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Large uncertainties in the determinations of the equation of state of densestellar matter allow the intriguing possibility that the bulk quark matter inbeta equilibrium might be the true ground state of the matter at zero pressure.And quarks will form Cooper pairs very readily since the dominant interactionbetween quarks is attractive in some channels. As a result, quark matter willgenerically exhibit color superconductivity, with the favored pairing patternat intermediately high densities being two-flavor pairing. In the light ofseveral possible candidates for such self-bound quark stars, including the verylow-mass central compact object in supernova remnant HESS J1731-347 reportedrecently, we carry out one field-theoretic model, the Nambu-Jona-Lasinio model,of investigation on the stability of beta-stable two-flavor colorsuperconducting (2SC) phase of quark matter, nevertheless find nophysically-allowed parameter space for the existence of 2SC quark stars.

Two-flavor color superconducting quark stars may not exist