The TP-AGB phase: A new model

This study deals with the TP-AGB phase of low and intermediate-mass stars (0.7 less than or similar to M/M(.) less than or similar to 5). To this aim, a semi-analytical model is constructed. A representative set of TP-AGB evolutionary models is calculated for two classes of initial metallicity (Z = 0.02 and Z = 0.008). A detailed analysis is performed to estimate the changes in the surface chemical composition caused by (1) the inter-shell nucleosynthesis and convective dredge-up; (2) nuclear burning in the deepest layers of the convective envelope; and (3) mass loss by stellar wind. The evolution of the abundances of 13 chemical elements (H, He-3, He-4, C-12, C-13, N-14, N-15, O-16, O-17, O-18, Ne-20, Ne-22, Mg-25) is followed. In particular, the formation of carbon stars is investigated. We use the observed luminosity function of carbon stars in the LMC as the constraint whose fulfillment determines the values of the parameters adopted in the model, namely: the minimum core mass for dredge-up M(c)(min) and the efficiency of the third dredge-up lambda. In this way, we derive a proper calibration which the reliability of the chemical analysis stands on. We calculate the stellar yields for both metallicities to provide new data for these key-ingredients in the process of chemical enrichment of the interstellar medium. The chemical composition of PNe is derived and compared to the latest experimental data both in the Galaxy and in the LMC, which leads to a partial agreement. Observed information on the correlation between luminosity and pulsational period of Mira and OH/IR variables is used to test further our results. Finally, we predict the initial-final mass relation and we compare it to the semi-empirically determined one for the solar neighbourhood. The agreement turns out to be satisfactory.