Pressure and chemical potentials in the inner crust of a cold neutron star within Hartree-Fock and extended Thomas-Fermi methods

TL;DR

This paper presents a method to accurately compute the full equation of state for the inner crust of neutron stars using Hartree-Fock and extended Thomas-Fermi methods, improving upon previous interpolation techniques.

Contribution

It derives exact formulas for chemical potentials and pressure within a self-consistent mean-field framework, enabling precise calculations of neutron star crust properties.

Findings

Derived formulas improve pressure and chemical potential calculations.

Applied methods to BSk24 equation of state for nonaccreted neutron stars.

Numerical examples demonstrate the accuracy of the approach.

Abstract

Self-consistent mean-field methods with Skyrme-type effective interactions and semiclassical approximations, such as the Thomas-Fermi approach and its extensions are particularly well-suited for describing in a thermodynamically consistent way the various phases of the dense matter present in the interior of neutron stars. These methods have been applied to predict the composition of the different regions, including the inner crust constituted by nuclear clusters coexisting with free neutrons and electrons. Because of the computational cost, the energy is typically calculated for a few selected average baryon number densities, and the results are interpolated to obtain the pressure numerically. However, this may introduce systematic errors in the calculations of the global structure of a neutron star and its dynamical evolution. In this paper, we show how the full equation of state can be consistently calculated within the same framework by deriving exact formulas for the chemical potentials and for the pressure that can be easily implemented in existing computer codes. These formulas are applicable to both catalyzed and accreted crusts. We discuss in each case the suitable conditions to impose to determine the composition. Numerical examples are also presented and discussed. Results from refined calculations of the BSk24 equation of state for the inner crust of nonaccreted neutron stars and the corresponding adiabatic index are provided.