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 p rofiles 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 fin d time scales of 1 divided by 5, 5 divided by 10 and 50 divided by 100 year s for the formation of a quasistationary temperature distribution in the ca ses Delta (q) = 0, 0.1 MeV and greater than or similar to 1 MeV, respective ly. 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 t o 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 f or Delta less than or similar to 1 MeV. If hot young compact objects will b e observed they can be interpreted as manifestation of large gap color supe rconductivity. 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 s urface temperature. Compared to the corresponding hadronic model which well fits existing data the model for the hybrid neutron star (with a large diq uark gap) shows too fast cooling. The same conclusion can be drawn for the corresponding self-bound objects.