Neutron stars and supernova explosions in the framework of Landau's theory
Abstract
In this paper, 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) CCSδ3 and CCSδ5 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, ρ0, K, S, L and Ksym). Furthermore, for one EoS we change Ksym and fix all the other gs parameters. We find that for some Ksym 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).
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