The effect of thermal non-equilibrium on kinetic nucleation

¹ Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
e-mail: sven.kiefer@kuleuven.be
² Centre for Exoplanet Science, University of St Andrews, North Haugh, St Andrews, KY169SS, UK
³ Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, 8042 Graz, Austria
⁴ TU Graz, Fakultät für Mathematik, Physik und Geodäsie, Petersgasse 16, 8010 Graz, Austria
⁵ Department of Chemistry & Molecular Biology, University of Gothenburg, 40530 Göteborg, Sweden

Received: 5 August 2022
Accepted: 13 February 2023

Abstract

Context. Nucleation is considered to be the first step in dust and cloud formation in the atmospheres of asymptotic giant branch (AGB) stars, exoplanets, and brown dwarfs. In these environments dust and cloud particles grow to macroscopic sizes when gas phase species condense onto cloud condensation nuclei (CCNs). Understanding the formation processes of CCNs and dust in AGB stars is important because the species that formed in their outflows enrich the interstellar medium. Although widely used, the validity of chemical and thermal equilibrium conditions is debatable in some of these highly dynamical astrophysical environments.

Aims. We aim to derive a kinetic nucleation model that includes the effects of thermal non-equilibrium by adopting different temperatures for nucleating species, and to quantify the impact of thermal non-equilibrium on kinetic nucleation.

Methods. Forward and backward rate coefficients are derived as part of a collisional kinetic nucleation theory ansatz. The endother-mic backward rates are derived from the law of mass action in thermal non-equilibrium. We consider elastic collisions as thermal equilibrium drivers.

Results. For homogeneous TiO₂ nucleation and a gas temperature of 1250 K, we find that differences in the kinetic cluster temperatures as small as 20 K increase the formation of larger TiO₂ clusters by over an order of magnitude. Conversely, an increase in cluster temperature of around 20 K at gas temperatures of 1000 K can reduce the formation of a larger TiO₂ cluster by over an order of magnitude.

Conclusions. Our results confirm and quantify the prediction of previous thermal non-equilibrium studies. Small thermal non-equilibria can cause a significant change in the synthesis of larger clusters. Therefore, it is important to use kinetic nucleation models that include thermal non-equilibrium to describe the formation of clusters in environments where even small thermal non-equilibria can be present.