1-2-3-flavor color superconductivity in compact stars

We suggest a scenario where the three light quark flavors are sequentially deconfined under increasing pressure in cold asymmetric nuclear matter as, e.g., in neutron stars. The basis for our analysis is a chiral quark matter model of Nambu– Jona-Lasinio (NJL) type with diquark pairing in the single flavor color-spin-locking (CSL), two-flavor (2SC) and three-flavor color-flavor locking (CFL) channels, and a Dirac-Brueckner Hartree-Fock (DBHF) approach in the nuclear matter sector. We find that nucleon dissociation sets in at about the saturation density, n0, when the downquark Fermi sea is populated (d-quark dripline) due to the flavor asymmetry imposed by β-equilibrium and charge neutrality. At about 3n0 u-quarks appear forming a twoflavor color superconducting (2SC) phase, while the s-quark Fermi sea is populated only at still higher baryon density. The hybrid star sequence has a maximum mass of 2.1 M⊙. Twoand three-flavor quark matter phases are found only in gravitationally unstable hybrid star solutions. Introduction Recent results from observations of compact star properties provide constraints on the nuclear equation of state (EoS) [1]. In particular, the high masses M ∼ 2.0 M⊙ of compact stars in low-mass X-ray binaries, e.g., 4U 1636-536 [2] and the indicated large radius R > 12 km of the isolated neutron star RX J1856.5-3754 [3] point to a stiff EoS at high densities. Other limits on the stiffness of the EoS comes from heavy-ion collision data for kaon production and elliptic flow (see [1] for references). A key question is whether the phase transition to quark matter can occur inside compact stars [4] and if it is accompanied by observable signatures. Based on a DBHF approach in the nuclear matter sector and a chiral quark matter model with a vector meanfield interaction a recently developed class of hybrid EoS [5, 6] obtained stable hybrid stars with masses from 1.2 M⊙ up to 2.1 M⊙ in accordance with modern mass-radius constraints. Under the β-equilibrium condition in compact stars the chemical potentials of quarks and electrons are related by μd = μs and μd = μu+μe. The mass difference between the strange and the light quark flavors ms > mu, md has two important consequences: (1) the down and strange quark densities are different so charge neutrality requires a finite electron density and, consequently, (2) μd > μu. When increasing the baryochemical potential, the d-quark chemical potential is the first to reach a critical value where the the partial density of free d-quarks becomes 1-2-3-flavor color superconductivity in compact stars 2 finite in a first order phase transition. Due to the finite value of μe the u-quark chemical potential is below the critical value and the s-quark density is zero due to the high squark mass. A single-flavor d-quark phase therefore forms. We discuss this phase here under the natural assumption that the neutralizing background is provided by nuclear matter, for details see [7]. 100