Full computation of massive AGB evolution - I. The large impact of convection on nucleosynthesis

It is well appreciated that the description of overadiabatic convection affects the structure of the envelopes of luminous asymptotic giant branch (AGB) stars in the phase of hot bottom burning (HBB). We stress that this important uncertainty in the modeling plays a role which is much more dramatic than the role which can be ascribed, e.g., to the uncertainty in the nuclear cross-sections. Due to the role tentatively attributed today to the HBB nucleosynthesis as the site of self-enrichment of Globular Clusters stars, it is necessary to explore the difference in nucleosynthesis obtained by different prescriptions for convection. We present results of detailed evolutionary calculations of the evolution of stars of intermediate mass during the AGB phase for the metallicity typical of the Globular Clusters that show the largest spread in CNO abundances (Z similar to 10(-3)). We follow carefully the nucleosynthesis at the base of the external convective region, showing that very different results can be obtained according to the presciption adopted to find out the temperature gradient within the instability regions. We discuss the uncertainties in the yields of the various chemical species and the role which these sources can play as polluters of the interstellar medium.