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 struct ure and dynamics of a variety of shallow stellar surface convection zo nes. Our present grid of models includes detailed simulations of surfa ce 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 a ccount a realistic equation of state (including the effects of ionizat ion) and adopting an elaborate treatment of non-local radiative transf er (with appropriate grey or frequency-dependent opacities), our simul ations are designed to represent specific stellar objects characterize d by T-eff, log g, and chemical composition. Contrary to solar-type st ars, the A-type stars and cool DA white dwarfs investigated here have shallow convection zones which fit into the computational domain toget her 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 convectivel y unstable region, with vertical velocities decaying exponentially wit h 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 di ffusion. For a quantitative description of convective mixing in the fa r over-shoot layers we have derived a depth dependent diffusion co-eff icient from the numerical simulations. In combination with otherwise i ndependent 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 K, log g = 4.34) the mass in the overshoot region exceeds the mass in the unstable reg ion by approximately a factor 10. The amount of overshoot in cool DA w hite dwarfs (around T-eff = 12200 K) is even larger: the convectively mixed mass is increased by roughly a factor 100.