Cooling of hybrid neutron stars and hypothetical self-bound objects with superconducting quark cores

We study the consequences of superconducting quark cores (with color-flavor-locked phase as representative example) for the evolution of temperature profiles and cooling curves in quark-hadron hybrid stars and in hypothetical self-bound objects having no hadron shell (quark core neutron stars). The quark gaps are varied from 0 to Delta (q) = 50 MeV. For hybrid stars we find time scales of 1 divided by 5, 5 divided by 10 and 50 divided by 100 years for the formation of a quasistationary temperature distribution in the cases Delta (q) = 0, 0.1 MeV and greater than or similar to 1 MeV, respectively. These time scales are governed by the heat transport within quark cores for large diquark gaps (Delta greater than or similar to 1 MeV) and within the hadron shell for small diquark gaps (Delta less than or similar to 0.1 MeV). For quark core neutron stars we find a time scale similar or equal to 300 years for the formation of a quasistationary temperature distribution in the case Delta greater than or similar to 10 MeV and a very short one for Delta less than or similar to 1 MeV. If hot young compact objects will be observed they can be interpreted as manifestation of large gap color superconductivity. Depending on the size of the pairing gaps, the compact star takes different paths in the log(T-s) vs. log(t) diagram where T-s is the surface temperature. Compared to the corresponding hadronic model which well fits existing data the model for the hybrid neutron star (with a large diquark gap) shows too fast cooling. The same conclusion can be drawn for the corresponding self-bound objects.