Bulk viscosity in a cold CFL superfluid

We compute one of the bulk viscosity coefficients of cold CFL quark matter in the temperature regime where the contribution of mesons, quarks and gluons to transport phenomena is Boltzmann suppressed. In that regime dissipation occurs due to collisions of superfluid phonons, the Goldstone modes associated to the spontaneous breaking of baryon symmetry. We first review the hydrodynamics of relativistic superfluids, and remind that there are at least three bulk viscosity coefficients in these systems. We then compute the bulk viscosity coefficient associated to the normal fluid component of the superfluid. In our analysis we use Son's effective field theory for the superfluid phonon, amended to include scale breaking effects proportional to the square of the strange quark mass m_s. We compute the bulk viscosity at leading order in the scale breaking parameter, and find that it is dominated by collinear splitting and joining processes. The resulting transport coefficient is zeta=0.011 m_s^4/T, growing at low temperature T until the phonon fluid description stops making sense. Our results are relevant to study the rotational properties of a compact star formed by CFL quark matter.Comment: 19 pages, 2 figures; one reference added, version to be published in JCA

Bulk viscosity in 2SC quark matter

The bulk viscosity of three-flavor color-superconducting quark matter originating from the nonleptonic process u+s u+d is computed. It is assumed that up and down quarks form Cooper pairs while the strange quark remains unpaired (2SC phase). A general derivation of the rate of strangeness production is presented, involving contributions from a multitude of different subprocesses, including subprocesses that involve different numbers of gapped quarks as well as creation and annihilation of particles in the condensate. The rate is then used to compute the bulk viscosity as a function of the temperature, for an external oscillation frequency typical of a compact star r-mode. We find that, for temperatures far below the critical temperature T_c for 2SC pairing, the bulk viscosity of color-superconducting quark matter is suppressed relative to that of unpaired quark matter, but for T >~ 10^(-3) T_c the color-superconducting quark matter has a higher bulk viscosity. This is potentially relevant for the suppression of r-mode instabilities early in the life of a compact star.Comment: 18 pages + appendices (28 pages total), 8 figures; v3: corrected numerical error in the plots; 2SC bulk viscosity is now larger than unpaired bulk viscosity in a wider temperature rang

Critical temperature for kaon condensation in color-flavor locked quark matter

We study the behavior of Goldstone bosons in color-flavor-locked (CFL) quark matter at nonzero temperature. Chiral symmetry breaking in this phase of cold and dense matter gives rise to pseudo-Goldstone bosons, the lightest of these being the charged and neutral kaons K^+ and K^0. At zero temperature, Bose-Einstein condensation of the kaons occurs. Since all fermions are gapped, this kaon condensed CFL phase can, for energies below the fermionic energy gap, be described by an effective theory for the bosonic modes. We use this effective theory to investigate the melting of the condensate: we determine the temperature-dependent kaon masses self-consistently using the two-particle irreducible effective action, and we compute the transition temperature for Bose-Einstein condensation. Our results are important for studies of transport properties of the kaon condensed CFL phase, such as bulk viscosity.Comment: 24 pages, 8 figures, v2: new section about effect of electric neutrality on critical temperature added; references added; version to appear in J.Phys.