Entrainment effects in neutron-proton mixtures within the nuclear-energy density functional theory. II. Finite temperatures and arbitrary currents

TL;DR

This paper develops a comprehensive theoretical framework to describe entrainment effects in hot neutron-proton superfluid mixtures at finite temperatures, with applications to neutron star cores, extending previous zero-temperature models.

Contribution

It provides analytical expressions for the entrainment matrix at finite temperatures and arbitrary currents, applicable to various energy-density functionals and neutron star modeling.

Findings

Derived formulas valid for all temperatures and currents.

Compared results with Landau's theory, showing consistency.

Laid groundwork for microscopic neutron star superfluid models.

Abstract

Mutual entrainment effects in hot neutron-proton superfluid mixtures are studied in the framework of the self-consistent nuclear energy-density functional theory. The local mass currents in homogeneous or inhomogeneous nuclear systems, which we derive from the time-dependent Hartree-Fock-Bogoliubov equations at finite temperatures, are shown to have the same formal expression as the ones we found earlier in the absence of pairing at zero temperature. Analytical expressions for the entrainment matrix are obtained for application to superfluid neutron-star cores. Results are compared to those obtained earlier using Landau's theory. Our formulas, valid for arbitrary temperatures and currents, are applicable to various types of functionals including the Brussels-Montreal series for which unified equations of state have been already calculated, thus laying the ground for a fully consistent microscopic description of superfluid neutron stars.