Diquark condensates and compact star cooling

The effect of color superconductivity on the cooling of quark stars and neu tron stars with large quark cores is investigated. Various known and new qu ark-neutrino processes are studied. As a result, stars in the color-flavor- locked color superconducting phase cool down extremely fast. Quark stars wi th no crust cool down too rapidly, in disagreement with X-ray data. The coo ling of stars in the N-f = 2 color superconducting phase with a crust is co mpatible with existing X-ray data. In addition, the cooling histories of st ars with hypothetical pion condensate nuclei and a crust do not contradict the data.