document: In the NJL model studied here, we find no stable stars with either CFL or normal quark matter cores. This is the opposite of the prediction of Ref. [15] where it was argued that there is no 2SC phase in compact stars. Let us be more precise: performing a Taylor expansion in the strange quark mass, the authors of Ref. [15] found that in beta-equilibrated electrically and color neutral quark matter the 2SC phase is always less favored than the CFL phase or normal quark matter. From this observation they concluded that the 2SC phase is absent in compact stars. In contrast to this result, it was shown in Ref. [16] in the framework of the NJL model that neutral 2SC matter could be the most favored quark phase in a certain regime. However, the authors argued that this interval might disappear if the hadronic phase is included more properly. This is indeed what we found for parameter set RKH, while for parameter set HK the 2SC phase survives only in a tiny window. Nevertheless, if Nature chooses to be similar to this equation of state, it will be this tiny window which gives rise to hybrid stars, whereas the CFL phase would be never present in compact stars.
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