Constraints on the H2O formation mechanism in the wind of carbon-rich AGB stars

Context. The recent detection of warm H ₂O vapor emission from the outflows of carbon-rich asymptotic giant branch (AGB) stars challenges the current understanding of circumstellar chemistry. Two mechanisms have been invoked to explain warm H ₂O vapor formation. In the first, periodic shocks passing through the medium immediately above the stellar surface lead to H ₂O formation. In the second, penetration of ultraviolet interstellar radiation through a clumpy circumstellar medium leads to the formation of H ₂O molecules in the intermediate wind. Aims. We aim to determine the properties of H ₂O emission for a sample of 18 carbon-rich AGB stars and subsequently constrain which of the above mechanisms provides the most likely warm H ₂O formation pathway. Methods. Using far-infrared spectra taken with the PACS instrument onboard the Herschel telescope, we combined two methods to identify H ₂O emission trends and interpreted these in terms of theoretically expected patterns in the H ₂O abundance. Through the use of line-strength ratios, we analyzed the correlation between the strength of H ₂O emission and the mass-loss rate of the objects, as well as the radial dependence of the H ₂O abundance in the circumstellar outflow per individual source. We computed a model grid to account for radiative-transfer effects in the line strengths. Results. We detect warm H ₂O emission close to or inside the wind acceleration zone of all sample stars, irrespective of their stellar or circumstellar properties. The predicted H ₂O abundances in carbon-rich environments are in the range of 10 ^-6 up to 10 ^-4 for Miras and semiregular-a objects, and cluster around 10 ^-6 for semiregular-b objects. These predictions are up to three orders of magnitude greater than what is predicted by state-of-the-art chemical models. We find a negative correlation between the H ₂O/CO line-strength ratio and gas mass-loss rate for ? _g> 5 × 10 ^-7 M _? yr ^-1, regardless of the upper-level energy of the relevant transitions. This implies that the H ₂O formation mechanism becomes less efficient with increasing wind density. The negative correlation breaks down for the sources of lowest mass-loss rate, the semiregular-b objects. Conclusions. Observational constraints suggest that pulsationally induced shocks play an important role in warm H ₂O formation in carbon-rich AGB stars, although photodissociation by interstellar UV photons may still contribute. Both mechanisms fail in predicting the high H ₂O abundances we infer in Miras and semiregular-a sources, while our results for the semiregular-b objects are inconclusive.