Two-component superfluid hydrodynamics of neutron star cores

Abstract

We consider the hydrodynamics of the outer core of a neutron star under conditions when both neutrons and protons are superfluid. Starting from the equation of motion for the phases of the wave functions of the condensates of neutron pairs and proton pairs we derive the generalization of the Euler equation for a onecomponent fluid. These equations are supplemented by the conditions for conservation of neutron number and proton number. Of particular interest is the effect of entrainment, the fact that the current of one nucleon species depends on the momenta per nucleon of both condensates. We find that the nonlinear terms in the Euler-like equation contain contributions that have not always been taken into account in previous applications of superfluid hydrodynamics. We apply the formalism to determine the frequency of oscillations about a state with stationary condensates and states with a spatially uniform counterflow of neutrons and protons. The velocities of the coupled sound-like modes of neutrons and protons are calculated from properties of uniform neutron star matter evaluated on the basis of chiral effective field theory. We also derive the condition for the two-stream instability to occur.

Final version. 9 pages, 5 figures

References in corpus (6)

• Models of Pulsar Glitches
• Entrainment parameters in cold superfluid neutron star core
• The entrainment matrix of a superfluid neutron-proton mixture at a finite temperature
• Temperature-dependent pulsations of superfluid neutron stars
• Tkachenko modes in rotating neutron stars: the effect of compressibility and implications for pulsar timing noise
• Nucleus--nucleus interactions in the inner crust of neutron stars

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• Dipole dynamics of an interacting bosonic mixture
• Dispersion and decay of collective modes in neutron star cores
• Application of superconducting-superfluid magnetohydrodynamics to nuclear "pasta" in neutron stars
• Superfluid liquid crystals: pasta phases in neutron star crusts
• Magnetoroton in a two-dimensional Bose-Bose mixture
• Surface energy of magnetized superconducting matter in the neutron star cores
• Roton instabilities in the superfluid outer core of neutron stars