Circumstellar envelopes around asymptotic giant branch (AGB) stars contain a rich diversity of molecules, whose spatial distribution is regulated by different chemical and physical processes. In the outer circumstellar layers, all molecules are efficiently destroyed due to interactions with interstellar ultraviolet photons. Here we aim to carry out a coherent and uniform characterization of the radial extent of three molecules (SiO, CS, and SiS) in envelopes around O- and C-rich AGB stars, and to study their dependence on mass-loss rate. To this end, we observed a reduced sample of seven M-type and seven C-type AGB envelopes in multiple lines of SiO, CS, and SiS with the Yebes 40 m and IRAM 30 m telescopes. The selected sources cover a wide range of mass-loss rates, from ~10−7 M⊙ yr−1 to a few times 10−5 M⊙ yr−1, and the observed lines cover a wide range of upper-level energies, from 2 K to 130 K. We carried out excitation and radiative transfer calculations over a wide parameter space in order to characterize the abundance and radial extent of each molecule. A χ2 analysis indicates that the abundance is usually well constrained while the radial extent is in some cases more difficult to constrain. Our results indicate that the radial extent of the molecules considered here increases with increasing envelope density, in agreement with previous observational findings. At high envelope densities of Ṁ/υ∞ > 10−6 M⊙ yr−1 km−1 s, SiO, CS, and SiS show a similar radial extent, while at low envelope densities of Ṁ/υ∞ < 10−7 M⊙ yr−1 km−1 s, differences in radial extent appear among the three molecules, in agreement with theoretical expectations based on destruction due to photodissociation. At low envelope densities, we find a sequence of increasing radial extent, SiS → CS → SiO. We also find a tentative dependence of the radial extent on the chemical type (O- or C-rich) of the star for SiO and CS. Interferometric observations and further investigation of the photodissociation of SiO, CS, and SiS should provide clarification of the situation in regards to the relative photodissociation radii of SiO, CS, and SiS in AGB envelopes and their dependence on envelope density and C/O ratio.
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