9. Conclusions and prospects

We tried to confirm and improve our present knowledge of the structural and nucleosynthetic evolution of intermediate-mass AGB stars. To do that, we have first presented in detail (i) the physics and numerical aspects of our stellar evolution code, (ii) results concerning evolution phases prior to the AGB one and (iii) comparisons with other works. These informations are essential to better understand and appraise the large set of predictions we discuss about the thermally pulsing AGB stage. We also compare our predictions with various observations (at different evolutionary stages) in order to clearly identify the processes that should be included in future models.

Let us just mention global key features stemming from our intermediate-mass evolution models.

• Concerning the structure (intensities, temperatures) of the thermal pulses as well as the thermal properties at the base of the convective envelope, the most decisive quantities are the total mass and core mass. Both change with time in a way that is governed by the increasing mass loss rate. This translates into a great sensitivity of the various nucleosynthesis processes to the adopted mass loss rate. Consequently, the evolution of the thermal pulse characteristics crucially depend on this last quantity, unfortunately still rather badly known. In addition, the lower the mass loss rates, the longer the TP-AGB phase, the more third dredge-up events have time to occur and the greater are the surface abundance changes due to HBB. This is clearly demonstrated by the high sensitiveness of the predicted surface evolution of almost all the isotopic ratios to the mass loss rate dependence on time.
• On the other hand, at a given total stellar mass, core masses are greater for lower metallicities, as a result of the central burning phases. As a consequence, for the reason mentioned at the former point, TP-AGB stars with Z = 0.005 mostly behave like Z = 0.02 ones with a total mass greater by . However, due to important differences in initial compositions that also influence the nuclear reactions, this is not completely true as far as isotopic ratios are concerned. At the end of the TP-AGB phase indeed, some yields are quite different for both Z we have studied.
• The neutron captures on intermediate-mass and heavy nuclides occur in two distinct sites inside TP-AGB stars, namely (i) at the base of the inter-shell zone during the inter-pulse phase and, as already known, (ii) inside the convective tongues associated with thermal pulses. Along the asymptotic TP-AGB, the amount of produced neutrons is rather independent of the initial total mass and metallicity (at least for intermediate-mass objects).
• Concerning chemical evolution of galaxies, intermediate-mass stars, at the end of their existence, appear to be rather significant producers of , , (most massive and/or higher Z stars), , , , , , , and . A found trend, compared to observations, however clearly supports the idea that most of the present in the interstellar medium has to come from low-mass AGB stars (that point has to be confirmed by forthcoming evolutionary models).

  Intermediate-mass AGB stars also substantially produce radio-nuclides, namely and . The former one mostly comes from lower mass stars while it is the contrary for the last one.

  These stars partially deplete the interstellar medium content in (less massive stars), , , , , and .

We finish by recalling the major problems that, among all the present intermediate-mass AGB models, remain to be solved.

• We have not yet identified the additional source needed to quantitatively explain the s-process. This process is however required in order to account for many observations unquestionably indicating that AGB stars are responsible for the main component of the solar system heavy element distribution. Some suggestions have been made. Radiative diffusion operating during the TP-AGB phase of low-mass stars could substantially help. Although already invoked, such a process has never been yet included in AGB star evolution models.
• The rather high level of production detected at the surface of some evolved but relatively faint AGB stars of our galaxy still remains unaccountable. Thus, the Cameron-Fowler mechanism does not explain all the super-lithium-rich AGB stars. As these galactic objects have relatively low initial masses, the explanation could also come from the radiative slow-transport processes above mentioned.
• Last but not least, some C stars are observed, especially in the galactic bulge, with low luminosities at which the models fail at predicting the occurrence of the third dredge-up. This is probably due to our bad knowledge (and treatment) of finely tuned convection motions in boundaries of stellar regions having strong chemical composition gradients. Clearly, some kind of extra-mixing (deeper inside nuclearly processed regions) has to be invoked. However, no self-consistent mechanism has been settled and tested through complete evolution models up to now.

Other confrontations with observations require the modeling of low-mass AGB stars. A clear distinction between low- and intermediate-mass stars is justified. Indeed, numerous observations indicate that ``non-standard'' particle transport processes are acting inside low-mass stars at different phases of their evolution, that substantially modify the chemical structure compared to what is obtained in classical models. During the various dredge-up episodes, matter up-heaved to the surface has consequently a different composition. This is not the case in intermediate-mass stars. In conclusion, low-mass AGB stellar models, maintaining to make detailed predictions concerning the evolution of surface isotopic ratios, have to include such slow-particle transport processes. They are currently being calculated and will be presented in a next-coming paper.

Acknowledgements

We are first indebted to Maurizio Busso, the referee, for its very careful reading of our manuscript that helped us to significantly improve and clarify it. We also thank him and Roberto Gallino for the very instructive discussions we already had together about these very complex AGB stars. Let us finally thank Lionel Siess for his always valuable contributions to improve the stellar evolution code and related utilities. Part of the computations presented in this paper (roughly representing 7 months of CPU time) were performed at the ``Center de Calcul Intensif de l'Observatoire de Grenoble''. Most of them have been realized at ``IMAG'' on a IBM SP1 computer financed by the MESR, CNRS and Région Rhône-Alpes. This work was supported by grants from the GDR ``Structure Interne des Etoiles et des Planètes Géantes'' (CNRS).