Water in IRC+10216: a genuine formation process by shock-induced chemistry in the inner wind

Context. The presence of water in the wind of the extreme carbon star IRC+10216 has been confirmed by the Herschel telescope. The regions where the high-J H2O lines have been detected are close to the star at radii r <= 15 R-star. Aims. We investigate the formation of water and related molecules in the periodically-shocked inner layers of IRC+10216 where dust also forms and accelerates the wind. Methods. We describe the molecular formation by a chemical kinetic network involving carbon-and oxygen-based molecules. We then apply this network to the physical conditions pertaining to the dust-formation zone which experiences the passage of pulsationdriven shocks between 1 and 5 R-star. We solve for a system of stiff, coupled, ordinary, and differential equations. Results. Non-equilibrium chemistry prevails in the dust-formation zone. H2O forms quickly above the photosphere from the synthesis of hydroxyl OH induced by the thermal fragmentation of CO in the hot post-shock gas. The derived abundance with respect to H-2 at 5 R-star is 1.4 x 10(-7), which excellently agrees with the values derived from Herschel observations. The non-equilibrium formation process of water will be active whatever the stellar C/O ratio, and H2O should then be present in the wind acceleration zone of all stars on the Asymptotic Giant Branch.