Determining the effects of clumping and porosity on the chemistry in a non-uniform AGB outflow

Context. In the inner regions of asymptotic giant branch (AGB) outflows, several molecules have been detected with abundances much higher than those predicted from thermodynamic equilibrium chemical models. The presence of the majority of these species can be explained by shock-induced non-equilibrium chemical models, where shocks caused by the pulsating star take the chemistry out of equilibrium in the inner region. Moreover, a non-uniform density structure has been detected in several AGB outflows. Both large-scale structures, such as spirals and disks, and small-scale density inhomogeneities or clumps have been observed. These structures may also have a considerable impact on the circumstellar chemistry. A detailed parameter study on the quantitative effects of a non-homogeneous outflow has so far not been performed. Aims. We examine the effects of a non-uniform density distribution within an AGB outflow on its chemistry by considering a stochastic, clumpy density structure. Methods. We implement a porosity formalism for treating the increased leakage of light associated with radiation transport through a clumpy, porous medium. We then use this method to examine the effects from the altered UV radiation field penetration on the chemistry, accounting also for the increased reaction rates of two-body processes in the overdense clumps. The specific clumpiness is determined by three parameters: the characteristic length scale of the clumps at the stellar surface, the clump volume filling factor, and the inter-clump density contrast. In this paper, the clumps are assumed to have a spatially constant volume filling factor, which implies that they expand as they move outward in the wind. Results. We present a parameter study of the effect of clumping and porosity on the chemistry throughout the outflow. Both the higher density within the clumps and the increased UV radiation field penetration have an important impact on the chemistry, as they both alter the chemical pathways throughout the outflow. The increased amount of UV radiation in the inner region leads to photodissociation of parent species, releasing the otherwise deficient elements. We find an increased abundance in the inner region of all species not expected to be present assuming thermodynamic equilibrium chemistry, such as HCN in O-rich outflows, H2O in C-rich outflows, and NH3 in both. Conclusions. A non-uniform density distribution directly influences the chemistry throughout the AGB outflow, both through the density structure itself and through its effect on the UV radiation field. Species not expected to be present in the inner region of the outflow assuming thermodynamic equilibrium chemistry are now formed in this region, including species that are not formed in greater abundance by shock-induced non-equilibrium chemistry models. Outflows whose clumps have a large overdensity and that are very porous to the interstellar UV radiation field yield abundances comparable to those observed in O-rich and C-rich outflows for most of the unexpected species investigated. The inner wind abundances of H2O in C-rich outflows and of NH3 in O-rich and C-rich outflows are however underpredicted.