Kilohertz Gravitational Waves from Binary Neutron Star Mergers: Full Spectrum Analyses and High-density Constraints on Neutron Star Matter

We demonstrate Bayesian analyses of the complete gravitational-wave spectrum of binary neutron star mergers events with the next-generation detector Einstein Telescope. Our mock analyses are performed for 20 different signals using the TEOBResumSPA_NRPMw waveform that models gravitational-waves from the inspiral to the postmerger phase. They are employed to validate a pipeline for neutron star’s extreme matter constraints with prospective detections and under minimal hypotheses on the equation of state. The proposed analysis stack delivers inferences for the mass-radius curve, the mass dependence of the quadrupolar tidal polarizability parameter, the neutron star’s maximum density, the maximum mass and the relative radius, and the pressure-density relation itself. We show that a single event at a signal-to-noise ratio close to the minimum threshold for postmerger detection is sufficient to tightly constrain all the above relations as well as quantities like the maximum mass (maximum density) to precision of ${\sim}6$% (${\sim}10$%) at 90% credibility level. We also revisit inferences of prompt black hole formation with full spectrum signals and find that the latter can be robustly identified, even when the postmerger is not detectable due to a low signal-to-noise ratio. New results on the impact of the initial signal frequency and of the detector configuration (triangular vs. two-L) on the source’s parameters estimation are also reported. An improvement of approximately one order of magnitude in the precision of the chirp mass and mass ratio can be achieved by lowering the initial frequency from 20 Hz to 2 Hz. The two-L configuration shows instead significant improvements on the inference of the source declination, due to geographical separation of the two detectors.

💡 Research Summary

This paper presents a comprehensive Bayesian framework for extracting the full gravitational‑wave (GW) spectrum—from inspiral through merger to post‑merger—of binary neutron‑star (BNS) coalescences as observed by the next‑generation Einstein Telescope (ET). Using the frequency‑domain effective‑one‑body (EOB) model TEOBResumSPA for the low‑frequency inspiral‑merger (IM) portion and the NR‑informed post‑merger (PM) model NRPMw, the authors construct a hybrid waveform TEOBResumSPA_NRPMw that smoothly joins the two regimes at the merger time and phase.

A set of 20 mock BNS signals is generated, spanning component masses 1.2–1.5 M⊙, mass ratios close to unity, tidal deformabilities Λ≈200–600, and distances of 20–40 Mpc. Two initial low‑frequency cut‑offs (20 Hz and 2 Hz) are examined, as well as two detector configurations: the triangular ET‑D design (three 10 km arms) and a “two‑L” layout consisting of two geographically separated interferometers.

Parameter estimation is performed with zero‑noise injections using the parallel‑bajes pipeline and the nested‑sampling algorithm dynesty (≥2048 live points). For the IM part, a relative‑binning technique dramatically reduces computational cost; for the PM part, the likelihood is evaluated up to 2048 Hz with relative binning and beyond that with a standard approach. The total log‑likelihood is the sum of the IM and PM contributions, ensuring a coherent treatment of the full spectrum.

Crucially, the analysis maps posterior samples of the total mass M and the dominant post‑merger frequency f₂ onto physically meaningful quantities—maximum central density ρ_TOV^max, radius at maximum mass R_TOV^max, and the maximum non‑rotating mass M_TOV^max—through EoS‑insensitive empirical relations (Eqs. 9–10). These relations are then used to re‑weight a large prior ensemble of two‑million candidate equations of state (EoSs) that satisfy minimal assumptions (general relativity, causality, observed pulsar mass lower bound, and GW170817 tidal constraints). The re‑weighted set yields posterior distributions for the pressure‑density curve p(ρ), the tidal deformability Λ(M), and the mass‑radius (M‑R) relation, all with 90 % credible intervals.

Key findings include:

1. Single‑event power – Even a marginal post‑merger detection (signal‑to‑noise ratio ≈ 15) suffices to constrain the maximum neutron‑star mass to ≲ 6 % and the maximum central density to ≲ 10 % (90 % credibility). This represents an order‑of‑magnitude improvement over current constraints from inspiral‑only analyses.

2. Impact of low‑frequency start – Lowering the analysis start frequency from 20 Hz to 2 Hz reduces the uncertainties on the chirp mass and mass ratio by roughly one order of magnitude, highlighting the importance of ET’s low‑frequency sensitivity for precise source characterization.

3. Detector geometry effects – The two‑L configuration yields significantly tighter constraints on the source declination compared with the triangular layout, owing to the longer baseline and differing antenna patterns of the separated interferometers.

4. Prompt collapse identification – By combining inspiral‑derived tidal information with the upper limits on f₂, the pipeline can robustly assess the probability of prompt black‑hole formation even when the post‑merger signal is undetectable, providing a valuable tool for multimessenger follow‑up strategies.

Overall, the study demonstrates that a full‑spectrum Bayesian analysis, enabled by accurate hybrid waveforms and efficient likelihood evaluation, can extract high‑density nuclear‑matter information from a single BNS detection with ET. The authors suggest future extensions such as incorporating additional NR‑calibrated waveform features, joint analyses of multiple events, and integration with electromagnetic counterparts to further sharpen constraints on the neutron‑star equation of state.