Deconfinement and color superconductivity in cold neutron stars

We study the deconfinement transition of hadronic matter into quark matter in neutron star conditions in the light of color superconductivity. Deconfinement is considered to be a first order phase transition that conserves color and flavor. It gives a short-lived {($\tau \sim \tau_{weak}$)} transitory colorless-quark-phase that is {\it not} in $\beta$-equilibrium. We deduce the equations governing deconfinement when quark pairing is allowed and find the regions of the parameter space (pairing gap $\Delta$ versus bag constant $B$) where deconfinement is possible inside cold neutron stars. We show that for a wide region of ($B,\Delta$) a pairing pattern is reachable within a strong interaction timescale, and the resulting ``2SC-like'' phase is preferred energetically to the unpaired phase. We also show that although $\beta$-stable hybrid star configurations are known to be possible for a wide region of the ($B,\Delta$)-space, many of these configurations could not form in practice because deconfinement is forbidden, i.e. the here studied non-$\beta$-stable \emph{intermediate} state cannot be reached.