The role of convection, overshoot, and gravity waves for the transport of dust in M dwarf and brown dwarf atmospheres

Context. Observationally, spectra of brown dwarfs indicate the presence of dust in their atmospheres while theoretically it is not clear what prevents the dust from settling and disappearing from the regions of spectrum formation. Consequently, standard models have to rely on ad hoc assumptions about the mechanism that keeps dust grains aloft in the atmosphere. Aims. We apply hydrodynamical simulations to develop an improved physical understanding of the mixing properties of macroscopic flows in M dwarf and brown dwarf atmospheres, in particular of the influence of the underlying convection zone. Methods. We performed two-dimensional radiation hydrodynamics simulations including a description of dust grain formation and transport with the CO5BOLD code. The simulations cover the very top of the convection zone and the photosphere including the dust layers for a sequence of effective temperatures between 900 K and 2800 K, all with log g = 5 assuming solar chemical composition. Results. Convective overshoot occurs in the form of exponentially declining velocities with small scale heights, so that it affects only the region immediately above the almost adiabatic convective layers. From there on, mixing is provided by gravity waves that are strong enough to maintain thin dust clouds in the hotter models. With decreasing effective temperature, the amplitudes of the waves become smaller but the clouds become thicker and develop internal convective flows that are more efficient in transporting and mixing material than gravity waves. The presence of clouds often leads to a highly structured appearance of the stellar surface on short temporal and small spatial scales (presently inaccessible to observations). Conclusions. We identify convectively excited gravity waves as an essential mixing process in M dwarf and brown dwarf atmospheres. Under conditions of strong cloud formation, dust convection is the dominant self-sustaining mixing component.