Dust in brown dwarfs and extra-solar planets. VII. Cloud formation in diffusive atmospheres

The precipitation of cloud particles in brown dwarf and exoplanet atmospheres establishes an ongoing downward flux of condensable elements. To understand the efficiency of cloud formation, it is therefore crucial to identify and quantify the replenishment mechanism that is able to compensate for these local losses of condensable elements in the upper atmosphere, and to keep the extrasolar weather cycle running. In this paper, we introduce a new cloud formation model by combining the cloud particle moment method we described previously with a diffusive mixing approach, taking into account turbulent mixing and gas-kinetic diffusion for both gas and cloud particles. The equations are of diffusion-reaction type and are solved time-dependently for a prescribed 1D atmospheric structure, until the model has relaxed toward a time-independent solution. In comparison to our previous models, the new hot-Jupiter model results (T_eff ≈ 2000 K, log g = 3) show fewer but larger cloud particles that are more concentrated towards the cloud base. The abundances of condensable elements in the gas phase are featured by a steep decline above the cloud base, followed by a shallower, monotonous decrease towards a plateau, the level of which depends on temperature. The chemical composition of the cloud particles also differs significantly from our previous models. Through the condensation of specific condensates such as Mg₂SiO₄[s] in deeper layers, certain elements, such as Mg, are almost entirely removed early from the gas phase. This leads to unusual (and non-solar) element ratios in higher atmospheric layers, which then favours the formation of SiO[s] and SiO₂[s], for example, rather than MgSiO₃[s]. These condensates are not expected in phase-equilibrium models that start from solar abundances. Above the main silicate cloud layer, which is enriched with iron and metal oxides, we find a second cloud layer made of Na₂S[s] particles in cooler models (T_eff ⪅ 1400 K).