Electrical conductivity of warm neutron star crust in magnetic fields: Neutron-drip regime

TL;DR

The paper addresses the transport properties of warm, non-pure inner-crust matter in magnetized neutron stars, focusing on the anisotropic electrical conductivity tensor in the neutron-drip regime. It extends previous outer-crust results by solving the Boltzmann transport equation with relaxation-time approximation, incorporating HTL screening, ionic correlations via a structure factor, and finite nuclear size through a form factor, across five inner-crust compositions. Key findings include a generally small composition-induced scatter ($\le 10$–$25\%$ depending on density), the onset of magnetic anisotropy at $B_{12}\gtrsim 30$ with $\omega_c\tau \sim 1$ throughout the crust for $B_{12}=100$, and the potential relevance of electron-neutron scattering near the crust-core boundary. These insights have direct implications for dissipative MHD simulations of BNS mergers and proto-neutron stars and highlight avenues for extending the framework to multi-component plasmas and higher-temperature regimes.

Abstract

We compute the anisotropic electrical conductivity tensor of the inner crust of a compact star at non-zero temperature by extending a previous work on the conductivity of the outer crust. The physical scenarios, where such crust is formed, involve proto-neutron stars born in supernova explosions, binary neutron star mergers and accreting neutron stars. The temperature-density range studied covers the transition from a non-degenerate to a highly degenerate electron gas and assumes that the nuclei form a liquid, i.e., the temperature is above the melting temperature of the lattice of nuclei. The electronic transition probabilities include (a) the dynamical screening of electron-ion interaction in the hard-thermal-loop approximation for the QED plasma, (b) the correlations of the ionic component in a one-component plasma, and (c) finite nuclear size effects. The conductivity tensor is obtained from the Boltzmann kinetic equation in relaxation time approximation accounting for the anisotropies introduced by a magnetic field. The sensitivity of the results towards the matter composition of the inner crust is explored by using several compositions of the inner crust which were obtained using different nuclear interactions and methods of solving the many-body problem. The standard deviation of relaxation time and components of the conductivity tensor from the average are below $\le 10\%$ except close to crust-core transition, where non-spherical nuclear structures are expected. Our results can be used in dissipative magneto-hydrodynamics (MHD) simulations of warm compact stars.

Figures (13)

• Figure 1: The proton number $Z$ (top panel) and the nucleon number $A$ (bottom panel) of the nuclei as functions of the mass density for five different compositions of the stellar matter labeled as NV Negele1973, D1M and D1M$^*$Mondal2020, Bsk24 Pearson:2018, and Sly9 Raduta2019.
• Figure 2: (a) The fraction of free neutrons $Y_n=n'_n/n_B$ and (b) the number density of ions (b) as functions of the mass density for five compositions of stellar matter.
• Figure 3: The phase diagram of dense plasma in the inner crust of the neutron star in the temperature-density plane for five different compositions. The lower curves show the melting temperature $T_m$ below which the ionic component solidifies. Upper curves show $T_{\rm C}$ above which the ionic component forms a Boltzmann gas. The present study covers the liquid portion of the phase diagram.
• Figure 4: The Fermi temperature $T_F$ of the electronic component of the stellar matter in the inner crust of a neutron star for five different compositions shown in Fig. \ref{['fig:compositions']}. The electron gas is becoming gradually non-degenerate above and degenerate below this temperature.
• Figure 5: The relaxation time $\tau$ and the Hall parameter $\omega_{c}\tau$ at the Fermi energy as functions of the mass density for five compositions as labeled in Fig. \ref{['fig:compositions']}. The temperature is fixed at $T=5$ MeV, and the magnetic field is fixed at $B_{12}=100$ for (b). The solid lines show the values of these quantities averaged over the five compositions. The solid and dashed curves in the inset show the standard deviations of $\log_{10}\tau$ and $\omega_{c}\tau$, respectively.