Electron-neutron scattering and transport properties of neutron stars

We show that electrons can couple to the neutron excitations in neutron stars, and find that this can limit their contribution to the transport properties of dense matter, especially the shear viscosity. The coupling between electrons and neutrons is induced by protons in the core, and by ions in the crust. We calculate the effective electron-neutron interaction for the kinematics of relevance to the scattering of degenerate electrons at high density. We use this interaction to calculate the electron thermal conductivity, electrical conductivity, and shear viscosity in the neutron star inner crust, and in the core where we consider both normal and superfluid phases of neutron-rich matter. In some cases, particularly when protons are superconducting and neutrons are in their normal phase, we find that electron-neutron scattering can be more important than the other scattering mechanisms considered previously.

Figure 1

Effective interaction between electrons and neutrons induced by protons in the medium. The wavy line represents the plasmon.

Figure 2

(a) The strength of the induced electron-neutron interaction defined in Eq. (5) as a function of $q$ at nuclear saturation density $n_0=0.16$ ${\mathrm{fm}}^{-3}$. (b) ${\mathcal{C}}_{\mathrm{enp}}^2(q=3q_{\mathrm{TF}})$ as a function of density.

Figure 3

(a) The strength of the induced electron-neutron interaction in the crust as a function of $q$ at various densities in the crust. (b) ${\mathcal{C}}_{\mathrm{enI}}^2(q=3q_{\mathrm{TFe}})$ as a function of density.

Figure 4

Effective interaction between electrons and neutrons induced by ion density fluctuations represented by a phonon.

Figure 5

The momentum averaged couplings for (a) ${\langle {\mathcal{C}}_{\mathrm{enp}}^2\rangle }_{\kappa }$ and (b) ${\langle {\mathcal{C}}_{\mathrm{enp}}^2\rangle }_{\eta }$, for densities of relevance in the core. It is assumed that neutrons are in the normal phase, and Eq. (32) is used to obtain the averages. Although it is not shown we remark that ${\langle {\mathcal{C}}_{\mathrm{enp}}^2\rangle }_{\sigma }\approx {\langle {\mathcal{C}}_{\mathrm{enp}}^2\rangle }_{\eta }$.

Figure 6

${\langle {\mathcal{C}}_{\mathrm{enI}}^2\rangle }_{\kappa /\sigma /\eta }$ in the crust as a function of density using $V_{\mathrm{nI}}$ derived from data presented in Ref. [20]

Figure 7

The ratio ${\kappa }_{\mathrm{ref}}/{\kappa }_{\mathrm{en}}$ for two proton critical temperatures: (a) $T_{\mathrm{c}}^{\mathrm{p}}={10}^9$ K and (b) $T_{\mathrm{c}}^{\mathrm{p}}={10}^{10}$ K, for densities of relevance to the core. When the ${\kappa }_{\mathrm{ref}}/{\kappa }_{\mathrm{en}}>1$, electron-neutron scattering dominates.

Figure 8

The ratio ${\eta }_{\mathrm{ref}}/{\eta }_{\mathrm{en}}$ for two proton critical temperatures: (a) $T_{\mathrm{c}}^{\mathrm{p}}={10}^9$ K and (b) $T_{\mathrm{c}}^{\mathrm{p}}={10}^{10}$ K, for densities in the core.