  The nearby oxygen-rich AGB star L2 Pup hosts a well-studied nearly edge-on
disk. To date, disks around AGB stars have not been chemically studied in
detail. By combining a parameterisation commonly used for protoplanetary disks
and archival ALMA observations, we retrieved an updated density and temperature
structure of this disk. This physical model was then used as input to the first
chemical model of an AGB disk. The model shows that the physical structure of
the disk has a large impact on its chemistry, with certain species showing
large changes in column density relative to a radial outflow, indicating that
chemistry could be used as a tracer of disks that cannot be directly imaged.
Despite its oxygen-rich nature, the daughter species formed within the disk are
surprisingly carbon-rich. Two chemical regimes can be distinguished: cosmic-ray
induced chemistry in the midplane and photochemistry induced by the
interstellar radiation field in the outer regions. Certain complex organic
molecules are formed in the midplane. This occurs via gas-phase chemistry only,
as the disk is too warm for dust-gas chemistry. The photochemistry in the outer
regions leads to the efficient formation of (long) carbon-chains. The
predictions of the model allow us to tentatively put the disk's age $\lesssim
10^5$ yr. Additional observations are necessary to better constrain the
physical structure of L2 Pup's disk and are essential to test the predictions
made by the chemical model. Our exploratory work paves the way for a more
general study of the chemistry of AGB disks.
