Two-component superfluid hydrodynamics of neutron star cores

TL;DR

This paper develops a comprehensive superfluid hydrodynamics framework for neutron star cores, incorporating entrainment effects, and analyzes oscillation modes and instabilities in neutron-proton superfluid mixtures.

Contribution

It generalizes superfluid hydrodynamics equations to include entrainment and applies them to neutron star core oscillations and instabilities.

Findings

Derived generalized Euler equations for superfluid neutron-proton mixtures.

Calculated velocities of coupled sound modes in neutron star matter.

Established conditions for two-stream instability in superfluid 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.