Transport coefficients of two-flavor superconducting quark matter

Background: The two-flavor color superconducting (2SC) phase of quark matter is a possible constituent of the core of neutron stars. To assess its impact on the observable behavior of the star one must analyze transport properties, which in 2SC matter are controlled by the scattering of gapless fermionic modes by each other and possibly also by color-magnetic flux tubes.

Purpose: We determine the electrical and thermal conductivities and the shear viscosity of 2SC matter.

Methods: We use a variational formulation of transport theory, treating the strong and electromagnetic interactions via a weak coupling expansion.

Results: We provide the leading order scaling of the transport coefficients with temperature and chemical potential as well as accurate fits to our numerical results. We also find that the scattering of fermions by color-magnetic flux tubes is insignificant for thermal conductivity, but may contribute to the electrical conductivity and shear viscosity in the limit of very low temperature or high magnetic field. We also estimate the transport coefficients in unpaired quark matter.

Conclusions: Our calculation has set the stage for exploration of possible signatures of the presence of 2SC quark matter in neutron stars.

Figure 1

Numerically calculated electrical $\left(\tilde{Q}\right)$ conductivity as a function of temperature, both expressed in units of the quark chemical potential ${\mu }_q$, taking strong interaction coupling ${\alpha }_s=1$. The electrons dominate because the $bu$ relaxation time is shortened by its strong interaction with the $bd$ quarks.

Figure 2

Numerically calculated thermal conductivity in units of quark chemical potential ${\mu }_q$ in the 2SC phase with ${\alpha }_s=1$. In this temperature range we see the crossover from electron domination at high temperature to blue down quark domination at low temperature (see Sec. 4a).

Figure 3

Numerical calculation of shear viscosity as a function of temperature, taking ${\alpha }_s=1$. In this temperature range we see the crossover from electron domination at high temperature to blue down quark domination at low temperature (see Sec. 4a).