Modelling the polarisation signatures detected from the first white dwarf pulsar AR Sco

Marsh et al. detected radio and optical pulsations from the binary system AR Scorpii (AR Sco). This system, with an orbital period of 3.56 h, is composed of a cool, low-mass star and a white dwarf with a spin period of 1.95 min. Optical observations by Buckley et al. showed that the polarimetric emission from the white dwarf is strongly linearly polarised ( up to $\sim40\%$) with periodically changing intensities. This periodic non-thermal emission is thought to be powered by the highly magnetised ($ 5 \times 10^{8} $ G) white dwarf that is spinning down. The morphology of the polarisation signal, namely the position angle plotted against the phase angle, is similar to that seen in many radio pulsars. In this paper, we demonstrate that we can fit the traditional pulsar rotating vector model to the optical position angle. We used a Markov-chain-Monte-Carlo technique to find the best fit for the model yielding a magnetic inclination angle of $\alpha = (86.6^{+3.0}_{-2.8})^{\circ}$ and an observer angle of $\zeta = (60.5^{+5.3}_{-6.1})^{\circ}$. This modelling supports the scenario that the synchrotron emission originates above the polar caps of the white dwarf pulsar and that the latter is an orthogonal rotator.