The wind of W Hya as seen by Herschel. II. The molecular envelope of W Hya

The evolution of low- and intermediate-mass stars on the asymptotic giant branch (AGB) is mainly controlled by the rate at which these stars lose mass in a stellar wind. Understanding the driving mechanism and strength of the stellar winds of AGB stars and the processes enriching their surfaces with products of nucleosynthesis are paramount to constraining AGB evolution and predicting the chemical evolution of galaxies. In a previous paper we have constrained the structure of the outflowing envelope of W Hya using spectral lines of the $^{12}$CO molecule. Here we broaden this study by modelling an extensive set of H$_{2}$O and $^{28}$SiO lines observed by the three instruments on board Herschel using a state-of-the-art molecular excitation and radiative transfer code. The oxygen isotopic ratios and the $^{28}$SiO abundance profile can be connected to the initial stellar mass and to crucial aspects of dust formation at the base of the stellar wind, respectively. The modelling of H$_{2}$O and $^{28}$SiO confirms the properties of the envelope model of W Hya derived from $^{12}$CO lines. We find an H$_2$O ortho-to-para ratio of 2.5\,$^{+2.5}_{-1.0}$, consistent with what is expected for an AGB wind. The O$^{16}$/O$^{17}$ ratio indicates that W Hya has an initial mass of about 1.5 M$_\odot$. Although the ortho- and para-H$_{2}$O lines observed by HIFI appear to trace gas of slightly different physical properties, a turbulence velocity of $0.7\pm0.1$ km s$^{-1}$ fits the HIFI lines of both spin isomers and those of $^{28}$SiO well. The ortho- and para-H$_2^{16}$O and $^{28}$SiO abundances relative to H$_{2}$ are $(6^{+3}_{-2}) \times 10^{-4}$, $(3^{+2}_{-1}) \times 10^{-4}$, and $(3.3\pm 0.8)\times 10^{-5}$, respectively. Assuming a solar silicon-to-carbon ratio, the $^{28}$SiO line emission model is consistent with about one-third of the silicon atoms being locked up in dust particles.