Absence of two-flavor color superconductivity in compact stars

The simplest pattern of color superconductivity involves BCS pairing between up and down quarks. We argue that this “2SC” phase, and variants of it, will not arise within a compact star. A macroscopic volume of quark matter must be electrically neutral and must be a color singlet. Satisfying these requirements imposes a significant free energy cost on the 2SC phase, but not on color-flavor locked (CFL) quark matter, in which up, down and strange quarks all pair. As a function of increasing density, therefore, one may see a single phase transition from hadronic matter directly to CFL quark matter. Alternatively, there may be an intervening phase in which the different flavors self-pair, or pair with each other in a non-BCS pattern, such as in a crystalline color superconductor.