Dust in brown dwarfs and extra-solar planets. VIII. TiO2 seed formation: 3D Monte Carlo versus kinetic approach

Context. Modelling the formation of cloud condensation nuclei (CCNs) is key for predicting cloud properties in planet and brown dwarf atmospheres. The large diversity of exoplanets (rocky planets, mini-Neptunes, giant gas planets) requires a fundamental approach to cloud formation modelling in order to allow a full analysis of observational data contributing to exoplanet characterisation. Aims. We aim to understand the onset of cloud formation and study the formation of TiO2-CCNs. The formation of (TiO2)N clusters as precursors to extrasolar cloud formation is modelled by two different methods in order to understand their potential, identify underlying shortcomings, and to validate our methods. We propose potential spectral tracers for TiO2-CCN formation. Methods. We applied three-dimensional Monte Carlo (3D MC) simulations to model the collision-induced growth of TiO2-molecules to (TiO2)N-clusters in the free molecular flow regime of an atmospheric gas. We derived individual, time-dependent (TiO2)N cluster number densities. For T = 1000 K, the results are compared to a kinetic approach that utilises thermodynamic data for individual (TiO2)N clusters. Results. The (TiO2)N cluster size distribution is temperature dependent and evolves in time until a steady state is reached. For T = 1000 K, the 3D MC and the kinetic approach agree well regarding the cluster number densities for N = 1 … 10, the vivid onset of cluster formation, and the long transition into a steady state. Collision-induced growth and evaporation simulated using a 3D MC approach enables a faster onset of cluster growth through nucleation bursts. Different size distributions develop for monomer-cluster and for cluster-cluster growth, with the largest cluste