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Magnetospheric interaction in white dwarf binaries AR Sco and AE Aqr

We develop a model of the white dwarf (WD) - red dwarf (RD) binaries AR Sco and AE Aqr as systems in a transient propeller stage of highly asynchronous intermediate polars. The WDs are relatively weakly magnetized with magnetic field of $\sim 10^6$ G. We explain the salient observed features of the systems due to the magnetospheric interaction of two stars. Currently, the WD's spin-down is determined by the mass loading of the WD's magnetosphere from the RD's at a mild rate of $\dot{M}_{WD} \sim 10^{-11} M_\odot $/yr. Typical loading distance is determined by the ionization of the RD's wind by the WD's UV flux. The WD was previously spun up by a period of high accretion rate from the RD via Roch lobe overflow with $\dot{M} \sim 10^{-9} M_\odot $/yr, acting for as short a period as tens of thousands of years. The non-thermal X-ray and optical synchrotron emitting particles originate in reconnection events in the magnetosphere of the WD due to the interaction with the flow from the RD. In the case of AR Sco, the reconnection events produce signals at the WD's rotation and beat periods - this modulation is due to the changing relative orientation of the companions' magnetic moments and resulting variable reconnection conditions. Radio emission is produced in the magnetosphere of the RD, we hypothesize, in a way that it is physically similar to the Io-induced Jovian decametric radiation.