Modelling the multi-wavelength emission and polarisation signatures of the novel white-dwarf pulsar system AR Sco

Abstract

The reclassification of AR Scorpii (AR Sco) from a delta Scuti variable star to a white dwarf binary system has initiated an in-depth exploration of this novel system. The main aim of this work was to develop a general emission code to concurrently model the emission maps, light curves, and spectra at various orbital phases for AR Sco. For the development of the emission code, I solved the general equations of motion with included classical radiation reaction forces (RRF) by implementing the Dormand-Prince 8(7) numerical integrator with adaptive time-step methods. This yielded improved accuracy and computational time vs. the commonly used Vay symplectic integrator, particularly for the high $B$-fields, $E_{\perp}$-fields, and RRF needed for pulsar and pulsar-like magnetospheres. Additionally, I demonstrated the novel result of the particles entering and conforming to the radiation reaction limit regime of Aristotelian Electrodynamics. As calibration for the radiation calculations, emission maps, and spectra I compared my model output with results from the code of the pulsar emission model of Harding and collaborators for a pulsar with $10\%$ the $B$-field strength of Vela and how my results converged to theirs. Next, I showed my exploratory modelling of the magnetic mirror scenario proposed for AR Sco. I demonstrate I could fit the observational spectral energy distribution including the recent \textit{NICER} pulsed X-ray spectrum well, constraining the white dwarf $B$-field to $B_{\rm S} = (2.5 - 3.0) \times 10^{8} \, \rm{G}$. Finally, I showed the effect the $B$-field, $E_{\perp}$-field, initial pitch angle, and initial particle Lorentz factor have on the mirror points, RRF, emission maps, and spectra. This demonstrates how crucial it is to include the general particle dynamics to accurately model the micro-physics present in magnetic mirror models.