Hydrodynamical models of stellar convection. The role of overshoot in DA white dwarfs, A-type stars, and the Sun.

Based on two-dimensional numerical radiation hydrodynamics simulations of time-dependent compressible convection, we have studied the structure and dynamics of a variety of shallow stellar surface convection zones. Our present grid of models includes detailed simulations of surface convection in solar-type stars, main-sequence A-type stars and cool DA white dwarfs, as well as numerical experiments to study convection and overshoot at the base of the solar convection zone. Taking into account a realistic equation of state (including the effects of ionization) and adopting an elaborate treatment of non-local radiative transfer (with appropriate grey or frequency-dependent opacities), our simulations are designed to represent specific stellar objects characterized by T_eff_, logg, and chemical composition. Contrary to solar-type stars, the A-type stars and cool DA white dwarfs investigated here have shallow convection zones which fit into the computational domain together with thick stable buffer layers on top and below, thus permitting a study of convective overshoot under genuine conditions. We find that convective motions extend well beyond the boundary of the convectively unstable region, with vertical velocities decaying exponentially with depth in the deeper parts of the lower overshoot region, as expected for linear g^-^-modes. Even though convective velocities are reduced by orders of magnitude, they are still able to counteract molecular diffusion. For a quantitative description of convective mixing in the far overshoot layers we have derived a depth dependent diffusion coefficient from the numerical simulations. In combination with otherwise independent 1D diffusion calculations for a trace element, this allows the determination of the "effective depth" of the overshoot region. For a typical main-sequence A-type star (T_eff_=7943#1, logg=4.34) the mass in the overshoot region exceeds the mass in the unstable region by approximately a factor 10. The amount of overshoot in cool DA white dwarfs (around T_eff_=12200#1) is even larger: the convectively mixed mass is increased by roughly a factor 100.