We present submillimeter observations of rotational transitions of carbon monoxide from J = 2 -> 1 up to 7 -> 6 for a sample of Asymptotic Giant Branch stars and red supergiants. It is the first time that the high transitions J = 6 -> 5 and 7 -> 6 are included in such a study. With line radiative transfer calculations, we aim to determine the mass-loss history of these stars by fitting the CO line intensities. We find that the observed line intensities of the high transitions, including the J = 4 -> 3 transition, are significantly lower than the predicted values. We conclude that the physical structure of the outflow of Asymptotic Giant Branch stars is more complex than previously thought. In order to understand the observed line intensities and profiles, a physical structure with a variable mass-loss rate and/or a gradient in stochastic gas velocity is required. A case study of the AGB star WX Psc is performed. We find that the CO line strengths may be explained by variations in mass-loss on time scales similar to those observed in the separated arc-like structures observed around post-AGB stars. In addition, a gradient in the stochastic velocity may play a role. Until this has been sorted out fully, any mass loss determinations based upon single CO lines will remain suspect.
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