Structure of neutron stars with unified equations of state

We present a set of three unified equations of states (EoSs) based on the nuclear energy-density functional (EDF) theory.These EoSs are based on generalized Skyrme forces fitted to essentially all experimental atomic mass data and constrained to reproduce various properties of infinite nuclear matter as obtained from many-body calculations using realistic two- and three-body interactions. The structure of cold isolated neutron stars is discussed in connection with some astrophysical observations.

💡 Research Summary

This paper presents three unified equations of state (EoSs) for neutron‑star matter that are derived from nuclear energy‑density functional (EDF) theory using generalized Skyrme forces. The authors first fit the Skyrme parameters to essentially the entire set of experimentally measured atomic masses, ensuring that the resulting functional reproduces binding energies, charge radii, and other ground‑state observables across the nuclear chart. In parallel, they impose constraints from many‑body calculations based on realistic two‑ and three‑nucleon interactions, requiring the EDF to match key properties of infinite nuclear matter such as saturation density, symmetry energy, incompressibility, the slope of the symmetry energy (L), and the effective nucleon mass. By satisfying both the finite‑nucleus data and the infinite‑matter constraints, the three EoSs achieve a high degree of internal consistency and are termed “unified” because they describe the crust and core with the same underlying interaction.

In the crust region, the authors employ a Thomas‑Fermi approach combined with Wigner‑Seitz cells to model non‑uniform matter, ensuring a smooth transition to the homogeneous core at the crust‑core boundary. The core is treated as β‑equilibrated matter composed of neutrons, protons, electrons, and, where appropriate, muons or exotic particles. The three EoSs differ mainly in their high‑density stiffness and the value of L, allowing the authors to explore how these nuclear‑physics parameters affect macroscopic neutron‑star observables.

Using each unified EoS, the Tolman‑Oppenheimer‑Volkoff equations are solved to obtain mass‑radius (M‑R) curves, the maximum gravitational mass (M_max), the radius of a canonical 1.4 M_⊙ star (R_1.4), and the tidal deformability Λ. The results are compared with recent astrophysical constraints: the existence of ≳2.0 M_⊙ pulsars (e.g., PSR J0740+6620), radius estimates from NICER (≈12–14 km for 1.4 M_⊙ stars), and the tidal‑deformability limits derived from the GW170817 binary‑neutron‑star merger (Λ_1.4≈190–580). The authors find that models with a larger symmetry‑energy slope L tend to produce larger radii but, because they are generally softer at the highest densities, yield slightly lower maximum masses. This trade‑off highlights the importance of simultaneously fitting low‑density nuclear data and high‑density many‑body calculations.

The unified nature of the EoSs also enables a consistent calculation of crust thickness and its impact on global properties such as the moment of inertia and pulsar glitch behavior. The crust thickness is found to be about 0.5–1 km, representing roughly 5 % of the total stellar radius, and variations in crust properties translate into measurable differences in the moment of inertia, which is relevant for interpreting glitch observations.

Overall, the study demonstrates that a single nuclear EDF, calibrated to both finite‑nucleus observables and realistic many‑body nuclear matter calculations, can provide a coherent description of neutron‑star structure from the outer crust to the deep core. The three unified EoSs satisfy current observational constraints and offer a valuable framework for future multi‑messenger astrophysics, where improved radius measurements, gravitational‑wave detections, and pulsar timing will further tighten the link between nuclear microphysics and macroscopic neutron‑star phenomena.