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Context: Mass loss plays a dominant role in the evolution of low mass starswhile they are on the Asymptotic Giant Branch (AGB). The gas and dust ejectedduring this phase are a major source in the mass budget of the interstellarmedium. Recent studies have pointed towards the importance of variations in themass-loss history of such objects. Aims: By modelling the full line profile oflow excitation CO lines emitted in the circumstellar envelope, we can study themass-loss history of AGB stars. Methods: We have developed a non-LTE radiativetransfer code, which calculates the velocity structure and gas kinetictemperature of the envelope in a self-consistent way. The resulting structureof the envelope provides the input for the molecular line radiativecalculations which are evaluated in the comoving frame. The code allows for theimplementation of modulations in the mass-loss rate. This code has beenbenchmarked against other radiative transfer codes and is shown to perform welland efficiently. Results: We illustrate the effects of varying mass-loss ratesin case of a superwind phase. The model is applied to the well-studied case ofVY CMa. We show that both the observed integrated line strengths as thespectral structure present in the observed line profiles, unambiguouslydemonstrate that this source underwent a phase of high mass loss (~ 3.2E-4Msun/yr) some 1000 yr ago. This phase took place for some 100 yr, and waspreceded by a low mass-loss phase (~ 1E-6 Msun/yr) taking some 800 yr. Thecurrent mass-loss rate is estimated to be in the order of 8E-5 Msun/yr.Conclusions: In this paper, we demonstrate that both the relative strength ofthe CO rotational line profiles and the (non)-occurrence of spectral structurein the profile offer strong diagnostics to pinpoint the mass-loss history.

Probing the mass-loss history of AGB and red supergiant stars from CO rotational line profiles