Stability of CFL cores in Hybrid Stars

We study the equation state of strongly interacting quark matter within a NJL-like model in which the chiral condensates and the color superconducting gaps are computed self-consistently as a function of the baryon density. A vector interaction term is added to the Lagrangian in order to render the quark matter equation of state stiffer. For the low density hadronic phase we use a relativistic mean field model. The phase transition to quark matter is computed by a Maxwell construction. We show that stable CFL cores in hybrid stars are possible if the superconducting gap is sufficiently large. Moreover we find stable stellar configurations in which two phase transitions occur, a first transition from hadronic matter to 2SC quark matter and a second transition from 2SC quark matter to CFL quark matter.