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

Abstract

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 ${\kappa }_{e\mu }\propto T^{-1}$. Comparing with the thermal conductivity of neutrons ${\kappa }_n$, we obtain ${\kappa }_{e\mu }\gtrsim {\kappa }_n$ for $T\gtrsim 2\times {10}^9\mathrm{K}$ in normal matter and for any $T$ in superconducting matter with proton critical temperatures $T_{cp}\gtrsim 3\times {10}^9\mathrm{K}$. The results are described by simple analytic formulae.