Proton fraction in neutron star matter: Dynamical mean-field approach

TL;DR

This paper applies dynamical mean-field theory to neutron star matter, revealing significant effects of local correlations on proton fraction, energy density, and pressure, which differ notably from standard mean field predictions.

Contribution

It introduces a DMFT approach to neutron star matter, providing new insights into the impact of correlations on the equation of state and proton fraction.

Findings

Proton fraction is several times higher with DMFT than with mean field.

Energy density and pressure are 30-40% lower in DMFT compared to mean field.

Correlations have a moderate effect on pure neutron matter but are significant when protons are included.

Abstract

Dynamical mean field theory (DMFT) is used to study neutron matter, both with and without admixture of the proton fraction. The system is approximated by the lattice Habbard model. The corresponding equation of state as a function of temperature/density/asymmetry is investigated. The results are compared with the standard mean field (MF) approach where the effect of local correlations is neglected. Whereas the influence of the correlations on the properties of a pure neutron matter is found to be moderate, it becomes strong when the proton admixture is taken into account. In particular, we calculate the proton fraction, energy density and pressure in outer core of neutron stars, taking into account the beta equilibrium condition. The DMFT predicts that the proton fraction is several times the MF based calculations, whereas the DMFT results for energy density and pressure are 30-40\% lower then the corresponding MF estimates. Physical implications of our findings for a neutron star dynamics are discussed.