Impact of positrons on electrical conductivity of hot and dense astrophysical plasma

TL;DR

The paper addresses electrical transport in hot, dense astrophysical plasmas of neutron-star outer crusts by treating electrons and thermally produced positrons via coupled Boltzmann equations in the relaxation-time framework. It develops a multicomponent conductivity formalism, deriving relaxation times from electron–ion, positron–ion, and electron–positron collisions, with in-medium screening described by HTL polarization tensors and one-plasmon exchange. Key results show that positrons can dominate conduction at $T \,\gtrsim\, T_F$ and that the conductivity scales as $\sigma \propto T^4$ near the semi-degenerate transition and $\sigma \propto T$ at higher temperatures when $ep$ collisions are important, with enhancements by orders of magnitude relative to positron-neglecting models. These findings underscore the necessity of including positrons in transport calculations for heated, dense plasmas in neutron-star crusts, affecting magnetic-field evolution and MHD behavior in such environments.

Abstract

We study the influence of positrons on the outer crusts of neutron stars and the interiors of white dwarfs, introducing them as a novel component in both the composition of matter and in transport processes. We solve a system of coupled Boltzmann kinetic equations for the electron and positron distribution functions in the relaxation-time approximation, taking into account electron-ion, positron-ion, and electron-positron collisions. The relevant scattering matrix elements are calculated from one-plasmon exchange diagrams, with in-medium polarization tensors derived within hard-thermal-loop effective theory. Numerical results are obtained for matter composed of carbon nuclei. We find that the conductivity rises with temperature, following a power law sigma proportional to the 4th power of T in the semi-degenerate regime and sigma proportional to T in the nondegenerate regime, due to the intense creation of thermal electron-positron pairs and the resulting collisions among them. These results highlight the importance of including positrons in the transport properties of heated, dense astrophysical plasmas.

Figures (8)

• Figure 1: Diagrams describing the electron-positron scattering and annihilation via exchange of a virtual plasmon. The plasmon self-energy is given by the polarization tensor $\Pi_{\mu\nu}(\omega,{\bm q})$ shown by the closed loops.
• Figure 2: Diagrams describing the electron-ion (left) and positron-ion (right) scattering via exchange of a virtual plasmon.
• Figure 3: The temperature-density phase diagram of crustal plasma composed of carbon. Ionic component of plasma forms a Boltzmann gas above the Coulomb temperature $T_C$, a classical liquid at $T_p\leq T\leq T_C$, and a quantum liquid below the plasma temperature $T_p$. Electrons become degenerate below the Fermi temperature $T_F$. The three curves around $T_F$ correspond to temperatures where the ratio of the total electron density $n^-$ to the net electron density $n_e$ reaches the value $r$.
• Figure 4: Dependence of electronic (dashed lines) and positronic (dash-double-dotted lines) partial conductivities and their sum (solid lines) for three values of the temperature indicated in the plot. These are the conductivities resulting only from $ei$ and $pi$ collisions. The dotted lines show the conductivity from Ref. Harutyunyan2016 where positrons' abundance in the matter is neglected.
• Figure 5: The temperature dependence of electronic (dashed lines) and positronic (dash-double-dotted lines) partial conductivities and their sum (solid lines) for three values of the density indicated in the plot. These are the conductivities resulting only from $ei$ and $pi$ collisions. The dotted lines show the conductivity from Ref. Harutyunyan2016 where positrons' abundance in the matter is neglected.