Shear Viscosity in a CFL Quark Star

We compute the shear viscosity in the color-flavor locked (CFL) phase of dense quark matter at low temperature T . Then the contributions of mesons, quarks and gluons to the transport coefficients are Boltzmann suppressed. CFL quark matter displays superfluid properties, and transport phenomena in such cold regime are dominated by phonon-phonon scattering. We study phonons within thermal field theory and compute the mean free path associated to their most relevant collision processes. While the mean free path relevant for shear viscosity usually concerns large-angle collisions, small-angle processes turn out to be more efficient for transport phenomena in the CFL matter. We find the same T -dependence for the phonon damping rate and mean free path as for that of superfluid He4. Our results are relevant for the study of rotational properties of compact stars, and correct wrong estimates existing in the literature.