Transport coefficients of leptons in superconducting neutron star cores

Abstract

I consider the thermal conductivity and shear viscosity of leptons (electrons and muons) in the nucleon NS cores where protons are in the superconducting state. I restrict the consideration to the case of not too high temperatures $T\lesssim 0.35T_{\mathrm{c}p}$, where $T_{\mathrm{c}p}$ is the critical temperature of the proton pairing. In this case, lepton collisions with protons can be neglected. Charged lepton collision frequencies are mainly determined by the transverse plasmon exchange and are mediated by the character of the transverse plasma screening. In our previous works [Shternin \& Yakovlev, Phys. Rev. D {\bf 75} 103004 (2007); {\bf 78} 063006 (2008)] the superconducting proton contribution to the transverse screening was considered in the Pippard limit $\Delta \ll \hslash q{v}_{\mathrm{F}p}$, where $\Delta$ is the proton pairing gap, $v_{\mathrm{F}p}$ is the proton Fermi velocity, and $\hslash q$ is the typical transferred momentum in collisions. However, for large critical temperatures (large $\Delta$) and relatively small densities (small $q$) the Pippard limit may become invalid. In the present study I show that this is indeed the case and that the older calculations severely underestimated the screening in a certain range of the parameters appropriate to the neutron star cores. As a consequence, the kinetic coefficients at $T\ll T_{\mathrm{c}p}$ are found to be smaller than in previous calculations.

18 pages, 11 figures, accepted for publication in PRD. In v.2 new figure 9 is added and BSK21 results are corrected

References in corpus (11)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Shear viscosity in neutron star cores
• Nucleon effective masses within the Brueckner-Hartree-Fock theory: Impact on stellar neutrino emission
• Shear viscosity of neutron matter from realistic nucleon-nucleon interactions
• Electron-muon heat conduction in neutron star cores via the exchange of transverse plasmons
• Viscosity of neutron star matter and $r$-modes in rotating pulsars
• Transport coefficients of two-flavor superconducting quark matter
• Transport equations and linear response of superfluid Fermi mixtures in neutron stars
• The Photon in Dense Nuclear Matter I: Random Phase Approximation
• Transport coefficients in neutron star cores in BHF approach. Comparison of different nucleon potentials
• Electron-neutron scattering and transport properties of neutron stars

Cited by in corpus (10)

• Nucleon effective mass in hot dense matter
• Bulk viscosity in neutron stars with hyperon cores
• Strengthening the bounds on the r-mode amplitude with X-ray observations of millisecond pulsars
• Diffusion as a leading dissipative mechanism in superconducting neutron stars
• Transport coefficients of nucleon neutron star cores for various nuclear interactions within the Brueckner-Hartree-Fock approach
• Instability windows of relativistic r-modes
• Transport coefficients of hyperonic neutron star cores
• Diffusion in superfluid Fermi mixtures: General formalism
• Estimation of transport coefficients of dense hadronic and quark matter
• Neutrino pair bremsstrahlung due to electromagnetic collisions in neutron star cores revisited