Dust in brown dwarfs and extra-solar planets II. Cloud formation for cosmologically evolving abundances

Context. Substellar objects have extremely long life spans. The cosmological consequence for older objects are low abundances for heavy elements, which in turn results in a wide distribution of objects over metallicity, hence over age. Within their cool atmosphere, dust clouds become a dominant feature, affecting the opacity and the remaining gas phase abundance of heavy elements. Aims. We investigate the influence of the stellar metallicity on the dust formation in substellar atmospheres and on the dust cloud structure and its feedback on the atmosphere. This work has implications for the general questions of star formation and of dust formation in the early universe. Methods. We utilise numerical simulations to solve a set of moment equations to determine the quasi-static dust cloud structure (Drift). These equations model the nucleation, the kinetic growth of composite particles, their evaporation, and the gravitational settling as a stationary dust formation process. Element conservation equations augment this system of equations by including the element replenishment by convective overshooting. The integration with an atmosphere code ( Phoenix) allows determination of a consistent (T, p, v(conv))-structure (T - local temperature, p - local pressure, v(conv) - convective velocity), hence, to calculate synthetic spectra. Results. A grid of Drift-Phoenix model atmospheres was calculated for a wide range of metallicity, [M/H] is an element of [+0.5, -0.0, -0.5, ... , -6.0], to allow for systematic study of atmospheric cloud structures throughout the evolution of the universe. We find dust clouds in even the most metal-poor ([M/H] = -6.0) atmosphere of brown dwarfs. Only the most massive among the youngest brown dwarfs and giant gas planets can resist dust formation. For very low heavy element abundances, a temperature inversion develops that has a drastic impact on the dust cloud structure. Conclusions. The combination of metal depletion by dust formation and the uncertainty of interior element abundances makes the modelling of substellar atmospheres an intricate problem in particular for old substellar objects. We furthermore show that the dust-togas ratio does not scale linearly with the object's [M/H] for a given effective temperature. The mean grain sizes and the composition of the grains change depending on [M/H], which influences the dust opacity that determines radiative heating and cooling, as well as the spectral appearance.