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Circumstellar molecular composition of the oxygen-rich AGB star IK~Tau: II. In-depth non-LTE chemical abundance analysis

Aims: Little information exists on the circumstellar molecular abundance stratifications of many molecules. The aim is to study the circumstellar chemical abundance pattern of 11 molecules and isotopologs ($^{12}$CO, $^{13}$CO, SiS, $^{28}$SiO, $^{29}$SiO, $^{30}$SiO, HCN, CN, CS, SO, SO$_2$) in the oxygen-rich evolved star IK~Tau. Methods: We have performed an in-depth analysis of a large number of molecular emission lines excited in the circumstellar envelope around IK~Tau. The analysis is done based on a non-local thermodynamic equilibrium (non-LTE) radiative transfer analysis, which calculates the temperature and velocity structure in a self-consistent way. The chemical abundance pattern is coupled to theoretical outer wind model predictions including photodestruction and cosmic ray ionization. Not only the integrated line intensities, but also the line shapes, are used as diagnostic tool to study the envelope structure. Results: The deduced wind acceleration is much slower than predicted from classical theories. SiO and SiS are depleted in the envelope, possibly due to the adsorption onto dust grains. For HCN and CS a clear difference with respect to inner wind non-equilibrium predictions is found, either indicating uncertainties in the inner wind theoretical modeling or the possibility that HCN and CS (or the radical CN) participate in the dust formation. The low signal-to-noise profiles of SO and CN prohibit an accurate abundance determination; the modeling of high-excitation SO$_2$ lines is cumbersome, possibly related to line misidentifications or problems with the collisional rates. The SiO isotopic ratios ($^{29}$SiO/$^{28}$SiO and $^{30}$SiO/$^{28}$SiO) point toward an enhancement in $^{28}$SiO compared to results of classical stellar evolution codes. Predictions for H$_2$O lines in the spectral range of the Herschel/HIFI mission are performed. [abbreviated]