Shear viscosity due to phonons in superfluid neutron stars

TL;DR

This paper calculates how phonons contribute to shear viscosity in superfluid neutron stars, showing a temperature dependence and highlighting its importance in star oscillation dynamics.

Contribution

It introduces a general framework using effective field theory to compute phonon shear viscosity in superfluid neutron stars, applicable to other superfluid systems.

Findings

Shear viscosity scales as 1/T^5.

Phonon contribution significantly affects star oscillation modes.

Method can be adapted to other superfluid systems.

Abstract

We compute the contribution of phonons to the shear viscosity $\eta$ in superfluid neutron stars, assuming neutron pairing in a $^1S_0$ channel. We use a Boltzmann equation amended by a collision term that takes into account the binary collisions of phonons. We use effective field theory techniques to extract the phonon scattering rates, written as a function of the equation of state (EoS) of the system. Our formulation is rather general, and can be used to extract the shear viscosity due to binary collisions of phonons for other superfluids, such as the cold Fermi gas in the unitarity limit. We find that $\eta \propto 1/T^5$, the proportionality factor depending on the EoS of the system. Our results indicate that the phonon contribution to $\eta$ cannot be ignored and might have relevant effects in the dynamics of the different oscillation modes of the star.