Résumé
The purpose of this study is to understand the processes underpinning the formation of dust in oxygen-rich AGB stars, reproduce molecular abundances in the dust-formation zone, and derive dust-to-gas mass ratios for specific condensates. We model the inner wind of the O-rich Mira IK Tau by considering layers of gas above the stellar photosphere that are periodically crossed by pulsation-induced shocks. The formation of molecules and dust clusters follows a chemical kinetic approach, which includes the formation pathways to small clusters of silicates, alumina, and metal oxides. In order to derive grain size distributions, the dust nucleation phase is coupled to the condensation phase, which is described by a Brownian formalism.
Our results on molecules agree well with the most recent observations and confirm the crucial role of shocks in the making of carbon-rich molecules, such as HCN, CO2 and CS, in O-rich AGB inner winds. Alumina grains readily form in the shocked photosphere and the gas layers just above it. The nucleation of small silicate grains with forsterite stoichiometry proceeds through a new chemical route involving the dimerisation of HSiO. These clusters grow and condense around 4 R-*, and keep growing over several pulsation periods. The dust-to-gas mass ratio for silicates is similar to 2 x 10(-3), in good agreement with values characteristic of O-rich AGB stars.