Axion Hair and Pulsar Electrodynamics: modelling, discharge dynamics, and particle-in-cell simulations

Abstract: In a companion paper, we demonstrated that static axion field gradients sourced by dense nuclear matter (\emph{axion hair}) can dominate the near-field electrodynamics of old rotation-powered pulsars, leading to new constraints on light QCD axions and on CP-violating axion-nucleon interactions. This article provides the extended theoretical and numerical framework underlying those results. We begin by providing a detailed description of the sourcing of axion hair from dense nuclear matter, computing self-consistent field profiles for each interaction across the relevant parameter space. We then study the modification to the electrodynamics induced in the polar gap region by these axion gradients; this is done at the analytic level by studying the modification induced by axion field gradients on the effective discharge parameter (computed in the force-free limit of the split monopole magnetic field configuration, and looking at leading deviations from the force-free limit for dipolar field configurations), and numerically by developing dedicated 1D particle-in-cell simulations which capture the leading order dynamical behavior near the star. Our results demonstrate that axion hair serves to either enhance acceleration, or enhance screening, where the relevant effect changes between the northern and southern hemispheres of the star, and between the field lines which support out-flowing and return currents.