Convective Overshoot and Macroscopic Diffusion in Pure-Hydrogen Atmosphere White Dwarfs

We present a theoretical description of macroscopic diffusion caused by convective overshootin pure-hydrogen DA white dwarfsusing three-dimensional (3D), closed-bottom, radiation hydrodynamics CO$^5$BOLD simulations. We rely on a new grid of deep 3D white dwarfmodels in the temperature range 11400 K $\leq T_{\mathrm{eff}} \leq$ 18000 K where tracer particles and a tracer density are used to derive macroscopic diffusion coefficients driven by convective overshoot. These diffusion coefficients are compared to microscopic diffusion coefficients from one-dimensional structures. We find that the mass of the fully mixed region is likely to increase by up to 2.5 ordersof magnitudewhile inferred accretion rates increase by a more moderate orderof magnitude. We present evidence that an increase in settling timeof up to 2 ordersof magnitudeis to be expected which is of significance for time-variability studies of polluted white dwarfs. Our grid also provides the most robust constraint on the onset of convective instabilitiesin DA white dwarfsto be in the effective temperaturerange from 18000 to 18250 K.