2 Theoretical background

The term "Hot Bottom Burning'' (HBB) refers to nuclear processing that can take place at the bottom of the convective envelope of massive Asymptotic Giant Branch (AGB) stars during the TP phase. The observations of these stars in the Magellanic Cloud fields (Smith & Lambert 1989, 1990; Plez et al. 1993; Smith et al. 1995) reveal that the most luminous AGB stars are lithium rich. That is indeed satisfactorily explained by the theoretical models including HBB.

During the giant phase preceding the AGB, lithium is depleted by convective dilution. Therefore, if we find on the TP-AGB an abundance much higher than the residual from the preceding phases, we can safely conclude that lithium is manufactured "in situ''. Both the computations performed by considering only envelope models (Sackmann et al. 1974) and those of complete evolutionary models (Sackmann & Boothroyd 1992) show that a temporary enhancement of the lithium abundance in the atmosphere - in agreement with the previously mentioned observations - can be achieved through the chain , provided that the mixing is a non-instantaneous process (Cameron & Fowler 1971). The occurrence of nuclear burning at the bottom of the convective envelope is exemplified in Fig. 1, which shows the time evolution of luminosity and lithium abundance for a 4 $M_\odot$ stellar model ascending the AGB (from Ventura et al. 1999). The model has helium and metal mass fraction, respectively, Y=0.26 and Z=0.01. The lithium evolution in the AGB can be sketched as a sequence of four different phases: i) at the beginning of the AGB, the stellar photosphere has a residual lithium content that is a remnant from a previous convective dilution phase; ii) lithium is totally destroyed when the temperature at the bottom of the envelope increases above 10⁷ K; iii) later on, production via the Cameron - Fowler mechanism proceeds and a high lithium abundance is reached; iv) finally, after 10⁵ yr, lithium is depleted again, as a consequence of the exhaustion of ³He in the convective envelope. The stellar mass is, at this stage, 1.7 $M_\odot$, its mass loss rate is  $M_\odot$ yr^-1, and the carbon oxygen core mass is 0.82 $M_\odot$. The evolution will last about  yr longer, until the whole envelope is lost and the star evolves to the white dwarf stage.

Figure 1: The evolution of the bolometric magnitude (bottom curve, scale on the right) and of the lithium abundance (top curve, scale on the left) during the TP phase for a 4 $M_\odot$ with Z=0.01 (Ventura et al. 1999). The vertical lines indicate the possible evolutionary phase of the two most luminous AGB stars in NGC 1866.

The determination of ⁷Li abundance along the AGB provides information about the physical processes influencing the efficiency and the extent of mixing, and can help to validate the physical modeling of these processes in stellar interiors.