We investigate the structure, dynamics, and chemistry of the molecule-rich nebula around the stellar symbiotic system R Aqr, which is significantly affected by the presence of a white dwarf (WD) companion. We study the effects of the strong dynamical interaction between the AGB wind and the WD and of photodissociation by the WD UV radiation on the circumstellar shells. We obtained high-quality ALMA maps of the 12CO J=2-1, J=3-2, and J=6-5 lines and of 13CO J=3-2. The maps were analyzed by means of a heuristic 3D model that is able to reproduce the observations. In order to interpret this description of the molecule-rich nebula, we performed sophisticated calculations of hydrodynamical interaction and photoinduced chemistry. We find that the CO-emitting gas is distributed within a relatively small region <~ 1.5. Its structure consists of a central dense component plus strongly disrupted outer regions, which seem to be parts of spiral arms that are highly focused on the orbital plane. The structure and dynamics of these spiral arms are compatible with our hydrodynamical calculations. We argue that the observed nebula is the result of the dynamical interaction between the wind and the gravitational attraction of the WD. We also find that UV emission from the hot companion efficiently photodissociates molecules except in the densest and best-shielded regions, that is, in the close surroundings of the AGB star and some shreds of the spiral arms from which the detected lines come. We can offer a faithful description of the distribution of nebular gas in this prototypical source, which will be a useful template for studying material around other tight binary systems.
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