Shear viscosity in superfluid neutron stars

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.