Context : Asymptotic giant branch ( AGB ) stars lose their envelopes by means of a stellar wind whose driving mechanism is not understood well .
Characterizing the composition and thermal and dynamical structure of the outflow provides constraints that are essential for understanding AGB evolution , including the rate of mass loss and isotopic ratios .

Aims : We characterize the CO emission from the wind of the low mass-loss rate oxygen-rich AGB star W Hya using data obtained by the HIFI , PACS , and SPIRE instruments onboard the Herschel Space Observatory and ground-based telescopes . ^ { 12 } CO and ^ { 13 } CO lines are used to constrain the intrinsic ^ { 12 } C/ ^ { 13 } C ratio from resolved HIFI lines .

Methods : We combined a state-of-the-art molecular line emission code and a dust continuum radiative transfer code to model the CO lines and the thermal dust continuum .

Results : The acceleration of the outflow up to about 5.5 km/s is quite slow and can be represented by a \beta -type velocity law with index \beta = 5 .
Beyond this point , acceleration up the terminal velocity of 7 km/s is faster .
Using the J = 10–9 , 9–8 , and 6–5 transitions , we find an intrinsic ^ { 12 } C/ ^ { 13 } C ratio of 18 \pm 10 for W Hya , where the error bar is mostly due to uncertainties in the ^ { 12 } CO abundance and the stellar flux around 4.6 \mu m. To match the low-excitation CO lines , these molecules need to be photo-dissociated at \sim 500 stellar radii .
The radial dust emission intensity profile of our stellar wind model matches PACS images at 70 \mu m out to 20 \arcsec ( or 800 stellar radii ) .
For larger radii the observed emission is substantially stronger than our model predicts , indicating that at these locations there is extra material present .

Conclusions : The initial slow acceleration of the wind may imply inefficient dust formation or dust driving in the lower part of the envelope .
The final injection of momentum in the wind might be the result of an increase in the opacity thanks to the late condensation of dust species .
The derived intrinsic isotopologue ratio for W Hya is consistent with values set by the first dredge-up and suggestive of an initial mass of 2 M _ { \odot } or more .
However , the uncertainty in the isotopologic ratio is large , which makes it difficult to set reliable limits on W Hya ’ s main-sequence mass .