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Astron. Astrophys. 358, L49-L52 (2000)

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2. Extra-mixing in red giants

The 1st dredge-up episode ends when the BCE stops its excursion into the star and begins to retreat. According to the standard theory, after this moment the surface composition is not expected to change further on the RGB. However, this expectation is not supported by observations. It appears that in low-mass field red giants the surface abundances of C, N, and Li as well as the 12C/13C ratio, and in globular cluster red giants even O, Na, Mg and Al, do continue to change up to the RGB tip. This discrepancy has been quite satisfactorily explained by red giants models with extra-mixing placed between the HBS and the BCE (see Denissenkov & Tout 2000, and references therein). Such extra-mixing is commonly believed to work only in radiative regions with a nearly uniform composition. Therefore, it is expected to come into play after the HBS, moving outwards in mass, will have erased the H-discontinuity left behind by the retreating BCE. Standard model calculations show that the HBS arrives at the H-discontinuity while the star is still on the RGB only in low-mass stars, which is well confirmed by observations (Charbonnel 1994).

Quite recently Gratton et al. (1999) have determined Li, C, N, O and Na abundances and 12C/13C ratios for a large sample of field stars with accurate luminosity estimates in the metallicity range [FORMULA] [Fe/H] [FORMULA]. In Fig. 1 we compare [FORMULA], [C/Fe] ([A/B] means [FORMULA]), [FORMULA] and [N/Fe] for these stars with results of calculations obtained with the method and code of Denissenkov & Weiss (1996) in which extra-mixing is modeled by diffusion in a post-processing approach, which uses full stellar evolution models as background models for the parameterized diffusion and nucleosynthesis. One can see that the behaviour of the plotted abundances on the upper-RGB ([FORMULA], following the nomenclature of Gratton et al. 1999) is quite well reproduced by the diffusive mixing with a depth [FORMULA] ([FORMULA] is a relative mass coordinate such that [FORMULA] at the bottom of the HBS and [FORMULA] at the BCE) and a rate [FORMULA] = [FORMULA] (for details about method and results, see also Denissenkov & Weiss 1996).

[FIGURE] Fig. 1. Li, C, N abundances and 12C/13C ratios in field stars with accurate luminosity estimates in the metallicity range [FORMULA] [Fe/H] [FORMULA] (Gratton et al. 1999); open squares are upper (for Li) or lower (for 12C/13C) limits). Dotted and dashed horizontal segments mark the main sequence and 1st dredge-up luminosity ranges, respectively. Solid lines were calculated with extra-mixing modeled by diffusion with depth [FORMULA] and rate [FORMULA] = [FORMULA].

From the upper panel of Fig. 1 one can infer that (i) most of the Pop. II main sequence stars preserve the initial Li abundance in their atmospheres ([FORMULA] for Pop. II stars), (ii) during the 1st dredge-up Li is diluted exactly down to the level predicted by the standard theory (Sackmann & Boothroyd 1999), and (iii) extra-mixing on the upper-RGB further decreases the surface Li abundance; extra-mixing is therefore a necessary ingredient to explain this behaviour.

Contrary to the field Pop. II giants which show neither O depletion nor Na enhancement, in globular clusters there are star-to-star variations of both O and Na on the RGB. Even more important is the fact that in globular cluster red giants Na anticorrelates with O (Fig. 2, symbols). A summary of the observational status can be found in Sneden (1999). The global anticorrelation of [Na/Fe] vs. [O/Fe] can be explained by extra-mixing as well (Denissenkov & Weiss 1996), but in this case deeper mixing is required. In Fig. 2 we compare observational data with a sample calculation (solid line, calculated with [FORMULA], [FORMULA] = [FORMULA]). The corresponding evolution of the surface Li abundance for this case is plotted in Fig. 3 (line 3a). We note that in all our cases (Fig. 1, solid lines; Figs. 2 and 3) the calculations with extra-mixing start from the same red giant model with [FORMULA], [FORMULA] and a heavy elements content of [FORMULA] ([Fe/H] [FORMULA]). Because of the shallower mixing in the models of the field Pop. II stars no Na was produced in that case, as observed (Gratton et al. 1999).

[FIGURE] Fig. 2. The global [Na/Fe] vs. [O/Fe] anticorrelation in globular cluster red giants and its theoretical reproduction by diffusive extra-mixing with depth [FORMULA] and rate [FORMULA] = [FORMULA] (solid line). Open squares are M 3 giants from the recent Li-study of Kraft et al. (1999). The Li-rich giant IV-101 is shown by the arrow. Data from Kraft et al. (1992; M3), Kraft et al. (1997; M13), Sneden et al. (1997; M15), Shetrone (1996; M92)

[FIGURE] Fig. 3. Evolution of the surface 7Li abundance on the upper-RGB caused by extra-mixing. The mixing parameters used in our calculations (for which we used code and method described in Denissenkov & Weiss 1996) are 1 : [FORMULA] ([FORMULA]), a - [FORMULA] = [FORMULA], b - [FORMULA] = [FORMULA], c - [FORMULA] = [FORMULA]; 2 : [FORMULA], [FORMULA] =[FORMULA]; 3a,b : [FORMULA], [FORMULA] = [FORMULA]; 3c : [FORMULA] decreases with time by 0.01 every [FORMULA] years from 0.16 to 0.06 and after that retains the constant value 0.06, [FORMULA] = [FORMULA] during all this time. Open squares and asterisks are M3 and Berkeley 21 giants from the recent Li-studies of Kraft et al. (1999) and Hill & Pasquini (1999), respectively.

To conclude, extra-mixing (with specific values for mixing depth and speed) is necessary to explain abundance trends in the majority of field giants and abundance anomalies in a large number of globular cluster giants. We now turn to the even more peculiar effect of Li-richness.

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Online publication: June 8, 2000