A minimal model for finite temperature superfluid dynamics

TL;DR

This paper develops a minimal hydrodynamical model for finite temperature superfluids, focusing on neutron star core dynamics, highlighting entrainment effects, and analyzing sound wave propagation across superfluid and normal phases.

Contribution

It introduces a simplified yet comprehensive model for finite temperature superfluids, emphasizing entrainment and sound modes relevant to neutron star physics.

Findings

Presence of second sound below critical temperature

Absence of second sound above critical temperature

Estimates for entrainment coefficients

Abstract

Building on a recently improved understanding of the problem of heat flow in general relativity, we develop a hydrodynamical model for coupled finite temperature superfluids. The formalism is designed with the dynamics of the outer core of a mature neutron star (where superfluid neutrons are coupled to a conglomerate of protons and electrons) in mind, but the main ingredients are relevant for a range of analogous problems. The entrainment between material fluid components (the condensates) and the entropy (the thermal excitations) plays a central role in the development. We compare and contrast the new model to previous results in the literature, and provide estimates for the relevant entrainment coefficients that should prove useful in future applications. Finally, we consider the sound-wave propagation in the system in two simple limits, demonstrating the presence of second sound if the temperature is sub-critical, but absence of this phenomenon above the critical temperature for superfluidity.