Single-flavor CSL phase in compact stars

Abstract

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 spin-1 single flavor (CSL), spin-0 two flavor (2SC) and three flavor (CFL) channels. We find that nucleon dissociation sets in at about the saturation density, n_0, when the down-quark Fermi sea is populated (d-quark dripline) due to the flavor asymmetry induced by beta-equilibrium and charge neutrality. At about 3n_0 u-quarks appear and a two-flavor color superconducting (2SC) phase is formed. The s-quark Fermi sea is populated only at still higher baryon density, when the quark chemical potential is of the order of the dynamically generated strange quark mass. We construct two different hybrid equations of state (EoS) using the Dirac-Brueckner Hartree-Fock (DBHF) approach and the EoS by Shen et al in the nuclear matter sector. The corresponding hybrid star sequences have maximum masses of, respectively, 2.1 and 2.0 M_solar. Two- and three-flavor quark-matter phases exist only in gravitationally unstable hybrid star solutions in the DBHF case, while the Shen-based EoS produce stable configurations with a 2SC phase component in the core of massive stars. Nucleon dissociation due to d-quark drip at the crust-core boundary fulfills basic criteria for a deep crustal heating process which is required to explain superbusts as well as cooling of X-ray transients.