Electron-muon heat conduction in neutron star cores via the exchange of transverse plasmons

We calculate the thermal conductivity of electrons and muons kappa(e mu) produced due to electromagnetic interactions of charged particles in neutron star cores and show that these interactions are dominated by the exchange of transverse plasmons (via the Landau damping of these plasmons in nonsuperconducting matter and via a specific plasma screening in the presence of proton superconductivity). For normal protons, the Landau damping strongly reduces kappa(e mu) and makes it temperature independent. Proton superconductivity suppresses the reduction and restores the Fermi-liquid behavior kappa(e mu)proportional to T-1. Comparing with the thermal conductivity of neutrons kappa(n), we obtain kappa(e mu)greater than or similar to kappa(n) for T greater than or similar to 2x10(9) K in normal matter and for any T in superconducting matter with proton critical temperatures T-cp greater than or similar to 3x10(9) K. The results are described by simple analytic formulae.