Constraining the emission geometry and mass of the white dwarf pulsar AR Sco using the rotating vector model

Abstract

We apply the standard radio pulsar rotating vector model to the white dwarf (WD) pulsar AR Sco's optical polarization position angle swings folded at the WD's spin period as obtained by Buckley et al. 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 $\cos \alpha ={0.060}_{-0.053}^{+0.050}$ and $\cos \zeta ={0.49}_{-0.08}^{+0.09}$, implying an orthogonal rotator with an observer angle $\zeta ={60\buildrel{\circ}\over{.} 4}_{-6\buildrel{\circ}\over{.} \,0}^{+5\buildrel{\circ}\over{.} \,3}$. This orthogonal nature of the rotator is consistent with the optical light curve consisting of two pulses per spin period, separated by 180° in phase. Under the assumption that ζ ≈ i, where i is the orbital inclination, and that the companion M star is Roche-lobe-filling, we obtain ${m}_{\mathrm{WD}}={1.00}_{-0.10}^{+0.16}{M}_{\odot }$ for the WD mass. These polarization modeling results suggest the that nonthermal emission arises from a dipolar WD magnetosphere and close to the star, with synchrotron radiation (if nonzero pitch angles can be maintained) being the plausible loss mechanism, marking AR Sco as an exceptional system for future theoretical and observational study