Fully time-dependent cloud formation from a non-equilibrium gas-phase in exoplanetary atmospheres

Context. Recent observations suggest the presence of clouds in exoplanet atmospheres, but they have also shown that certain chemical species in the upper atmosphere might not be in chemical equilibrium. Present and future interpretation of data from, for example, CHEOPS, JWST, PLATO, and Ariel require a combined understanding of the gas-phase and the cloud chemistry. Aims. The goal of this work is to calculate the two main cloud formation processes, nucleation, and bulk growth consistently from a non-equilibrium gas phase. The aim is also to explore the interaction between a kinetic gas-phase and cloud microphysics. Methods. The cloud formation is modelled using the moment method and kinetic nucleation, which are coupled to a gas-phase kinetic rate network. Specifically, the formation of cloud condensation nuclei is derived from cluster rates that include the thermochemical data of (TiO₂)_N from N = 1 to 15. The surface growth of nine bulk Al, Fe, Mg, O, Si, S, and Ti binding materials considers the respective gas-phase species through condensation and surface reactions as derived from kinetic disequilibrium. The effect of the completeness of rate networks and the time evolution of the cloud particle formation is studied for an example exoplanet, HD 209458 b. Results. A consistent, fully time-dependent cloud formation model in chemical disequilibrium with respect to nucleation, bulk growth, and the gas-phase is presented and first test cases are studied. This model shows that cloud formation in exoplanet atmospheres is a fast process. This confirms previous findings that the formation of cloud particles is a local process. Tests on selected locations within the atmosphere of the gas-giant HD 209458 b show that the cloud particle number density and volume reach constant values within 1 s. The complex kinetic polymer nucleation of TiO₂ confirms results from classical nucleation models. The surface reactions of SiO[s] and SiO₂[s] can create a catalytic cycle that dissociates H₂ to 2 H, resulting in a reduction of the CH₄ number densities.