Context. This paper explores the role of initial elemental abundances in the nuclosynthesis of massive asymptotic giant branch (AGB) stars and second generation abundances in globular clusters. Aims. We look at the difficulties found with AGB models when fully reproducing the abundance patterns in second generation stars of globular clusters, and we focus on sodium destruction in models that reach the high hot bottom burning temperatures needed to efficiently cycle oxygen to nitrogen. Methods. We built AGB models at the nominal Fe/H of the cluster NGC 2808. We increased the initial neon abundance by a factor of two to four with respect to the ‘standard’ abundances obtained by scaling the solar values down to the metallicity of this cluster, and explored the average abundances in the ejecta obtained by adopting smaller mass-loss rates. Results. Higher neon produces higher sodium in the AGB envelope. Lowering the mass-loss rate enables reasonably large sodium abundances to be kept and the depletion of oxygen and magnesium to increase. A balance between the lower mass-loss rates and the necessity of not increasing the episodes of third dredge up too much gives a neon abundance that is larger by a factor of two and a mass-loss rate thgbt is smaller by a factor of four as the best compromise. A comparison with the abundances in NGC 2808 shows a better breement than the standard models for all the patterns of abundances, but the extreme stars (group E) cannot be explained in this way. Models with an initial mass ≥ 6.5 M⊙ for the same chemistry (super-AGBs) are closer to the E data, but the oxygen depletion remains too small. We also computed models slightly less rich in iron, and show that the super-AGB ejecta composition becomes more compatible with the data. Thus, we propose that the extreme population in NGC 2808 is composed of stars that have a slightly smaller metallicity, and we sketch a possible scenario for its formation within the framework of the hierarchical clusters assembly scenario. Finally, abundances of potassium are larger by ∼0.2 dex in the E group. An explanation in terms of burning of the initial argon requires a drastic increase of the relevant cross section that is similar to the adjustment required in the exploratory models for cluster NGC 2419, but it becomes easier when we assume a larger initial argon abundance. Conclusions. The abundances of the noble gases neon and argon at low metallicities may be an important tool to better reproduce the abundances of light elements in the framework of the AGB model for globular clusters. The larger Ne and Ar abundances we need may either be a plain consequence of the uncertainties in the solar abundances of these elements or in part arise from an incomplete summing up of the sources for their nucleosynthesis at low metallicity. Thus we launch a plea for a better understanding of their galactic chemical evolution of noble gases.
Ventura et al. (Thu,) studied this question.