find between 40 and 100 successful matches per year where they spot the gravitational wave and the flash of light (the kilonova) from the same event.
The Power Duo (Einstein Telescope + Cosmic Explorer): If we team up the Einstein Telescope with the Cosmic Explorer, the numbers jump significantly. They project finding between 200 and 500 multi-messenger events per year.
The Afterglow: Even if they miss the initial flash, they might catch the "afterglow"—the fading glow of the explosion—years later using radio telescopes. Depending on the setup, they could find anywhere from 70 to 350 of these late-time signals.

The team also noted that the type of stars matters. If the stars are mostly the standard, lighter kind, we get more bright flashes. If the stars are a mix of heavy and light, many of them collapse immediately into black holes, which are much dimmer and harder to spot. So, the "narrow" star universe gives us more targets to look at.

Unlocking the Secrets: What Can We Learn?

Finding these events is just the first step. The real magic happens when the scientists use these sightings to solve cosmic puzzles. They ran a massive statistical analysis, treating the data like a giant jigsaw puzzle where every piece helps refine the picture.

The Size of a Neutron Star: One of the biggest mysteries is how big a neutron star actually is. The team found that with their best-case scenario (using the Einstein Telescope and Cosmic Explorer together), they could pin down the radius of a standard 1.4-solar-mass neutron star to within 0.2 km. That's incredibly precise for an object that is essentially a solid ball of nuclear matter!
The Speed of the Universe: They also looked at the Hubble constant, which measures how fast the universe is expanding. By combining the gravitational wave data with the distance to the host galaxy, they projected they could measure this expansion rate to within 1 km s⁻¹ Mpc⁻¹. This is a huge step forward in solving the "Hubble Tension," a current disagreement among scientists about exactly how fast the universe is growing.
The Mass of the Stars: They were able to recover the general shape of the mass distribution, figuring out if the stars are mostly the same weight or a wild mix. However, they found that the "wide" mix is harder to pin down perfectly if the stars collapse too quickly.

The Fine Print: What We Don't Know Yet

The scientists are careful to point out that these are projections based on simulations, not final measurements. Their results depend on several assumptions:

The Models: They assumed specific ways that stars explode and how light travels. If the real physics is different, the number of detectable events could change.
The Light Curves: Interestingly, they found that the actual light curves (the brightness over time) didn't help much with figuring out the size of the stars (the equation of state). The gravitational waves did almost all the heavy lifting there. However, the light curves did help a lot with measuring the expansion of the universe by correcting for the angle at which we see the explosion.
The "Prompt Collapse": A major uncertainty is how often stars collapse instantly into black holes. If this happens often, we get fewer bright flashes to study.

The Bottom Line

This paper doesn't claim to have solved the mysteries of the universe yet. Instead, it's a roadmap. It suggests that when our next-generation detectors come online, we are in for a treasure trove of data. We could be looking at hundreds of new cosmic events every year, giving us the statistical power to finally measure the size of neutron stars and the expansion rate of the universe with unprecedented precision. It's a promise that the future of astronomy will be loud, bright, and full of answers.

Technical Summary: Binary Neutron Stars in the Next-Generation Era

Problem Statement
While the detection of GW170817 demonstrated the potential of multi-messenger astronomy to constrain the equation of state (EOS) of dense nuclear matter and the Hubble constant ( $H_0$ ), current detection rates are insufficient for robust statistical inference. The next generation of gravitational wave (GW) observatories, specifically the Einstein Telescope (ET) and Cosmic Explorer (CE), promises a significant increase in detection volume. However, the number of detectable electromagnetic (EM) counterparts (kilonovae, GRBs, and afterglows) remains uncertain due to unknown merger rates, complex EM emission modeling, and the sensitivity of ejecta properties to the binary's mass distribution and EOS. Furthermore, projecting the statistical precision with which hierarchical parameters (EOS, mass distribution, cosmology) can be recovered from these future populations requires a comprehensive framework that accounts for selection effects and the interplay between GW and EM data.

Methodology
The authors construct a comprehensive simulation pipeline to estimate detection prospects and infer physical parameters for a one-year observation run in 2050.

Population Synthesis: Two distinct binary neutron star (BNS) catalogues were generated with a local merger rate of $10^{6.6} \text{ Gpc}^{-3} \text{ yr}^{-1}$ .
- Narrow Mass Distribution: Based on Galactic double pulsars, centered around $1.4 M_\odot$ .
- Wide Mass Distribution: Based on confirmed GW detections, ranging from $1.1$ to $2.0 M_\odot$ .
- Both catalogues utilize a specific QMC-RMF3 EOS ( $M_{\text{TOV}} = 2.14 M_\odot$ , $R_{1.4} = 12.16 \text{ km}$ ) and standard cosmological parameters ( $\Lambda$ CDM, Planck 2018).
Electromagnetic Modeling:
- Kilonovae (KN): Ejecta properties (mass, velocity, electron fraction) were derived using numerical relativity (NR)-informed fitting formulas, distinguishing between prompt collapse and stable remnant scenarios. Light curves were generated using a machine-learning surrogate trained on the possis radiation transport code.
- GRBs and Afterglows: Short GRB production was modeled based on black hole formation and jet breakout conditions. Prompt emission fluences and kinetic energies were estimated, and afterglow light curves (radio, optical, X-ray) were computed using a machine-learning surrogate based on pyblastafterglow and the Sadeh et al. (2023) synchrotron model.
Detection Algorithm: A mock follow-up strategy was implemented across four GW detector networks (ET $\Delta$ , ETL, ET $\Delta$ +CE, ETL+CE). The algorithm simulates:
- GW detection (SNR > 12) and sky localization ( $\Delta\Omega_{\text{GW}}$ ).
- Prompt GRB detection by wide-field $\gamma$ -ray instruments (Fermi/GBM, Swift/BAT, GECAM, SVOM/ECLAIRs).
- Targeted UVOIR searches (Rubin, Pan-STARRS, ZTF, Roman, ULTRASAT) for KN and GRB afterglows within the first few days.
- Late-time afterglow searches (radio/X-ray) for events with and without early counterparts.
- Detection criteria required at least two independent detection flags (different epochs, filters, or instruments).
Hierarchical Inference: A fully Bayesian hierarchical inference framework was employed to recover the EOS, mass distribution, and cosmological parameters ( $H_0, \Omega_0$ ).
- Technique: Individual event posteriors were sampled using IMRPhenomXAS_NRTidalv3 and normalizing flows (NFs) to approximate the likelihoods efficiently.
- Data Integration: The study compared inferences using GW data alone versus joint GW + host galaxy redshift + KN light curve data.
- Bias Correction: Selection effects were addressed by reweighting hyperposterior samples with an estimated detection probability $p_{\text{det}}(\lambda)$ , though the authors note this remains a coarse approximation.

Key Contributions and Results

Detection Prospects:
- For ET alone, the study projects 40–100 successfully identified EM counterparts per year, depending on the detector layout (ET $\Delta$ vs. ETL) and mass distribution. The narrow mass distribution yields more detections due to a lower prompt collapse rate and brighter kilonovae.
- In a joint network with CE, the number of multi-messenger detections increases to 200–500 per year.
- The Vera Rubin telescope is projected to dominate the counterpart search.
- Late-time afterglow searches (radio/X-ray) are expected to identify an additional 70–350 events, many without early UVOIR counterparts.
Equation of State (EOS) Constraints:
- Using the largest catalogue (narrow mass distribution + ETL, 78 events), the canonical NS radius is constrained to $R_{1.4} = 12.04^{+0.18}_{-0.14} \text{ km}$ (95% credibility) when using full multi-messenger data.
- The EOS constraints are dominated by high-SNR GW signals. The inclusion of KN light curve data provides a negligible impact on EOS constraints for high-SNR events, though it may assist in lower-SNR regimes.
- The $M-\Lambda$ relationship is tightly constrained, but the $M-R$ relationship exhibits a modest bias toward smaller radii due to the specific EOS parametrization (CSE) and the dominance of tidal deformability measurements.
Mass Distribution and Cosmology:
- The general shape of the mass distribution is well recovered, though specific parameters (e.g., the weight of the secondary Gaussian peak) show some bias due to selection effects and imperfect detection probability modeling.
- Cosmological parameters are recovered with high precision: $H_0 = 68.2^{+0.9}_{-0.9} \text{ km s}^{-1} \text{ Mpc}^{-1}$ for the narrow+ETL case.
- Crucially, the inclusion of KN light curve data significantly improves cosmological inference by mitigating inclination-distance degeneracies and biases present in GW-only analyses.

Significance and Claims
The paper claims to provide a comprehensive overview of the multi-messenger detection landscape for the next-generation era, bridging the gap between population synthesis and hierarchical parameter inference. Its primary significance lies in demonstrating that:

Next-generation detectors will enable the statistical recovery of the BNS mass distribution and EOS with unprecedented precision, provided a sufficient number of multi-messenger events are identified.
While KN light curves do not substantially tighten EOS constraints for high-quality GW signals, they are vital for breaking degeneracies in cosmological inference (specifically $H_0$ and $\Omega_0$ ) and correcting for inclination biases.
The study highlights the computational feasibility of fully Bayesian hierarchical inference using normalizing flows and GPU acceleration, allowing for the analysis of large event populations within hours.

The authors remain modest regarding their claims, acknowledging that systematic uncertainties in EM emission modeling (ejecta masses, GRB launch mechanisms) and the coarse approximation of detection probabilities could bias the results. They emphasize that the exact number of detections and the precision of constraints depend heavily on the true merger rate, the actual mass distribution, and the final operational configurations of future telescopes.

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