Cooling of Neutron Stars with Color Superconducting Quark Cores

We show that within a recently developed nonlocal, chiral quark model the critical densities for a phase transition to color superconducting quark matter under neutron star conditions can be low enough that these phases occur in compact star configurations with masses below 1.4 M_⊙. We study the cooling of these objects in isolation for different values of the gravitational mass and thus different composition and structure of the interior. Our equation of state allows for a 2SC phase with a large quark gap Δ ~ 100 MeV for u and d quarks of two colors, a normal quark matter phase and their coexistence in a mixed phase within the hybrid star interior. We argue that, if the phases with unpaired quarks were allowed, the corresponding hybrid stars would cool too fast to describe the neutron star cooling data existing by today. We incorporate other attractive channels permitting a weak pairing of the residual quarks which remained unpaired in the 2SC phase and demonstrate that the model does not contradict the cooling data if the weak pairing gaps are of the order of 0.1 MeV.