Connecting the evolution of thermally pulsing asymptotic giant branch stars to the chemistry in their circumstellar envelopes - I. Hydrogen cyanide

We investigate the formation of hydrogen cyanide (HCN) in the inner circumstellar envelopes of thermally pulsing asymptotic giant branch (TP-AGB) stars. A dynamic model for periodically shocked atmospheres, which includes an extended chemo-kinetic network, is for the first time coupled to detailed evolutionary tracks for the TP-AGB phase computed with the COLIBRI code. We carried out a calibration of the main shock parameters (the shock formation radius rs,0 and the effective adiabatic index γeffad) using the circumstellar HCN abundances recently measured for a populous sample of pulsating TP-AGB stars. Our models recover the range of the observed HCN concentrations as a function of the mass-loss rates, and successfully reproduce the systematic increase of HCN moving along the M-S-C chemical sequence of TP-AGB stars, which traces the increase of the surface C/O ratio. The chemical calibration brings along two important implications for the physical properties of the pulsation-induced shocks: (i) the first shock should emerge very close to the photosphere (rs,0 ≃ 1R), and (ii) shocks are expected to have a dominant isothermal character (γ eff ad ≃ 1) in the denser region close to the star (within ~ 3-4R), implying that radiative processes should be quite efficient. Our analysis also suggests that the HCN concentrations in the inner circumstellar envelopes are critically affected by the H-H2 chemistry during the post-shock relaxation stages. Given the notable sensitiveness of the results to stellar parameters, this paper shows that such chemodynamic analyses may indeed provide a significant contribution to the broader goal of attaining a comprehensive calibration of the TP-AGB evolutionary phase. © 2015 The Authors.