Neutrino emissivities and bulk viscosity in neutral two-flavor quark matter

We study thermodynamic and transport properties for the isotropic color-spin-locking (iso-CSL) phase of two-flavor superconducting quark matter under compact star constraints within a Nambu-Jona-Lasinio-type chiral quark model. Chiral symmetry breaking and the phase transition to superconducting quark matter leads to a density dependent change of quark masses, chemical potentials, and diquark gap. A self-consistent treatment of these physical quantities influences the microscopic calculations of transport properties. We present results for the iso-CSL direct URCA emissivities and bulk viscosities, which fulfil the constraints on quark matter derived from cooling and rotational evolution of compact stars. We compare our results with the phenomenologically successful, but yet heuristic 2 SC +X phase. We show that the microscopically founded iso-CSL phase can replace the purely phenomenological 2 SC +X phase in modern simulations of the cooling evolution for compact stars with color-superconducting quark matter interior.