Equation of State of Highly Asymmetric Neutron-Star Matter from Liquid Drop Model and Meson Polytropes

TL;DR

This paper develops a physically transparent equation of state for highly asymmetric neutron-star matter by merging degenerate Fermi gas thermodynamics with a liquid drop description of nuclei and a high-density meson-exchange mean-field (σ, ω, ρ) treatment to ensure causality up to supranuclear densities. The EOS smoothly bridges the crust and core, with a polytropic high-density component calibrated via mappings to RMF couplings, and is solved within the Tolman–Oppenheimer–Volkoff framework to predict mass–radius relations, compactness, and surface/redshift observables. By comparing with NICER and other astrophysical constraints, the study shows that macroscopic neutron-star properties are mainly sensitive to the overall stiffness of the EOS, rather than the fine details of microphysics, while providing a versatile baseline for incorporating additional degrees of freedom. The framework offers a simple, extensible tool for probing the impact of stiff versus soft dense-matter behavior on neutron-star structure and for testing how future observations could distinguish between competing microphysical scenarios.

Abstract

We present a unified description of dense matter and neutron-star structure based on simple but physically motivated models. Starting from the thermodynamics of degenerate Fermi gases, we construct an equation of state for cold, catalyzed matter by combining relativistic fermion statistics with the liquid drop model of nuclear binding. The internal stratification of matter in the outer crust is described by $β$-equilibrium, neutron drip and a gradual transition to supranuclear matter. Short-range repulsive interactions inspired by Quantum Hadrodynamics are incorporated at high densities in order to ensure stability and causality. The resulting equation of state is used as input to the Tolman--Oppenheimer--Volkoff equations, yielding self-consistent neutron-star models. We compute macroscopic stellar properties including the mass-radius relation, compactness and surface redshift that can be compared with recent observational data. Despite the simplicity of the underlying microphysics, the model produces neutron-star masses and radii compatible with current observational constraints from X-ray timing and gravitational-wave measurements. This work demonstrates that physically transparent models can already capture the essential features of neutron-star structure and provide valuable insight into the connection between dense-matter physics and astrophysical observables while they can also be used as easy to handle models to test the impact of more complicated phenomena and variations in neutron stars.

Figures (8)

• Figure S1: Pressure--density relation at high densities for a one-term polytropic equation of state with different values of $K$ and $\gamma$. Each curve is compared against the SLy equation of state, which serves as a benchmark for realistic nuclear matter behaviour.
• Figure S2: Mass--radius relations obtained for multiple $(K,\gamma)$ combinations. Observational constraints are indicated for comparison, together with the SLy4 prediction.
• Figure S3: Mass--radius relations for the subset of polytropic equations of state that satisfy observational constraints and yield physically viable neutron stars.
• Figure S4: Pressure as a function of density for the adopted set of mesonic couplings $G_i$, compared with the SLy4 equation of state. The individual contributions from neutrons and electrons in the relativistic Fermi gas are shown separately, illustrating the expected behaviour across different density regimes.
• Figure S5: Mass--radius diagram obtained within the $\sigma\omega\rho$ meson-exchange model in the mean-field approximation. The SLy4 result is included for direct comparison.