Thermal conduction and thermopower of inner crusts of magnetized neutron stars

TL;DR

This paper addresses heat and charge transport in the warm, magnetized inner crust of neutron stars by solving the Boltzmann equation in the relaxation-time framework, including anisotropy from magnetic fields up to $B \le 10^{14}$ G. It incorporates detailed microphysics—HTL-screened electron–ion interactions with structure factors, finite nuclear-size form factors, ion correlations, and a subleading electron–neutron channel via the neutron’s anomalous magnetic moment—and analyzes five crust compositions to quantify composition dependence. The authors deliver full tensor transport coefficients (thermal conductivity and thermopower) and identify regimes where anisotropy and thermoelectric effects strongly influence magnetic-field evolution, showing the nuclear form factor dominates magnitudes and composition scatter, while electron–neutron scattering remains negligible. Implications include updated microphysical inputs for magneto-hydrodynamic simulations of proto-neutron stars and mergers, with thermoelectric effects potentially governing crustal-field evolution at moderate temperatures and fields.

Abstract

We compute the thermal conductivity and thermoelectric power (thermopower) of the inner crust of compact stars across a broad temperature-density domain relevant for proto-neutron stars, binary neutron-star mergers, and accreting neutron stars. The analysis covers the transition from a semi-degenerate to a highly degenerate electron gas and assumes temperatures above the melting threshold of the nuclear lattice, such that nuclei form a liquid. The transport coefficients are obtained by solving the Boltzmann kinetic equation in the relaxation-time approximation, fully incorporating the anisotropies generated by non-quantizing magnetic fields. Electron scattering rates include (i) dynamical screening of the electron-ion interaction in the hard-thermal-loop approximation of QED, (ii) ion-ion correlations within a one-component plasma, and (iii) finite nuclear-size effects. As an additional refinement, we evaluate electron-neutron scattering induced by the coupling of electrons to the anomalous magnetic moment of free neutrons; this contribution is found to be subdominant throughout the parameter range explored. To assess the sensitivity of transport coefficients to the underlying microphysics, we perform calculations for several inner-crust compositions obtained from different nuclear interactions and many-body methods. Across most of the crust, variations in relaxation times and in the components of the anisotropic thermal-conductivity and thermopower tensors reach up to factors 3-4 and 1.5-2, respectively, with the exception of the region where pasta phases are expected. These results provide updated, composition-dependent microphysical inputs for dissipative magneto-hydrodynamic simulations of warm neutron stars and post-merger remnants, where anisotropic heat and charge transport are of critical importance.

Figures (20)

• Figure 1: (a) The ratio of the nucleus radius $r_c$ to that of the Wigner-Seitz cell and (b) the volume fraction $(1-V_Nn_i)$ occupied by neutron gas as functions of density for five compositions of stellar matter.
• Figure 2: (a) The relaxation time $\tau$ and (b) the Hall parameter $\omega_c\tau$ as functions of density for five compositions as labeled in Fig. \ref{['fig:radii']}. The temperature is fixed at $T=5$ MeV, and the magnetic field is fixed at $B_{12}=100$.
• Figure 3: Density-dependence of the relaxation time for two models evaluated with full nuclear formfactor $F(q)$ (filled symbols) and with $F(q)=1$ (empty symbols). The temperature is fixed at $T=5$ MeV.
• Figure 4: Dependence of the scalar conductivity on density for five compositions. The temperature is fixed at $T=5$ MeV.
• Figure 5: The temperature dependence of the scalar conductivity for various values of the density for composition D1M*.