Neutron stars and the dense matter equation of state: from microscopic theory to macroscopic observations

The past years have witnessed tremendous progress in understanding the properties of neutron stars and of the dense matter in their cores, made possible by electromagnetic observations of neutron stars and the detection of gravitational waves from their mergers. These observations provided novel constraints on neutron-star structure, that is intimately related to the properties of dense neutron-rich matter described by the nuclear equation of state. Nevertheless, constraining the equation of state over the wide range of densities probed by astrophysical observations is still challenging, as the physics involved is very broad and the system spans many orders of magnitude in densities. Here, we review theoretical approaches to calculate and model the neutron-star equation of state in various regimes of densities, and discuss the related consequent properties of neutron stars. We describe how the equation of state can be calculated from nuclear interactions that are constrained and benchmarked by nuclear experiments. We review neutron-star observations, with particular emphasis on information provided by gravitational-wave signals and electromagnetic observations. Finally, we discuss future challenges and opportunities in the field.

💡 Research Summary

This review provides a comprehensive synthesis of the current understanding of the dense‑matter equation of state (EOS) that governs neutron‑star interiors, bridging microscopic nuclear theory, terrestrial experiments, and multimessenger astrophysical observations. The authors begin by outlining the historical development of neutron‑star observations, from the discovery of radio pulsars in 1967 to the precise mass measurements of heavy pulsars (> 2 M⊙) via pulsar timing, and the breakthrough detection of gravitational waves from binary neutron‑star (BNS) mergers (GW170817) by LIGO/Virgo. These observations have supplied the first direct constraints on the EOS at supranuclear densities.

The core of the paper is devoted to the theoretical construction of the EOS across the wide density range encountered in neutron stars. At densities near nuclear saturation (n₀≈0.16 fm⁻³) the authors employ the standard expansion of the energy per particle in terms of the isospin asymmetry β, introducing key bulk parameters: binding energy B, incompressibility K, symmetry energy S, and its slope L. They emphasize how these quantities are linked to measurable nuclear observables such as giant monopole resonances, neutron‑skin thickness, and heavy‑ion collision flow data. The slope L, in particular, determines the pressure of pure neutron matter at n₀ and therefore directly influences neutron‑star radii and tidal deformabilities.

In the low‑density regime (n ≲ 10⁻² n₀) the review highlights the remarkable universality between dilute neutron matter and ultracold atomic Fermi gases. Because the neutron‑neutron scattering length is anomalously large while the effective range is tiny, many properties become independent of microscopic details. This universality allows experimental studies of atomic gases to inform the pairing gap and superfluid dynamics of neutron matter, which are crucial for cooling and glitch phenomena.

For densities up to a few times n₀, the authors discuss state‑of‑the‑art many‑body techniques that start from chiral effective field theory (ChEFT) nucleon‑nucleon and three‑nucleon forces. Quantum Monte Carlo, self‑consistent Green’s function, coupled‑cluster, and many‑body perturbation theory are presented as complementary approaches that yield EOS predictions with quantified uncertainties. The paper also treats β‑equilibrium conditions, incorporating electrons and muons, to produce a charge‑neutral composition appropriate for the outer core.

At higher densities (≥ 2–3 n₀) the possibility of exotic degrees of freedom is examined. The appearance of hyperons, pion or kaon condensates, and deconfined quark matter can soften or stiffen the EOS depending on the interaction models. The authors review recent parameterizations that allow for first‑order phase transitions and discuss how such features would manifest in observable quantities like the maximum mass, radius, and tidal deformability.

The review then connects these theoretical EOS models to astrophysical observables. Solving the Tolman‑Oppenheimer‑Volkoff equations yields mass‑radius curves that can be compared with measurements from NICER pulse‑profile modeling and X‑ray spectral fitting. Tidal deformability Λ, extracted from the inspiral phase of BNS gravitational‑wave signals, is shown to be a sensitive probe of the pressure at 1–2 n₀, and thus of L. The authors illustrate how multimessenger events that provide simultaneous mass, radius, and Λ constraints dramatically reduce EOS uncertainties.

A dedicated section on compact‑binary mergers details the inspiral dynamics, the role of tidal effects on the gravitational‑wave phase, and the post‑merger evolution, including prompt black‑hole formation, delayed collapse, or long‑lived hypermassive remnants. Electromagnetic counterparts—short gamma‑ray bursts, kilonovae, and radio afterglows—are discussed as additional diagnostics of the ejecta composition and the EOS‑dependent merger outcome.

The final part of the paper outlines future challenges and opportunities. The authors argue that progress will hinge on (i) improving high‑density nuclear theory, especially the treatment of possible phase transitions; (ii) tighter integration of nuclear‑experiment constraints from facilities such as FRIB; (iii) exploiting next‑generation gravitational‑wave detectors (Einstein Telescope, Cosmic Explorer) and X‑ray missions (eXTP, Athena) for higher‑precision multimessenger data; and (iv) adopting Bayesian inference frameworks and machine‑learning emulators to efficiently explore the high‑dimensional EOS parameter space.

In summary, the review emphasizes that a synergistic, multi‑disciplinary approach—combining microscopic nuclear physics, laboratory experiments, and multimessenger astrophysics—is essential to pin down the dense‑matter EOS and to uncover any new physics (e.g., deconfined quark matter) that may reside in the cores of neutron stars.