Silicate condensation in Mira variables

Context. The formation of dust in winds of cool and highly evolved stars and the rate of injection of dust into the interstellar medium is not yet completely understood, despite the importance of the process for the evolution of stars and galaxies. This holds in particular for oxygen-rich stars, where it is still not known which process is responsible for the formation of the necessary seed particles of their silicate dust. Aims. We study whether the condensation of silicate dust in Mira envelopes could be caused by cluster formation by the abundant SiO molecules. Methods. We solve the dust nucleation and growth equations in the co-moving frame of a fixed mass element for a simplified model of the pulsational motions of matter in the outer layers of a Mira variable, which is guided by a numerical model for Mira pulsations. It is assumed that seed particles form through the clustering of SiO. The calculation of the nucleation rate is based on published experimental data. The quantity of dust formed is calculated via a moment method and the calculation of radiation pressure on dusty gas is based on a dirty silicate model. Results. Dust nucleation occurs in the model at the upper culmination of the trajectory of a gas parcel where it stays for a considerable time at low temperatures. Subsequent dust growth occurs during the descending part of the motion and continues after the next shock reversed motion. It is found that sufficient dust forms that radiation pressure exceeds the gravitational pull of the stars such that the mass element is finally driven out of the star. Conclusions. Nucleation of dust particles by clustering of the abundant SiO molecules could be the mechanism that triggers silicate dust formation in Miras.