Fluctuational mechanism of formation of proton vortices in the “npe” phase of a neutron star

Abstract

The superfluid core (“npe” phase) of a neutron star, consisting of superfluid neutrons, superconducting protons, and normal electrons, is considered. The Gibbs thermodynamic potential of a superconducting proton vortex in a proton superconductor of the second kind, interacting with the normal core of a neutron vortex of radius r ≪ λ parallel to it (λ is the depth of penetration), is calculated. It is shown that under this assumption, the capture by the core of only one vortex turns out to be energetically favored. The force exerted on the proton vortex by the entrainment current, always directed toward the core, is found. The corresponding force for a proton antivortex is directed outward toward the outer boundary of the neutron vortex. It is shown that the fluctuational formation of a vortex-antivortex pair is possible at a large distance from the core under the action of the entrainment current. Under the action of the entrainment current, the antivortex travels outward, while the vortex remains inside the neutron vortex. It is shown that the formation of new proton vortices is possible only in the region in which the entrainment magnetic field strength is H(ρ) > H_cl (H_cl is the first critical field).