Correlation of the neutron star crust-core properties with the slope of the symmetry energy and the lead skin thickness

TL;DR

This study explores how the properties of neutron star crusts relate to the symmetry energy slope and lead skin thickness, revealing correlations dependent on relativistic model parametrizations and comparing different computational methods.

Contribution

It demonstrates the impact of relativistic mean field parametrizations on crust-core transition properties and establishes correlations with symmetry energy slope and lead skin thickness.

Findings

Linear correlation between transition density and symmetry energy slope when using the $ ho$-meson.

Different behaviors of transition properties depending on $\sigma$ or $\omega$ meson modifications.

Similar transition density predictions by RRPA and Vlasov methods.

Abstract

The correlations of the crust-core transition density and pressure in neutron stars with the slope of the symmetry energy and the neutron skin thickness are investigated, using different families of relativistic mean field parametrizations with constant couplings and non-linear terms mixing the $\sigma$, $\omega$ and $\rho$-meson fields. It is shown that the modification of the density dependence of the symmetry energy, involving the $\sigma$ or the $\omega$ meson, gives rise to different behaviors: the effect of the $\omega$-meson may also be reproduced within non-relativistic phenomenological models, while the effect of the $\sigma$-meson is essentially relativistic. Depending on the parametrization with $\sigma-\rho$ or $\omega-\rho$ mixing terms, different values of the slope of the symmetry energy at saturation must be considered in order to obtain a neutron matter equation of state compatible with results from chiral effective field theory. This difference leads to different pressures at the crust-core transition density. A linear correlation between the transition density and the symmetry energy slope or the neutron skin thickness of the $^{208}$Pb nucleus is obtained, only when the $\omega$-meson is used to describe the density dependence of the symmetry energy. A comparison is made between the crust-core transition properties of neutron stars obtained by three different methods, the Relativistic Random Phase Approximation (RRPA), the Vlasov equation and Thermodynamical method. It is shown that the RRPA and the Vlasov methods predict similar transition densities for $pne$ $\beta$-equilibrium stellar matter.