Neutron Star Physics and Equation of State Analysis

Neutron stars are the compact remnants of massive stars that have undergone core-collapse supernovae. Packing more than the mass of the Sun into a sphere roughly 10–15 km in radius, they present the densest stable matter in the Universe outside black holes. Their internal structure is governed by the equation of state (EoS), which links pressure to density and temperature and determines global properties such as mass, radius and tidal response. At subnuclear densities, the crust consists of neutron-rich nuclei embedded in a degenerate electron sea, whereas the core may contain superfluid neutrons, superconducting protons and leptons. At the highest densities, novel phases—hyperons, deconfined quarks or colour-superconducting condensates—may emerge, each imprinting subtle signatures on macroscopic observables. Progress in nuclear theory, heavy-ion experiments and astrophysical measurements now permits stringent tests of competing EoS models. Observations of pulsar timing, X-ray flux modulations and gravitational waves from binary mergers deliver complementary constraints, enabling a multimessenger approach. A precise characterisation of the EoS is critical not only for nuclear physics and astrophysics but also for fundamental insights into strong-interaction dynamics and the behaviour of matter under extreme conditions.

Research from Nature Portfolio

Recent studies have quantified the likelihood that the cores of the most massive neutron stars host deconfined quark matter. By combining astrophysical observations with theoretical calculations through a Bayesian framework, researchers have demonstrated that at the highest densities probed by maximally heavy stars the EoS is consistent with restoration of approximate conformal symmetry and with the number of active degrees of freedom expected for quark matter. The analysis further shows that remaining EoSs exhibit rapid crossover behaviours akin to a phase transition, indicating a smooth but pronounced change in composition rather than a sharp discontinuity.

Neutron Star Physics and Equation of State Analysis publication trend

The graph below shows the total number of articles in neutron star physics and equation of state analysis across all publications each year (not limited to Nature Index journals).

Technical terms

Neutron star: Dense remnant of a supernova composed primarily of neutrons, with a mass around 1.4 M⊙ compressed into a sphere of radius ~10–15 km.

Equation of state (EoS): Relationship between pressure, density and temperature that characterises the internal structure and composition of neutron star matter.

Tidal deformability: Measure of the degree to which a neutron star’s shape is deformed by the gravitational field of its companion, providing insight into its internal structure.

Quark matter: Hypothetical phase in which neutrons dissolve into their constituent quarks, potentially occurring in the cores of the most massive neutron stars.

Phase transition: Change in the state of matter within a neutron star, such as from hadronic to quark matter, that can alter its EoS and observable properties.

References

1. Theoretical and experimental constraints for the equation of state of dense and hot matter. Living Reviews in Relativity (2024).
2. Strongly interacting matter exhibits deconfined behavior in massive neutron stars. Nature Communications (2023).
3. A NICER View of the Nearest and Brightest Millisecond Pulsar: PSR J0437–4715. The Astrophysical Journal Letters (2024).
4. GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral. Physical Review Letters (2017).
5. Gravitational-Wave Constraints on the Neutron-Star-Matter Equation of State. Physical Review Letters (2018).