Equation of state and core behavior of neutron star matter

Determine the equation of state of neutron star matter over the relevant density ranges and ascertain whether qualitative changes or discontinuities occur approaching the core, integrating QCD-based theory with multi-messenger and gravitational-wave observations.

Background

The paper emphasizes QCD’s growing role in astrophysics, particularly for neutron stars, which probe extreme nuclear matter conditions. Despite having the governing QCD equations, translating them into reliable macroscopic predictions for neutron star structure is currently inadequate.

Key unresolved issues include a definitive equation of state across interior densities and the potential for phase transitions or discontinuities toward the core, questions now accessible to multi-messenger astronomy and gravitational-wave data but still lacking convincing answers.

References

What is the equation of state? Are there qualitative changes and discontinuities approaching the core? Despite knowing the governing equations, we don't have convincing answers even to such basic questions.

— QCD at 50: Golden Anniversary, Golden Insights, Golden Opportunities  (2403.06038 - Wilczek, 2024) in Subsection A Tool for Astrophysics and Nuclear Technology

On the other hand, the impact of a finite strange quark mass on these constraints in EoS inference remains unclear.

— MUSES workflows for pQCD constraints on dense matter with finite quark masses  (2609.09530 - Danhoni et al., 8 Sep 2026) in Section 3, opening paragraph of “pQCD Constraints with Massive Strange Quarks”

We caution that the constraints depend on the matching point through both $P*$ and $n_B*$, so a quantitative statement requires recomputing the accepted EoS fractions under scale variation, which we leave to future work.

— MUSES workflows for pQCD constraints on dense matter with finite quark masses  (2609.09530 - Danhoni et al., 8 Sep 2026) in Section 2.3, “Quark-matter equation of state”

Our median coincides with $\Delta_{\mathrm{TOV} = -0.01 \pm 0.03$ of Marczenko~et al. (Fig.~\ref{fig:cs2_diagnostics}c), on a negatively skewed interval that still admits the conjectured bound $\Delta \ge 0$ while leaning towards the $\Delta < 0$ strongly favoured by the NICER-updated Brandes~et al.~analysis, leaving the sign of the trace anomaly unresolved.

— Generative artificial intelligence for reconstructing neutron-star matter  (2608.17457 - Panteleeva et al., 18 Aug 2026) in Section 4, Neutron-star structure

A quantitative criterion for a significant deviation from the universal relation in terms of the transition parameters $(\Delta\epsilon,p_t)$ requires a more complete treatment.

— Universal Relations for Neutron Stars from Asymptotic Analysis  (2608.19939 - Kamata et al., 20 Aug 2026) in Section 5.2.3, "Implications for realistic equations of state"

The precise mechanism by which particle excitations arrange themselves such that the system becomes pseudo-conformal with a parity-doubled structure in the nucleon sector is not yet clear, and how the populations of $N_+$ and $N_-$ in the parity-doubled structure evolve with density in the pseudo-conformal phase has not been properly discussed, while related aspects have been discussed in various contexts either in the PDM or in the pseudo-conformality.

— Scale Invariance and Compact Star Matter  (2608.27193 - Lee et al., 27 Aug 2026) in Section 4, “Summary and Discussion”

Because the density-resolved quadrupolar susceptibility increases sharply beyond $0.06\,\mathrm{fm{-3}}$ (Section~\ref{sec:qkernel}), the unmodelled continuation to the crust--core boundary is a genuine component of the theoretical uncertainty of the non-relaxed response. We do not assign it a sign or convert the matched-domain result into a bound, since the fixed-composition profile in that layer has not been calculated.

— Vortex pinning and the elastic response of neutron-star crusts II. Non-axisymmetric loading and Magnus mountains  (2609.02863 - Giliberti, 2 Sep 2026) in Section 2.2, subsection “Equilibrium and fixed-composition compression”; see also Section 4.4, subsection “Domain of validity”

Although it has been widely studied for decades, the EOS of cold, ultra-dense matter at high density is still poorly constrained (see, e.g., \citealp{2001ApJ...550..426L}).

— Exploring the connection between Fast Radio Bursts and binary neutron star mergers  (2609.05209 - Patricelli et al., 4 Sep 2026) in Section 2.3, “The EOS and the BNS merger outcome”

Even without a sourced axion, the equation of state at densities in neutron stars is unknown.

— Axion Hair and Pulsar Electrodynamics: modelling, discharge dynamics, and particle-in-cell simulations  (2609.08840 - Witte et al., 8 Sep 2026) in Section 2, “The sourcing of axion hair by neutron stars”