Cooling Evolution of Hybrid Stars
  The cooling of compact isolated objects for different values of the gravitational mass has been simulated for two alternative assumptions. One is that the interior of the star is purely hadronic and second that the star can have a rather large quark core. It has been shown that within a 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_sun. For a realistic choice of parameters the equation of state (EoS) allows for 2SC quark matter with a large quark gap ~ 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 in the hadronic phase the neutron pairing gap in 3P_2 channel is larger than few keV and the phases with unpaired quarks are allowed, the corresponding hybrid stars would cool too fast.   Even in the case of the essentially suppressed 3P_2 neutron gap if free quarks occur for M < 1.3 M_sun, as it follows from our EoS, one could not appropriately describe the neutron star cooling data existing by today.   It is suggested to discuss a "2SC+X" phase, as a possibility to have 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 to fit the cooling data. Only the presence of an X-gap that decreases with increase of the density could allow to appropriately fit the data in a similar compact star mass interval to that following from a purely hadronic model. 
H. Grigorian (U. Rostock, U. Yerevan)