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Constraining the Emission Geometry and Mass of the White Dwarf Pulsar AR Sco using the Rotating Vector Model

We apply the standard radio pulsar rotating vector model to the white dwarf pulsar AR Sco's optical polarization position angle swings folded at the white dwarf's spin period as obtained by Buckley et al. (2017). Owing to the long duty cycle of spin pulsations with a good signal-to-noise ratio over the entire spin phase, in contrast to neutron star radio pulsars, we find well-constrained values for the magnetic obliquity $α$ and observer viewing direction $ζ$ with respect to the spin axis. We find $\cosα=0.060^{+0.050}_{-0.053}$ and $\cosζ=0.49^{+0.09}_{-0.08}$, implying an orthogonal rotator with an observer angle $ζ={60.4^\circ}^{+5.3^\circ}_{-6.0^\circ}$. This orthogonal nature of the rotator is consistent with the optical light curve consisting of two pulses per spin period, separated by $180^\circ$ in phase. Under the assumption that $ζ\approx i$, where $i$ is the orbital inclination, and a Roche-lobe-filling companion M star, we obtain $m_{\rm WD} = 1.00^{+0.16}_{-0.10} M_\odot$ for the white dwarf mass. These polarization modeling results suggest the that non-thermal emission arises from a dipolar white dwarf magnetosphere and close to the star, with synchrotron radiation (if non-zero pitch angles can be maintained) being the plausible loss mechanism, marking AR Sco as an exceptional system for future theoretical and observational study.