Accretion-driven Spin-up of the White Dwarfs in AR Scorpii and AE Aquarii

The problem caused by the inconsistency between the age and spin-down time scale of the white dwarfs in the systems AR Sco and AE Aqr is discussed within the hypothesis of their accretion-driven spin-up during the previous epoch. Considering a scenario of accretion from a Keplerian disk, we conclude that the white dwarfs in these systems could be spun-up to the currently observed periods provided the radius of their magnetospheres at the spin-up phase was substantially smaller than the Alfven radius. We show that the required magnetospheric radius value can be reached if the accretion flow penetrates the magnetic field of the white dwarf at its magnetospheric boundary due to anomalous (Bohm) diffusion. In this case the spin-up of the white dwarfs in the systems under consideration can be described based on a model of stationary accretion from the Keplerian disk at an average rate of \(10^{-9}{-}10^{-8}M_{\odot}\) yr \({}^{-1}\) without any additional assumptions about the evolution of the intrinsic magnetic field of the white dwarfs during the spin-up phase.