r-modes in low temperature colour-flavour-locked superconducting quark star

Abstract

We present the first multi-fluid analysis of a dense neutron star core with a deconfined colour-flavour-locked superconducting quark component. Accounting only for the condensate and (finite temperature) phonons, we make progress by taking over results for superfluid $^4$He. The resultant two-fluid model accounts for a number of additional viscosity coefficients (compared to the Navier-Stokes equations) and we show how they enter the dissipation analysis for an oscillating star. We provide simple estimates for the gravitational-wave driven r-mode instability, demonstrating that the various phonon processes that we consider are not effective damping agents. Even though the results are likely of little direct astrophysical importance (since we consider an overly simplistic stellar model) our analysis represents significant technical progress, laying the foundation for more detailed numerical studies and preparing the ground for the inclusion of additional aspects (in particular associated with kaons) of the problem.