ALMA observations show a non-detection of carbon monoxide around the four most luminous asymptotic giant branch (AGB) stars in the globular cluster 47 Tucanae. Stellar evolution models and star counts show that the mass-loss rates from these stars should be ~1.2-3.5 x 10^-7 solar masses per year. We would naively expect such stars to be detectable at this distance (4.5 kpc). By modelling the ultraviolet radiation field from post-AGB stars and white dwarfs in 47 Tuc, we conclude CO should be dissociated abnormally close to the stars. We estimate that the CO envelopes will be truncated at a few hundred stellar radii from their host stars and that the line intensities are about two orders of magnitude below our current detection limits. The truncation of CO envelopes should be important for AGB stars in dense clusters. Observing the CO (3-2) and higher transitions and targeting stars far from the centres of clusters should result in the detections needed to measure the outflow velocities from these stars.
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