Dust in brown dwarfs and extra-solar planets

IV. Assessing TiO₂ and SiO nucleation for cloud formation modelling^⋆

¹ SUPA, School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews KY16 9SS, UK
e-mail: ch80@st-and.ac.uk
² Departament de Quimica Fisica and IQTCUB, Universitat de Barcelona, Marti i Franques 1, 08028 Barcelona, Spain
³ Institucio Catalana de Recerca i Estudis Avancats (ICREA), 08010 Barcelona, Spain

Received: 16 July 2014
Accepted: 23 October 2014

Abstract

Context. Clouds form in atmospheres of brown dwarfs and planets. The cloud particle formation processes, seed formation and growth/evaporation are very similar to the dust formation process studied in circumstellar shells of AGB stars and in supernovae. Cloud formation modelling in substellar objects requires gravitational settling and element replenishment in addition to element depletion. All processes depend on the local conditions, and a simultaneous treatment is required.

Aims. We apply new material data in order to assess our cloud formation model results regarding the treatment of the formation of condensation seeds. We look again at the question of the primary nucleation species in view of new (TiO₂)_N-cluster data and new SiO vapour pressure data.

Methods. We applied the density functional theory (B3LYP, 6-311G(d)) using the computational chemistry package Gaussian 09 to derive updated thermodynamical data for (TiO₂)_N clusters as input for our TiO₂ seed formation model. We tested different nucleation treatments and their effect on the overall cloud structure by solving a system of dust moment equations and element conservation for a prescribed Drift-Phoenixatmosphere structure.

Results. Updated Gibbs free energies for the (TiO₂)_N clusters are presented, as well as a slightly temperature dependent surface tension for T = 500 ... 2000 K with an average value of σ_∞ = 480.6 erg cm^-2. The TiO₂ seed formation rate changes only slightly with the updated cluster data. A considerably larger effect on the rate of seed formation, and hence on grain size and dust number density, results from a switch to SiO nucleation. The question about the most efficient nucleation species can only be answered if all dust/cloud formation processes and their feedback are taken into account. Despite the higher abundance of SiO over TiO₂ in the gas phase, TiO₂ remains considerably more efficient at forming condensation seeds by homogeneous nucleation. The paper discusses the effect on the cloud structure in more detail.