Shear viscosity due to phonons in superfluid neutron stars

We compute the contribution of phonons to the shear viscosity eta in superfluid neutron stars, assuming neutron pairing in a S-1(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 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 alpha 1/T-5, the proportionality factor depending on the equation of state 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.