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 evolution of temperature profiles and the cooling curves in quark-hadron hybrid stars and in hypothetical self-bounded objects having no a 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 $1\div5$, $5\div10$ and $50\div100$ years for the formation of a quasistationary temperature distribution in the cases $\Delta_q =0$, 0.1 MeV and $\gsim$ 1 MeV, respectively. These time scales are governed by the heat transport within quark cores for large diquark gaps ($\Delta \gsim$ 1 MeV) and within the hadron shell for small diquark gaps ($\Delta \lsim 0.1$ MeV). For quark core neutron stars we find a time scale $\simeq 300$ years for the formation of a quasistationary temperature distribution in the case $\Delta \gsim$ 10 MeV and a very short one for $\Delta \lsim$ 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 ${lg}T_s $ vs. ${lg} t$ 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.