Nucleation rate of color superconducting droplets in protoneutron stars

Abstract: We analyse the nucleation of quark matter droplets under protoneutron star conditions. We adopt a two-phase framework in which the hadronic phase is described through a non-linear Walecka model and the just deconfined matter by the MIT bag model including color superconductivity. Surface tension and curvature energy are calculated self-consistently within the MRE formalism. We impose flavour conservation during the transition, which means that the just deconfined quark droplet is transiently out of equilibrium with respect to weak interactions. Our results show that trapped neutrinos slightly increase the critical density for deconfinement and that color superconductivity significantly decreases such density at low temperatures. We also show that the nucleation rate is negligible for droplets larger than 100-200 fm and is huge for smaller droplets provided that the temperature is low enough. We compare our results with previous calculations using the Nambu-Jona-Lasinio model with color superconductivity and the MIT bag model without color superconductivity. We conclude that the deconfinement transition should be triggered instantaneously when a density slightly larger than the bulk transition density is reached at some layer of a protoneutron star. Since color superconductivity lowers the transition density at low temperatures, the transition is likely to occur after significant cooling in a massive enough protoneutron star.