Neutron stars and supernova explosions in the framework of Landau's theory

TL;DR

This paper develops a generalized symmetry energy formula within Landau's theory to study neutron stars, revealing how different equations of state influence star properties and potential phase transitions leading to supernovae.

Contribution

It introduces a generalized approach to symmetry energy and extends equations of state within Landau's theory for asymmetric nuclear matter, analyzing their impact on neutron star stability and supernova conditions.

Findings

Different EoS yield varying neutron star mass-radius relations.

Adjusting $K_{sym}$ can cause EoS instability at high densities.

Neutron star instability regions may correspond to phase transitions to quark-gluon plasma.

Abstract

A general formula of the symmetry energy for many-body interaction is proposed and the commonly used two-body interaction symmetry energy is recovered. Within Landau's theory (Lt), we generalize two equations of state (EoS) CCS$\delta$3 and CCS$\delta$5 to asymmetric nuclear matter. We assume that the density and density difference between protons and neutrons divided by their sum are order parameters. We use different EoS to study neutron stars by solving the TOV equations. We demonstrate that different EoS give different mass and radius relation for neutron stars even when they have exactly the same ground state (gs) properties ($E/A$, $\rho_0$, $K$, $S$, $L$ and $K_{sym}$). Furthermore, for one EoS we change $K_{sym}$ and fix all the other gs parameters. We find that for some $K_{sym}$ the EoS becomes unstable at high density even for neutron matter. This suggests that a neutron star (NS) can exist below and above the instability region but in different states: a quark gluon plasma (QGP) at high density and baryonic matter at low density. If the star's central density is in the instability region, then we associate these conditions to the occurrence of Supernovae (SN).