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

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 $(τ_1,σ_1)$ 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.

Figures (8)

• Figure 1: Schematic, not-to-scale representation of the NS interior as modeled here. The stellar core ($\varepsilon > \varepsilon_0$) is characterized by a modified vdW–type EoS, whereas the crustal region ($\varepsilon \leq \varepsilon_0$) is represented by a two-term polytropic EoS. The transition region around $r_1$ is the transition layer, where the two descriptions are approximately valid.
• Figure 2: Plot of the parameter space ($\tau_1,\sigma_1$) showing the validity region where $\varepsilon_c>0$.
• Figure 3: Mass–radius relations from the TOV equations for the parameter sets in Table \ref{['tab:tabparam1']}. Panels (a), (c), and (e): $M(r)$ profiles for the configurations in each regime. Panels (b), (d), and (f): families of $M/M_\odot$ vs. $R$ curves obtained by scanning over central densities $\varepsilon_c$.
• Figure 4: Mass–radius relations for the parameter sets in Table \ref{['tab:tabparam3_4']}, corresponding to the most phase-transition–sensitive regimes. Panels (a), (c), and (e) show $M(r)$ for each configuration. Panels (b), (d), and (f): $M/M_\odot$ vs. $R$ as central densities are varied.
• Figure 5: Mass–radius relations for the parameter sets of Table \ref{['tab:tabparam2']}. Panels (a), (c), and (e): $M(r)$ for selected configurations in each regime. Panels (b), (d), and (f): $M/M_\odot$ vs. $R$ for several central densities, highlighting how the choice of $(\tau_1,\sigma_1)$ affects the stiffness of the EoS and the maximum mass. Observe that the increase in $\sigma_1$ turns the EoS more rigid and displaces the maximum amount of mass.