Deep Mixing in Evolved Stars. II. Interpreting Li Abundances in RGB and AGB Stars

We reanalyze the problem of Li abundances in red giants of nearly solar metallicity. After an outline of the problems affecting our knowledge of the Li content in low-mass stars (M<3Mo), we discuss deep-mixing models for the RGB stages suitable to account for the observed trends and for the correlated variations of the carbon isotope ratio; we find that Li destruction in these phases is limited to masses below about 2.3 Mo. Subsequently, we concentrate on the final stages of evolution for both O-rich and C-rich AGB stars. Here, the constraints on extra-mixing phenomena previously derived from heavier nuclei (from C to Al), coupled to recent updates in stellar structure models (including both the input physics and the set of reaction rates used), are suitable to account for the observations of Li abundances below A(Li)= log e(Li) = 1.5 (and sometimes more). Also their relations with other nucleosynthesis signatures of AGB phases (like the abundance of F, the C/O and 12C/13C ratios) can be explained. This requires generally moderate efficiencies (\dot M <= 0.3 - 0.5 x 10^-6 Mo/yr) for non-convective mass transport. At such rates, slow extra-mixing does not modify remarkably Li abundances in early-AGB phases; on the other hand, faster mixing encounters a physical limit in destroying Li, set by the mixing velocity. Beyond this limit, Li starts to be produced; therefore its destruction on the AGB is modest. Li is then significantly produced by the third dredge up. We also show that effective circulation episodes, while not destroying Li, would easily bring the 12C/13C ratios to equilibrium, contrary to the evidence in most AGB stars, and would burn F beyond the limits shown by C(N) giants. Hence, we do not confirm the common idea that efficient extra-mixing drastically reduces the Li content of C-stars with respect to K-M giants.