Bulk viscosity coefficients due to phonons and kaons in superfluid color-flavor locked quark matter

We evaluate the three bulk viscosity coefficients $\zeta_1, \zeta_2$ and $\zeta_3$ in the color-flavor locked (CFL) superfluid phase due to phonons and kaons, which are the lightest modes in that system. We first show that the computation is rather analogous to the computation of the same coefficients in superfluid $^4$He, as due to phonons and rotons. For astrophysical applications, we also find the value of the viscosities when there is a periodic disturbance, and the viscosities also depend on the frequency of the disturbance. In a temperature regime that might be of astrophysical relevance, we find that the contributions of both the phonons and kaons should be considered, and that $\zeta_2$ is much less that the same coefficient in unpaired quark matter