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Some properties of magnetized two flavor color superconducting (2SC) colddense quark matter under compact star conditions (COSC) are investigated withina $SU(2)_f$ Nambu Jona-Lasinio type model. We study the phase diagram forseveral model parametrizations. The features of each phase are analyzed throughthe behavior of the chiral and superconducting condensates for increasingchemical potential or magnetic field. We show how the phases are modified inthe presence of $\beta$-equilibrium as well as color and electric chargeneutrality conditions.

Phase structure of magnetized 2SC quark matter under compact star conditions