Chemical modelling of dust-gas chemistry within AGB outflows -- II. Effect of the dust-grain size distribution

AGB stars are, together with supernovae, the main contributors of stellar dust to the interstellar medium (ISM). Dust grains formed by AGB stars are thought to be large. However, as dust nucleation and growth within their outflows are still not understood, the dust-grain size distribution (GSD) is unknown. This is an important uncertainty regarding our knowledge of the chemical and physical history of interstellar dust, as AGB dust forms $\sim$ 70% of the starting point of its evolution. We expand on our chemical kinetics model, which uniquely includes a comprehensive dust-gas chemistry. The GSD is now allowed to deviate from the commonly assumed canonical Mathis et al. (1977) distribution. We find that the specific GSD can significantly influence the dust-gas chemistry within the outflow. Our results show that the level of depletion of gas-phase species depends on the average grain surface area of the GSD. Gas-phase abundance profiles and their possible depletions can be retrieved from observations of molecular emission lines when using a range of transitions. Due to degeneracies within the prescription of GSD, specific parameters cannot be retrieved, only (a lower limit to) the average grain surface area. Nonetheless, this can discriminate between dust composed of predominantly large or small grains. We show that when combined with other observables such as the spectral energy distribution and polarised light, depletion levels from molecular gas-phase abundance profiles can constrain the elusive GSD of the dust delivered to the ISM by AGB outflows.