Cooling of neutron stars with color superconducting quark cores

We show that within a recently developed nonlocal, chiral quark model the critical density for a phase transition to color superconducting quark matter under neutron star conditions can be low enough for these phases to occur in compact star configurations with masses below 1.3 M. We study the cooling of these objects in isolation for different values of the gravitational mass. Our equation of state (EoS) allows for two-flavor color superconductivity (2SC) quark matter with a large quark gap (similar to 100 MeV) for u and d quarks of two colors that coexists with normal quark matter within a mixed phase in the hybrid star interior. We argue that, if the phases with unpaired quarks were allowed, the corresponding hybrid stars would cool too fast. If they occurred for M < 1.3 M, as follows from our EoS, one could not appropriately describe the neutron star cooling data existing today. We discuss a "2SC+X" phase as a possibility for having all quarks paired in two-flavor quark matter under neutron star constraints, where the X gap is of the order of 10 keV-1 MeV. Density-independent gaps do not allow us to fit the cooling data. Only the presence of an X gap that decreases with increasing density would allow us to appropriately fit the data in a similar compact star mass interval to that following from a purely hadronic model. This scenario is suggested as an alternative explanation of the cooling data in the framework of a hybrid star model.