Low-Mass Neutron Stars and Effective Phase Transitions from a Hybrid Van der Waals-Polytropic Equation of State

TL;DR

This paper presents an analytically tractable model of neutron stars with phase transitions using a hybrid van der Waals-polytropic equation of state, revealing low-mass neutron star configurations and phase transition signatures.

Contribution

It introduces a simplified, analytical EOS model coupling a van der Waals core with a polytropic crust to study phase transitions in neutron stars.

Findings

Low-mass neutron stars with masses 0.99-2.05 solar masses.

Identification of phase transition signatures in chemical potential.

Reproduction of key phase transition phenomenology with analytic models.

Abstract

We study phase-transition-like behavior in neutron stars using a simplified, piecewise equation of state that couples a modified van der Waals-type core to a polytropic crust. The model remains analytically tractable while allowing for nonlinear density dependence. We impose thermodynamic and causal consistency conditions and determine the critical densities at which the curvature of the pressure-energy density relation changes. In the non-relativistic limit, the generalized Lane-Emden equations describe a smooth core-crust transition layer. We integrate the Tolman-Oppenheimer-Volkoff equations across different $(\tau_1,\sigma_1)$ regimes, where these parameters encode thermal and interaction effects in the core. The resulting mass-radius sequences yield low neutron star masses $(0.99-2.05)M_{\odot}$, and the chemical potential exhibits the characteristic signatures of phase-transition behavior at densities well above the matching point. Our results show that analytic EOS models can reproduce the key phenomenology of phase transitions and provide a controlled framework for exploring low-mass neutron star configurations.