Probing the mass-loss history of AGB and red supergiant stars from CO   rotational line profiles I. Theoretical model -- Mass-loss history unravelled   in VY CMa
  Context: Mass loss plays a dominant role in the evolution of low mass stars while they are on the Asymptotic Giant Branch (AGB). The gas and dust ejected during this phase are a major source in the mass budget of the interstellar medium. Recent studies have pointed towards the importance of variations in the mass-loss history of such objects. Aims: By modelling the full line profile of low excitation CO lines emitted in the circumstellar envelope, we can study the mass-loss history of AGB stars. Methods: We have developed a non-LTE radiative transfer code, which calculates the velocity structure and gas kinetic temperature of the envelope in a self-consistent way. The resulting structure of the envelope provides the input for the molecular line radiative calculations which are evaluated in the comoving frame. The code allows for the implementation of modulations in the mass-loss rate. This code has been benchmarked against other radiative transfer codes and is shown to perform well and efficiently. Results: We illustrate the effects of varying mass-loss rates in case of a superwind phase. The model is applied to the well-studied case of VY CMa. We show that both the observed integrated line strengths as the spectral structure present in the observed line profiles, unambiguously demonstrate that this source underwent a phase of high mass loss (~ 3.2E-4 Msun/yr) some 1000 yr ago. This phase took place for some 100 yr, and was preceded by a low mass-loss phase (~ 1E-6 Msun/yr) taking some 800 yr. The current 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 of the CO rotational line profiles and the (non)-occurrence of spectral structure in the profile offer strong diagnostics to pinpoint the mass-loss history. 
L. Decin, S. Hony, A. de Koter, K. Justtanont, A.G.G.M. Tielens,   L.B.F.M. Waters