Deep Mixing in Evolved Stars. II. Interpreting Li Abundances in Red Giant Branch and Asymptotic Giant Branch Stars

We reanalyze the problem of Li abundances in red giants of nearly solar metallicity. After outlining the problems affecting our knowledge of the Li content in low-mass stars (M <= 3 M sun), we discuss deep-mixing models for the red giant branch 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 M sun. Subsequently, we concentrate on the final stages of evolution for both O-rich and C-rich asymptotic giant branch (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 epsilon(Li) ~= 1.5 (and sometimes more). Also, their relations with other nucleosynthesis signatures of AGB phases (like the abundance of F, and the C/O and 12C/13C ratios) can be explained. This requires generally moderate efficiencies (\dot{M} \lesssim 0.3{--}0.5 \times 10^{-6} \,M_{\odot } yr-1) for non-convective mass transport. At such rates, slow extra mixing does not remarkably modify 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. This misleading appearance is induced by biases in the data, namely: (1) the difficulty of measuring very low Li abundances in O-rich AGB stars due to the presence of TiO bands and (2) the fact that many, relatively massive (M > 3 M sun) K- and M-type giants may remain Li-rich, not evolving to the C-rich stages. Efficient extra mixing on the AGB is instead typical of very low masses (M <~ 1.5 M sun). It also characterizes CJ stars, where it produces Li and reduces F and the carbon isotope ratio, as observed in these peculiar objects.