text: The only known place in the universe where the baryon density might possibly be high enough to produce quark matter, and the temperature is low enough for color superconductivity to occur, is the core of a compact star (often called a "neutron star", a term which prejudges the question of its actual makeup). There are many open questions here:
  * We do not know the critical density at which there would be a phase transition from nuclear matter to some form of quark matter, so we do not know whether compact stars have quark matter cores or not.
  * On the other extreme, it is conceivable that nuclear matter in bulk is actually metastable, and decays into quark matter (the "stable strange matter hypothesis"). In this case, compact stars would consist completely of quark matter all the way to their surface.
  * Assuming that compact stars do contain quark matter, we do not know whether that quark matter is in a color superconducting phase or not. At infinite density one expects color superconductivity, and the attractive nature of the dominant strong quark-quark interaction leads one to expect that it will survive down to lower densities, but there may be a transition to some strongly coupled phase (e.g. a Bose–Einstein condensate of spatially bound di- or hexaquarks).