The Crusts of Neutron Stars Revisited: Approximations within a Polytropic Equation of State Approach

TL;DR

This paper revisits thin-crust approximations in neutron star models, compares them with exact solutions, and finds that simplified crust treatments are sufficiently accurate for structural analysis despite uncertainties in the sub-nuclear equation of state.

Contribution

It introduces a simplified approach to neutron star crust modeling using TOV solutions and various EoSs, demonstrating good agreement with exact solutions across different theoretical frameworks.

Findings

Relativistic and corrected Newtonian approximations align well with exact solutions.

Simplified crust models are adequate for structural purposes despite EoS uncertainties.

Modifications in gravity theories create degeneracies in mass-radius relations.

Abstract

In this work, we revisit several thin-crust approximations presented in the literature and compare them with the exact solutions of the Tolman--Oppenheimer--Volkoff (TOV) equations. In addition, we employ three different equations of state (EoSs), including one with a pasta phase, each based on a distinct theoretical framework: the variational method, relativistic Brueckner--Hartree--Fock theory, and relativistic mean-field theory. We emphasize that these approximations require only the TOV solutions for the core and the EoS properties at the core--crust interface; in our approach, only the energy density is needed. Finally, the relativistic approximation, as well as the Newtonian approximation with corrections, shows good agreement with the exact solutions. This indicates that a simple treatment of the crust is sufficient for structural purposes, independently of the uncertainties in the sub-nuclear equation of state, which are not very large. The unified EoS SINPA (relativistic mean-field theory), including the pasta phase, was used to study the thin-crust approximation, while degeneracy in the $M$--$R$ relation is demonstrated through: (i) anisotropic pressure in the modified TOV equations, (ii) the $f(R, L_m, T)$ gravity model, and (iii) dark matter admixture. As demonstrated, modifications to the description of gravitation introduce degeneracies in the mass--radius relation that are challenging to disentangle or quantify precisely.