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Quark deconfinement in protoneutron star cores: effect of color superconductivity within the MIT bag model

We analyze the effect of color superconductivity in the transition from hot hadron matter to quark matter in the presence of a gas of trapped electron neutrinos. To describe strongly interacting matter we adopt a two-phase picture in which the hadronic phase is described by means of a non-linear Walecka model and just deconfined matter through the MIT bag model including color superconductivity. We impose flavor conservation during the transition in such a way that just deconfined quark matter is transitorily out of equilibrium with respect to weak interactions. Our results show that color superconductivity facilitates the transition for temperatures below $T_c$. This effect may be strong if the superconducting gap is large enough. As in previous work we find that trapped neutrinos increase the critical density for deconfinement; however, if the just deconfined phase is color superconducting this effect is weaker than if deconfined matter is unpaired. We also explore the effect of different parametrizations of the hadronic equation of state (GM1 and NL3) and the effect of hyperons in the hadronic phase. We compare our results with those previously obtained employing the Nambu-Jona-Lasinio model in the description of just deconfined matter and show that they are in excellent agreement if the bag constant $B$ is properly chosen.