Nuclear fourth-order symmetry energy and its effects on neutron star properties in the relativistic Hartree-Fock theory

TL;DR

This study investigates the nuclear fourth-order symmetry energy using relativistic mean-field and Hartree-Fock theories, revealing its impact on neutron star properties and highlighting the importance of Fock terms in the equation of state.

Contribution

It provides a detailed analysis of the fourth-order symmetry energy within covariant density functional theory and its effects on neutron star characteristics, emphasizing the role of Fock terms.

Findings

Fock terms suppress fourth-order symmetry energy at high densities.

RHF predicts smaller transition densities and proton fractions than RMF.

An anti-correlation between transition density and symmetry energy slope L.

Abstract

Adopting the density dependent relativistic mean-field (RMF) and relativistic Hartree-Fock (RHF) approaches, the properties of the nuclear fourth-order symmetry energy $S_4$ are studied within the covariant density functional (CDF) theory. It is found that the fourth-order symmetry energies are suppressed in RHF at both saturation and supranuclear densities, where the extra contribution from the Fock terms is demonstrated, specifically via the isoscalar meson-nucleon coupling channels. The reservation of $S_4$ and higher-order symmetry energies in the nuclear equation of state then affects essentially the prediction of neutron star properties, which is illustrated in the quantities such as the proton fraction, the core-crust transition density as well as the fraction of crustal moment of inertia. Since the Fock terms enhance the density dependence of the thermodynamical potential, the RHF calculations predict systematically smaller values of density, proton fraction and pressure at the core-crust transition boundary of neutron stars than density dependent RMF ones. In addition, a linear anti-correlation between the core-crust transition density $\rho_t$ and the density slope of symmetry energy $L$ is found which is then utilized to constrain the core-crust transition density as $\rho_t\thicksim[0.069, 0.098]~\rm{fm}^{-3}$ with the recent empirical information on $L$. The study clarifies the important role of the fourth-order symmetry energy in determining the properties of nuclear matter at extreme isospin or density conditions.