Developing a self-consistent AGB wind model: II. Non-classical, non-equilibrium polymer nucleation in a chemical mixture

Unravelling the composition and characteristics of gas and dust lost by asymptotic giant branch (AGB) stars is important as these stars play a vital role in the chemical life cycle of galaxies. The general hypothesis of their mass loss mechanism is a combination of stellar pulsations and radiative pressure on dust grains. However, current models simplify dust formation, which starts as a microscopic phase transition called nucleation. Various nucleation theories exist, yet all assume chemical equilibrium, growth restricted by monomers, and commonly use macroscopic properties for a microscopic process. Such simplifications for initial dust formation can have large repercussions on the type, amount, and formation time of dust. By abandoning equilibrium assumptions, discarding growth restrictions, and using quantum mechanical properties, we have constructed and investigated an improved nucleation theory in AGB wind conditions for four dust candidates, TiO$_2$, MgO, SiO and Al$_2$O$_3$. This paper reports the viability of these candidates as first dust precursors and reveals implications of simplified nucleation theories. Monomer restricted growth underpredicts large clusters at low temperatures and overpredicts formation times. Assuming the candidates are present, Al$_2$O$_3$ is the favoured precursor due to its rapid growth at the highest considered temperatures. However, when considering an initially atomic chemical mixture, only TiO$_2$-clusters form. Still, we believe Al$_2$O$_3$ to be the prime candidate due to substantial physical evidence in presolar grains, observations of dust around AGB stars at high temperatures, and its ability to form at high temperatures and expect the missing link to be insufficient quantitative data of Al-reactions.