Bottom-up dust nucleation theory in oxygen-rich evolved stars

II. Magnesium and calcium aluminate clusters^★

¹ Department of Chemistry and Molecular Biology, Gothenburg University, Box 462, 40530 Gothenburg, Sweden
e-mail: dave@gobrecht.ch
² School of Chemistry, University of Leeds, Leeds LS2 9JT, UK
³ Departament de Ciència de Materials i Química Física, Institut de Química Teórica i Computacional (IQTCUB), Universitat de Barcelona, 08028 Barcelona, Spain
⁴ Institució Catalana de Recerca i Estudis Avanćats (ICREA), 08010 Barcelona, Spain
⁵ Institute of Astronomy, KU Leuven, 3000 Leuven, Belgium

Received: 24 July 2023
Accepted: 3 October 2023

Abstract

Context. Spinel (MgAl₂O₄) and krotite (CaAl₂O₄) are alternative candidates to alumina (Al₂O₃) as primary dust condensates in the atmospheres of oxygen-rich evolved stars. Moreover, spinel was proposed as a potential carrier of the circumstellar 13 μm feature. However, the formation of nucleating spinel clusters is challenging; in particular, the inclusion of Mg constitutes a kinetic bottleneck.

Aims. We aim to understand the initial steps of cosmic dust formation (i.e. nucleation) in oxygen-rich environments using a quantum-chemical bottom-up approach.

Methods. Starting with an elemental gas-phase composition, we constructed a detailed chemical-kinetic network that describes the formation and destruction of magnesium-, calcium-, and aluminium-bearing molecules as well as the smallest dust-forming (MgAl₂O₄)₁ and (CaAl₂O₄)₁ monomer clusters. Different formation scenarios with exothermic pathways were explored, including the alumina (Al₂O₃) cluster chemistry studied in Paper I of this series. The resulting extensive network was applied to two model stars, a semi-regular variable and a Mira-type star, and to different circumstellar gas trajectories, including a non-pulsating outflow and a pulsating model. We employed global optimisation techniques to find the most favourable (MgAl₂O₄)_n, (CaAl₂O₄)_n, and mixed (Mg_xCa_(1−x)Al₂O₄)_n isomers, with n = 1–7 and x∈[0..1], and we used high level quantum-chemical methods to determine their potential energies. The growth of larger clusters with n = 2–7 is described by the temperature-dependent Gibbs free energies.

Results. In the considered stellar outflow models, spinel clusters do not form in significant amounts. However, we find that in the Mira-type non-pulsating model CaAl₂O₃(OH)₂, a hydroxylated form of the calcium aluminate krotite monomer forms at abundances as large as 2 × 10⁻⁸ at 3 stellar radii, corresponding to a dust-to-gas mass ratio of 1.5 × 10⁻⁶. Moreover, we present global minimum (GM) candidates for (MgAl₂O₄)_n and (CaAl₂O₄)_n, where n = 1–7. For cluster sizes n = 3–7, we find new, hitherto unreported GM candidates. All spinel GM candidates found are energetically more favourable than their corresponding magnesium-rich silicate clusters with an olivine stoichiometry, namely (Mg₂SiO₄)_n. Moreover, calcium aluminate clusters, (CaAl₂O₄)_n, are more favourable than their Mg-rich counterparts; the latter show a gradual enhancement in stability when Mg atoms are substituted step by step with Ca.

Conclusions. Alumina clusters with a dust-to-gas mass ratio of the order of 10⁻⁴ remain the favoured seed particle candidate in our physico-chemical models. However, CaAl₂O₄ could contribute to stellar dust formation and the mass-loss process. In contrast, the formation of MgAl₂O₄ is negligible due to the low reactivity of the Mg atom.