Could strange stars be in the color-flavor-locked phase: Tested by their thermal evolutions

Abstract

The thermal evolution of strange stars in both normal and color-flavor-locked (CFL) phases are investigated together with the evolutions of the stellar rotation and the $r$-mode instability. The heating effects due to the deconfinement transition of the stellar crust and the dissipation of the $r$-modes are considered. As a result, the cooling of the stars in the normal phase is found to be not very different from the standard one. In contrast, for the stars in the CFL phase, a big bump during the first hundred years and a steep decay ($\ensuremath{\sim}7%$ in ten years) at the ages of $\ensuremath{\sim}{10}^{4\ensuremath{-}6}\text{ }\text{ }\mathrm{yrs}$ are predicted in their thermal evolution curves. These unique features provide an effective observational test for determining whether or not the CFL phase is reached in strange stars. This thermal test method is independent of and complementary to the rotational test method, which is a direct consequence of the $r$-mode instability [see J. Madsen, Phys. Rev. Lett. 85, 10 (2000)].