Isolating finite-temperature dense-matter physics in binary-neutron-star post-merger gravitational-wave spectra with next-generation detectors

Raithel & Paschalidis (2024) showed that uncertainties in the finite-temperature part of the dense-matter equation of state change the post-merger gravitational-wave spectrum of a binary neutron star merger by an amount comparable to changing the cold equation of state by about 120 m in the characteristic neutron-star radius, and that next-generation detectors could distinguish thermal prescriptions out to roughly 83-208 Mpc. They also showed that this detectability estimate is provisional: it was derived for equal-mass, non-rotating binaries with simplified transport, and it ignores competing spectral distortions of similar magnitude from bulk viscosity, hyperons, pions, trapped neutrinos, and hadron-quark phase transitions, as well as template incompleteness. The open problem is to determine, quantitatively and self-consistently, under what conditions post-merger gravitational-wave observations with next-generation detectors can robustly isolate finite-temperature dense-matter physics from these confounding effects.

Background

A binary neutron star (BNS) merger leaves behind a hot, differentially rotating remnant whose oscillations emit gravitational waves (GWs) at kilohertz frequencies, producing a post-merger spectrum dominated by a few broad peaks (conventionally labeled $f_1$, the dominant $f_2$ peak, and $f_3$). These frequencies probe the dense-matter equation of state (EoS), i.e. the relation between pressure, density, temperature, and composition, at supranuclear densities unreachable in terrestrial experiments. Whereas the inspiralling neutron stars are thermodynamically cold, the merger shock-heats the remnant so that thermal pressure can exceed 10% of the cold pressure at supranuclear densities. The finite-temperature EoS can be approximated by adding a thermal pressure component, often parametrized by a power-law index $\Gamma_{\rm th}$ or, in the effective-mass parametrization used by Raithel and collaborators, by the density dependence of the nucleon effective mass. Different plausible thermal prescriptions shift the dominant post-merger peak frequency $f_2$ by tens to hundreds of hertz. Building on their earlier simulations of realistic finite-temperature effects (Raithel, Paschalidis & Özel 2021; Raithel & Paschalidis 2023), Raithel & Paschalidis (2024) quantified how distinguishable these prescriptions are. Using spectra mismatch $\mathcal{M}$ (a noise-weighted inner product measuring the difference between two signals) and horizon distances (the distance to which two signals are distinguishable at 90% confidence), they found that current uncertainties in the thermal physics produce spectral changes comparable to varying the cold EoS by -54 to +116 m in the radius $R_{1.4}$ of a 1.4-solar-mass neutron star; with next-generation ground-based detector concepts — the Cosmic Explorer (CE) and the Einstein Telescope (ET) — these would be measurable out to 83-208 Mpc in CE's CE-20pm configuration (the range depending on the cold EoS), provided the cold EoS is pinned down to roughly 120 m in $R_{1.4}$ by inspiral measurements. The study, however, evolved equal-mass, non-spinning binaries and modeled the spectra with smoothed three-peak templates. The authors therefore flagged five unresolved issues: (1) the strength and spectral location of thermal signatures likely depend on total mass, mass ratio, and non-zero initial spins; (2) the results may be sensitive to the treatment of neutrino transport and out-of-equilibrium composition, which were not modeled self-consistently; (3) bulk viscosity (dissipation from weak-interaction-driven chemical equilibration of the oscillating remnant) and other transport effects may damp or distort the spectrum by similar amounts; (4) additional degrees of freedom — hadron-quark phase transitions, hyperons, pions, trapped muons and neutrinos — can produce spectral distortions that mimic thermal signatures and that inspiral data alone may not exclude; and (5) three-peak templates miss emergent features such as spiral density modes and the $m=1$ one-arm instability (a non-axisymmetric deformation of the remnant that powers low-frequency emission). Subsequent work quantified several of these confounders individually: bulk viscosity changes the post-merger spectrum by up to about 100 Hz (Chabanov & Rezzolla 2025); hyperons raise $f_2$ by up to about 150 Hz (Blacker et al. 2024); muons, pions, and trapped neutrinos shift the signal by 100-200 Hz (Pajkos & Most 2025); and hadron-quark transitions have been mapped across 245 hybrid EoSs (Blacker & Bauswein 2025). All of these are of the same order as the thermal signatures, so the disentanglement problem — deciding which piece of dense-matter physics a measured post-merger spectrum actually constrains — is real and unresolved.

Problem Statement

Determine whether, and under what conditions, the post-merger gravitational-wave spectrum of a binary neutron star merger observed with next-generation detectors (Cosmic Explorer, Einstein Telescope) can robustly isolate finite-temperature dense-matter physics, by carrying out a self-consistent quantification and disentanglement assessment that addresses, jointly rather than one at a time: (1) how the strength and spectral location of thermal signatures in the post-merger spectrum vary across total mass, mass ratio, and realistic non-zero initial spins, extending the equal-mass non-spinning simulations of Raithel & Paschalidis (2024); (2) the sensitivity of the predicted post-merger spectrum to the treatment of neutrino transport, neutrino trapping, and out-of-equilibrium composition; (3) the impact of bulk viscosity and other transport-induced damping on the spectral amplitudes, frequencies, and lifetimes against which thermal effects are measured; (4) whether distortions from additional degrees of freedom — hadron-quark phase transitions, hyperons, pions, trapped muons and neutrinos — mimic or overwhelm the thermal signatures and are not already excluded by inspiral data; and (5) what post-merger waveform templates beyond three-peak models (including spiral modes, the $m=1$ one-arm instability, and late-time frequency evolution) are required so that detectability and parameter-inference claims are not biased by template incompleteness. The question is which finite-temperature EoS parameters, if any, can be extracted from a next-generation post-merger observation at a given distance and signal-to-noise ratio once all of the above competing effects and uncertainties are folded in, and the determination concerns a single joint assessment of (1)-(5) rather than an effect-by-effect treatment, using self-consistent modeling where feasible and otherwise clearly stated approximations whose residual systematics are quantified.

References

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