$^1$S$_0$ pairing gaps, chemical potential and entrainment matrix in superfluid neutron-star cores for the Brussels-Montreal functionals

TL;DR

This paper provides a comprehensive, self-consistent calculation of temperature and velocity-dependent superfluid pairing gaps, chemical potentials, and entrainment matrix in neutron star cores using the Brussels-Montreal functional, aiding neutron star modeling.

Contribution

It introduces fully self-consistent numerical solutions for superfluid properties in neutron star cores across all relevant temperatures and velocities, using the time-dependent Hartree-Fock-Bogoliubov framework with the BSk24 functional.

Findings

Calculated superfluid gaps, chemical potentials, and entrainment matrix for neutron star cores.

Assessed accuracy of various approximations in superfluid modeling.

Clarified physical meaning of velocities and momentum densities in superfluid theory.

Abstract

Temperature and velocity-dependent $^1$S$_0$ pairing gaps, chemical potentials and entrainment matrix in dense homogeneous neutron-proton superfluid mixtures constituting the outer core of neutron stars, are determined fully self-consistently by solving numerically the time-dependent Hartree-Fock-Bogoliubov equations over the whole range of temperatures and flow velocities for which superfluidity can exist. Calculations have been made for $npe\mu$ in beta-equilibrium using the Brussels-Montreal functional BSk24. The accuracy of various approximations is assessed and the physical meaning of the different velocities and momentum densities appearing in the theory is clarified. Together with the unified equation of state published earlier, the present results provide consistent microscopic inputs for modeling superfluid neutron-star cores.