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

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 $\beta$-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.