Dust in brown dwarfs and extra-solar planets - I. Chemical composition and spectral appearance of quasi-static cloud layers

Aims. Brown dwarfs are covered by dust cloud layers which cause inhomogeneous surface features and move below the observable tau = 1 level during the object's evolution. The cloud layers have a strong influence on the structure and spectral appearance of brown dwarfs and extra-solar planets, e. g. by providing high local opacities and by removing condensable elements from the atmosphere causing a sub-solar metalicity in the atmosphere. We aim at understanding the formation of cloud layers in quasi-static substellar atmospheres that consist of dirty grains composed of numerous small islands of different solid condensates. Methods. The time-dependent description is a kinetic model describing nucleation, growth and evaporation. It is extended to treat gravitational settling and is applied to the static-stationary case of substellar model atmospheres. From the solution of the dust moments, we determine the grain size distribution function approximately which, together with the calculated material volume fractions, provides the basis for applying effective medium theory and Mie theory to calculate the opacities of the composite dust grains. Results. The cloud particles in brown dwarfs and hot giant-gas planets are found to be small in the high atmospheric layers (a approximate to 0.01 mu m), and are composed of a rich mixture of all considered condensates, in particular MgSiO(3)[s], Mg(2)SiO(4)[s] and SiO(2)[s]. As the particles settle downward, they increase in size and reach several 100 mu m in the deepest layers. The more volatile parts of the grains evaporate and the particles stepwise purify to form composite particles of high-temperature condensates in the deeper layers, mainly made of Fe[s] and Al(2)O(3)[s]. The gas phase abundances of the elements involved in the dust formation process vary by orders of magnitudes throughout the atmosphere. The grain size distribution is found to be relatively broad in the upper atmospheric layers but strongly peaked in the deeper layers. This reflects the cessation of the nucleation process at intermediate heights. The spectral appearance of the cloud layers in the mid IR (7-20 mu m) is close to a grey body with only weak broad features of a few percent, mainly caused by MgSiO(3)[s], and Mg(2)SiO(4)[s]. These features are, nevertheless, a fingerprint of the dust in the higher atmospheric layers that can be probed by observations. Conclusions. Our models predict that the gas phase depletion is much weaker than phase-equilibrium calculations in the high atmospheric layers. Because of the low densities, the dust formation process is incomplete there, which results in considerable amounts of left-over elements that might produce stronger and broader neutral metallic lines.