Bulk viscosity of spin-one color superconducting strange quark matter

The bulk viscosity in spin-one color superconducting strange quark matter is calculated by taking into account the interplay between the nonleptonic and semileptonic week processes. In agreement with previous studies, it is found that the inclusion of the semileptonic processes may result in non-negligible corrections to the bulk viscosity in a narrow window of temperatures. The effect is generally more pronounced for pulsars with longer periods. Compared to the normal phase, however, this effect due to the semileptonic processes is less pronounced in spin-one color superconductors. Assuming that the critical temperature of the phase transition is much larger than 40 keV, the main effect of spin-one color superconductivity in a wide range of temperatures is an overall increase of the bulk viscosity with respect to the normal phase. The corresponding enhancement factor reaches up to about 9 in the polar and $A$ phases, about 25 in the planar phase, and about 29 in the color-spin-locked (CSL) phase. This factor is determined by the suppression of the nonleptonic rate in color superconducting matter and, therefore, may be even larger if all quark quasiparticles happen to be gapped.

Figure 1

Diagrammatic representation of the $\beta$ processes that contribute to the bulk viscosity of dense quark matter.

Figure 2

Temperature dependence of bulk viscosity $\zeta$ and the ratio $\zeta /{\zeta }_{\mathrm{non}}$ for model parameters in Set A and the spin-one color superconducting critical temperature $T_c=2\mathrm{MeV}$. The results for two fixed frequencies of the density oscillations are shown.

Figure 3

The contour plot of the bulk viscosity enhancement factor due to spin-one color superconductivity. The results are for the CSL phase in a model with the parameters in Set A. The results for two frequencies of the density oscillations are shown: ${\tau }^{-1}=10\mathrm{Hz}$ (left panel) and ${\tau }^{-1}=1000\mathrm{Hz}$ (right panel). The ratio ${\zeta }_{\mathrm{CSL}}/{\zeta }_{\mathrm{normal}}$ is larger than 1 in the colored regions and is equal to or less than 1 in the white region. The contours are labeled by the corresponding values of the ratio ${\zeta }_{\mathrm{CSL}}/{\zeta }_{\mathrm{normal}}$.

Figure 4

Temperature dependence of bulk viscosity $\zeta$ and the ratio $\zeta /{\zeta }_{\mathrm{non}}$ for model parameters in Set B and the spin-one color superconducting critical temperature $T_c=2\mathrm{MeV}$. The results for two fixed frequencies of the density oscillations are shown.