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

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 Hubbard 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 than the corresponding MF estimates. Physical implications of our findings for a neutron star dynamics are discussed.

Automated summary

The Dynamical Mean Field Theory (DMFT) is applied to study neutron matter, with a focus on the presence or absence of proton fraction. The results show that while the influence of correlations on pure neutron matter properties is moderate, it becomes significant when proton admixture is taken into account. Comparison with standard mean field (MF) approach reveals differences in predictions, especially in terms of proton fraction, energy density, and pressure.