Phase diagram of three-flavor quark matter under compact star constraints

The phase diagram of three-flavor quark matter under compact star constraints is investigated within a Nambu--Jona-Lasinio model. Global color and electric charge neutrality is imposed for $\ensuremath{\beta}$-equilibrated superconducting quark matter. The constituent quark masses and the diquark condensates are determined self-consistently in the plane of temperature and quark chemical potential. Both strong and intermediate diquark coupling strengths are considered. We show that in both cases, gapless superconducting phases do not occur at temperatures relevant for compact star evolution, i.e., below $T\ensuremath{\sim}50\text{ }\text{ }\mathrm{MeV}$. The stability and structure of isothermal quark star configurations are evaluated. For intermediate coupling, quark stars are composed of a mixed phase of normal (NQ) and two-flavor superconducting (2SC) quark matter up to a maximum mass of $1.21\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. At higher central densities, a phase transition to the three-flavor color flavor locked (CFL) phase occurs and the configurations become unstable. For the strong diquark coupling we find stable stars in the 2SC phase, with masses up to $1.33\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. A second family of more compact configurations (twins) with a CFL quark matter core and a 2SC shell is also found to be stable. The twins have masses in the range $1.30\dots{}1.33\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. We consider also hot isothermal configurations at temperature $T=40\text{ }\text{ }\mathrm{MeV}$. When the hot maximum mass configuration cools down, due to emission of photons and neutrinos, a mass defect of $0.1\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ occurs and two final state configurations are possible.