A Model for AR~Scorpii: Emission from Relativistic Electrons Trapped by Closed Magnetic Field Lines of Magnetic White Dwarfs

AR~Scorpii is an intermediate polar system composed of a magnetic white dwarf (WD) and an M-type star, and shows non-thermal, pulsed, and highly linearly polarized emission. The radio/optical emission modulates with the WD's spin and show the double peak structure in the light curves. In this paper, we discuss a possible scenario for the radiation mechanism of AR~Scorpii. The magnetic interaction on the surface of the companion star produces an outflow from the companion star, the heating of the companion star surface, and the acceleration of electrons to a relativistic energy. The accelerated electrons, whose typical Lorentz factor is $\sim 50-100$, from the companion star move along the magnetic field lines toward the WD surface. The electrons injected with the pitch angle of $\sin\theta_{p,0}>0.05$ are subject to the magnetic mirror effect and are trapped in the closed magnetic field line region.We find that the emission from the first magnetic mirror points mainly contributes to the observed pulsed emission and the formation of the double-peak structure in the light curve. For the inclined rotator, the pulse peak in the calculated light curve shifts the position in the spin phase, and a Fourier analysis exhibits a beat frequency feature, which are consistent with the optical/UV observations. The pulse profile also evolves with the orbital phase owing to the effect of the viewing geometry. The model also interprets the global features of the observed spectral energy distribution in radio to X-ray energy bands. We also discuss the curvature radiation and the inverse-Compton scattering process in the outer gap accelerator of the WD in AR Scorpii and discuss the possibility of the detection by future high-energy missions.

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