Shear viscosity in superfluid neutron stars

TL;DR

This paper calculates the shear viscosity contributed by phonons in superfluid neutron stars, showing it scales as 1/T^5 and depends on the equation of state, potentially affecting stellar oscillation modes.

Contribution

It introduces a novel calculation of phonon shear viscosity in superfluid neutron stars using variational methods and effective field theory, linking it to the equation of state.

Findings

Shear viscosity scales as 1/T^5.

Viscosity depends on the system's equation of state.

Phonon contribution impacts star oscillation modes.

Abstract

The phonon contribution to the shear viscosity $\eta$ in superfluid neutron stars is calculated by assuming neutron pairing in a $^1S_0$ channel. The shear viscosity is obtained by means of variational methods for the solution of the Boltzmann equation amended by a collision term which takes into account the binary collisions of phonons. Effective field theory techniques are used to extract the phonon scattering rates in terms of the equation of state (EoS) of the system. 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 $\eta$ might have important effects for the different oscillation modes of the star.