Dust in Brown Dwarfs and Extra-solar Planets I. Chemical composition and spectral appearance of quasi-static cloud layers

We aim at understanding the formation of cloud layers in quasi-static substellar atmospheres. The time-dependent description presented in (Helling & Woitke 2006) 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 for the dust moments, we determine the grain size distribution function which, together with the calculated material volume fractions, provides the basis to calculate the opacities of the composite dust grains. The cloud particles in brown dwarfs and hot giant-gas planets are found to be small in the high atmospheric layers (0.01mum), and composed of a rich mixture of all considered condensates, in particular the abundant MgSiO3[s], Mg2SiO4[s] and SiO2[s]. As the particles settle downward, they increase in size and reach several 100mum 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 Fe[s] and Al2O3[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 often strongly peaked in the deeper layers. The spectral appearance of the cloud layers in the mid IR (7-20mum) is close to a grey body with only weak broad features on a few percent level, mainly caused by MgSiO3[s], and Mg2SiO4[s]. Our models predict that the gas phase depletion is much weaker as compared to phase-equilibrium calculations in the high atmospheric layers. [abridged]