Dang Pham, Aster G. Taylor, Tim Cunningham

Many white dwarfs are polluted by metals, which are generally understood to be the accreted remnants of a planetary system. Modeling these systems typically assumes that the metal concentration is homogeneous throughout the white dwarf's atmosphere. However, the magnetic fields of a white dwarf may affect the accretion geometry of the white dwarf via magnetospheric accretion. Convection in the white dwarf's photosphere will then transport the metals across the surface, with a structure set by the relative sinking versus spreading timescales. In this work, we construct models for the accretion geometry, subsequent spreading, and observed pollution of magnetic white dwarfs. We show that the magnetic fields will initially concentrate the pollution into a narrow region of the white dwarf's surface. The relative spreading and sinking timescales determine whether the metals become uniformly distributed or remain confined to localized patches. If the magnetic field and spin poles are misaligned, then patchy white dwarfs exhibit periodically variable pollution signatures, which enable constraints on the patch area. We explore this model as a possible explanation for the recent detection of periodically variable pollution signatures in magnetic white dwarfs. Finally, we also demonstrate that the concentration of material due to the magnetic field may lead to systematic underestimates of the mass accretion rate onto these objects.