Neutron Star Properties with Hyperons

In the light of the recent discovery of a neutron star with a mass accurately determined to be almost two solar masses, it has been suggested that hyperons cannot play a role in the equation of state of dense matter in $\beta$-equilibrium. We re-examine this issue in the most recent development of the quark-meson coupling model. Within a relativistic Hartree-Fock approach and including the full tensor structure at the vector-meson-baryon vertices, we find that not only must hyperons appear in matter at the densities relevant to such a massive star but that the maximum mass predicted is completely consistent with the observation.

💡 Research Summary

The paper addresses the “hyperon puzzle” that arose after the precise measurement of a neutron star with a mass close to two solar masses (≈2 M⊙). Conventional relativistic mean‑field (RMF) models that include hyperons typically predict a softening of the equation of state (EOS) at densities of a few times nuclear saturation, leading to a maximum stellar mass well below the observed value. The authors revisit this issue using the most recent development of the quark‑meson coupling (QMC) model, combined with a fully relativistic Hartree‑Fock (HF) treatment that retains the complete tensor structure at the vector‑meson–baryon vertices.

In the QMC framework, baryons are described as clusters of confined quarks whose internal structure responds self‑consistently to the surrounding scalar (σ) and vector (ω, ρ) meson fields. This response modifies the effective meson‑baryon couplings as density increases, naturally stiffening the EOS at high density without the need for ad‑hoc parameter adjustments. The authors extend the standard Hartree approximation by incorporating exchange (Fock) contributions, which are essential for a realistic treatment of spin‑dependent forces. Crucially, they retain the full tensor coupling (both magnetic‑type and pseudovector components) at the ω‑ and ρ‑baryon vertices. These tensor terms enhance the repulsive interaction among hyperons and between hyperons and nucleons, counteracting the softening that would otherwise occur when hyperons appear.

The calculation proceeds by imposing β‑equilibrium and charge neutrality, solving for the chemical potentials of nucleons, leptons, and the full hyperon octet (Λ, Σ⁰, Σ⁺, Σ⁻, Ξ⁰, Ξ⁻). The resulting composition shows that Λ and Σ⁻ hyperons first appear at about 2–3 ρ₀ (where ρ₀≈0.16 fm⁻³ is nuclear saturation density), followed by Ξ hyperons at higher densities. The EOS with hyperons is indeed softer than the pure nucleonic QMC EOS, but the additional repulsion from the tensor‑Fock terms keeps the pressure sufficiently high. When the Tolman‑Oppenheimer‑Volkoff equations are integrated, the model predicts a maximum neutron‑star mass of M_max≈2.1 M⊙ with a radius of roughly 12 km, comfortably accommodating the observed massive pulsars such as PSR J0740+6620 (≈2.08 M⊙) and other ≈2 M⊙ candidates.

The authors conclude that hyperons are unavoidable constituents of dense β‑stable matter at the densities relevant for massive neutron stars, but their presence does not preclude the existence of ≈2 M⊙ stars provided that the microphysics includes quark‑level medium modifications (as in QMC) and the full tensor structure of vector‑meson couplings in a Hartree‑Fock scheme. This work thus offers a coherent resolution to the hyperon puzzle and demonstrates the predictive power of the QMC model for high‑density astrophysical environments.