Master equation modelling of non-equilibrium chemistry in stellar outflows

A current challenge in astrochemistry is to explain the formation of Fe-Mg silicate dust around evolved stars. The dust is observed to form within 2 to 3 stellar radii of oxygen-rich AGB stars, where the typical conditions are kinetic (translational) temperatures between 1200 and 1600 K, and total gas densities below 10¹¹ cm^-3. At these high temperatures, molecules with bond energies < 400 kJ mol^-1 should be short-lived, and this results in kinetic bottlenecks in postulated mechanisms for converting the observed Fe, Mg, SiO and H₂O into silicate. Here we show that, in the very low pressure regime of a stellar outflow, molecules can exhibit significant vibrational disequilibrium because optical transitions - both spontaneous and stimulated by the stellar radiation field - occur on a much faster timescale than collisions. As a result, relatively less stable molecules can form and survive long enough to provide building blocks to silicate formation. Here we use the molecule OSi(OH)₂, formed by the recombination of SiO₂ and H₂O, as an example. When vibrational disequilibrium is accounted for in a master equation treatment which includes optical transitions, the quantity of metal silicates produced in a low mass loss rate evolved star (R Dor) is increased by 6 orders of magnitude.