Towards Modelling AR Sco: Calibration -- Reproducing High-Energy Pulsar Emission and Testing Convergence to Aristotelian Electrodynamics

Abstract

In recent years, kinetic simulations have been crucial to further our understanding of pulsar electrodynamics. Yet, due to the large-scale separation between the gyro-period vs the stellar rotation period, resolving the particle gyration has been computationally unfeasible for realistic pulsar parameters. The main aim of this work is comparing our gyro-phase-resolved model with a gyro-centric pulsar model, where our model solves the general equations of motion with included radiation reaction using a higher-order numerical solver with adaptive time steps. Specifically, we aim to (i) reproduce a pulsar's high-energy emission maps, namely one with $10\%$ the surface $B$-field strength of Vela, and spectra produced by an independent gyro-centric pulsar emission model; (ii) test convergence of these results to the radiation-reaction limit of Aristotelian Electrodynamics. (iii) Additionally, we identify the effect that a large $E_{\parallel}$-field has on the trajectories and radiation calculations. We find that we can reproduce the curvature radiation emission maps and spectra well, using $10\%$ field strengths of the Vela pulsar and injecting our particles at a higher altitude in the magnetosphere. Using sufficiently large $E_{\parallel}$-fields, our numeric results converge to the analytic radiation-reaction limit trajectories. Additionally, we illustrate the importance of accounting for the $\mathbf{E}\times \mathbf{B}$-drift in the particle trajectories and radiation calculations, validating the Harding and collaborators' model approach. Lastly, we found that our model deals very well with the high-radiation-reaction and high-field regimes present in pulsars.