Abstract
Temperature and velocity-dependent 1S0 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 npeμ 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.
Highlights
Different superfluid and superconducting phases are predicted to exist in neutron stars
The outer core is expected to be made of a neutron–proton superfluid mixture in beta-equilibrium with a normal gas of leptons
The neutron and proton superfluids in the core do not flow freely. They are mutually coupled by entrainment effects of the same kind as the ones discussed by Andreev and Bashkin [6] in the context of superfluid 4 He-3 He mixtures: the mass currents ρq are expressible as linear combinations of the velocity v N of the normal fluid and of the so-called “superfluid velocities” Vq as Licensee MDPI, Basel, Switzerland
Summary
Different superfluid and superconducting phases are predicted to exist in neutron stars (see, e.g., [1] for a review). We have derived the entrainment matrix self-consistently for arbitrary superfluid velocities and temperatures within the nuclear-energy-density functional theory by solving exactly the time-dependent Hartree–Fock–Bogoliubov (TDHFB) equations [16,17]. We have calculated various properties of homogeneous neutron–proton superfluid mixtures in the outer core of neutron stars by solving numerically the selfconsistent TDHFB equations using the Brussels–Montreal functional BSk24 [18] for which unified equations of state are already available [19,20,21,22] as well as gravitoelectric and gravitomagnetic tidal Love numbers up to = 5 [23,24]. After briefly recapitulating the general principles of the TDHFB theory in Section 2.1 and the functionals, the exact solution in homogeneous nuclear matter is given, where explicit expressions for various quantities entering the calculations of superfluid properties are derived.
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