Nonlinear approach to the entrainment matrix of superfluid nucleon mixture at zero temperature

Abstract

The superfluid drag effect, in hydrodynamics of pulsating neutron stars, is conventionally described with the aid of the entrainment matrix relating the mass currents with the velocities of superfluid flows in the system. Equations for the entrainment matrix of a superfluid mixture of neutrons and protons are derived with allowance for the strong dependence of the energy gaps on the velocities of superfluid flows. The calculations are carried out in the frame of the Fermi-liquid theory. The equations obtained are highly nonlinear. Numerical solutions to the equations for some typical cases demonstrate that the components of the entrainment matrix possess a highly nonlinear dependence on the velocities of the two superflows simultaneously. This effect, previously ignored, can greatly influence the dynamics of neutron stars.

arXiv comment14 pages, 5 figures, Accepted for publication in MNRAS

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• ${}^1$S${}_0$ pairing gaps, chemical potential and entrainment matrix in superfluid neutron-star cores for the Brussels-Montreal functionals
• The entrainment matrix of a superfluid nucleon mixture at finite temperatures
• Gapless superfluidity in neutron stars: Thermal properties
• Gapless superfluidity in neutron stars: Normal-fluid fraction
• Detecting Entrainment in Fermi-Bose Mixtures
• Diffusion in superfluid Fermi mixtures: General formalism
• Instability windows of relativistic r-modes in stably stratified neutron stars with hyperonic cores