How robust is a 2SC quark matter phase under compact star constraints?

We study the phase structure and equation of state for two-flavor quark matter at low temperature under compact star constraints within a nonlocal chiral quark model. We find that the occurence of a two-flavor color superconducting (2SC) phase is sensitive to variations of both the formfactor of the interaction and the ratio \eta between the coupling constants in the diquark and the scalar meson channels. Our study suggests that for standard values of the coupling ratio 0.5<\eta<0.75 either the 2SC phase does not occur (Gaussian formfactor) or it exists only in a mixed phase with normal quark matter (NQ-2SC) with a volume fraction less than 20 - 40 %, occuring at high baryon chemical potentials \mu_B >1200 MeV and most likely not relevant for compact stars. We also present the relevant region of the phase diagram for compact star applications and obtain that no gapless 2SC occurs at low temperatures.