Anisotropic electron transport in the nuclear pasta phase

TL;DR

This paper investigates how the anisotropic shapes of nuclear pasta in neutron star crusts affect electron transport, deriving analytical expressions and quantifying the impact on conductivity at high temperatures.

Contribution

It provides the first analytical derivation of anisotropic collision frequencies for electron transport in nuclear pasta phases and quantifies their effect on conductivity.

Findings

Anisotropy in collision frequencies increases with pasta length.

Presence of rod and slab phases reduces conductivity by over an order of magnitude.

No strong anisotropies in conduction are expected above crustal melting temperatures.

Abstract

The presence of nuclear pasta is expected to modify the transport properties in the mantle of neutron stars. The non-spherical geometry of the pasta nuclear clusters leads to anisotropies in the collision frequencies, impacting the thermal and electrical conductivity. We derive analytical expressions for the anisotropic collision frequencies using the Boltzmann equation in the relaxation time approximation. The average parallel, perpendicular and Hall electrical conductivities are computed in the high-temperature regime above crustal melting, considering incoherent elastic electron-pasta scattering and randomly oriented pasta structures. Numerical values are obtained at different densities and temperatures by using the IUFSU parametrization of the non-linear Walecka model to determine the crustal structure. We find that the anisotropy of the collision frequencies grows with the length of the pasta structures and, independently of the magnetic field, the presence of rod and slab phases decreases the conductivity by more than one order of magnitude. Our numerical results indicate that, even if the pasta structures might survive above the crustal melting point, no strong anisotropies are to be expected in the conduction properties in this temperature regime, even in the presence of a very high magnetic field.