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Astron. Astrophys. 332, 204-214 (1998)

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3. The onset of extra-mixing on the observed evolutionary sequence

Our observational results are summarized by referring to Figs. 1 to 3. We show in Fig. 1 the observed dependence of [FORMULA] ratio on [FORMULA]. This sequence for our sample of stars with moderate metal deficiencies reveals a behavior of the surface [FORMULA] ratio very similar to the one previously observed at solar metallicity in M67. Three main features appear: (i) The least luminous star, [FORMULA] Ori, shows a depletion of Li by 2.7 dex below the level accepted for young stars and a limit on the [FORMULA] ratio in agreement with standard predictions for dilution 2 This indicates that the standard theoretical main sequence profiles of [FORMULA] and [FORMULA] match the real chemical profiles, and that the extra-mixing is only efficient after the completion of the first dredge-up (see C94). (ii) Then between [FORMULA] = +0.9 and +0.5, the observed isotopic ratio drops to values near 7, well below the standard predicted post-dilution ratio. It is interesting to note that in the RGB luminosity function of 47 Tuc, King, et al. (1985) localize the bump at [FORMULA], i.e. precisely in the region where the disagreement between standard predictions and observations of the carbon isotopic ratio appears in our sample. This confirms that the extra-mixing which leads to very low [FORMULA] ratios in low-mass and metal-deficient evolved stars becomes efficient exactly when the hydrogen-burning shell crosses the chemical discontinuity created by the outward moving convective envelope. (iii) Finally, from [FORMULA] = +0.4 to -2, there is no further change in the [FORMULA] ratio.

[FIGURE] Fig. 1. The ratio of [FORMULA] is plotted against the bolometric magnitude of the program stars. Uncertainties of [FORMULA] 2 for the isotope ratios are estimated for each star except for Arcturus, for which [FORMULA] 1 is estimated. The absolute magnitudes are derived from the HIPPARCOS parallaxes. Note that 47 Tuc 3501 and 4418 have both the same luminosity and carbon isotopic ratio. The horizontal line indicates the position of the bump in the luminosity function of 47 Tuc (King et al. 1985).

[FIGURE] Fig. 2. Carbon isotopic ratios for the old disk giants by Cottrell & Sneden (1986; crosses) and Shetrone et al.(1993; open circles and triangles)). Our program stars are also shown (black circles and triangle). Observations for the same stars are connected by broken lines. The absolute magnitudes are derived from the HIPPARCOS parallaxes. The horizontal line indicates the position of the bump in the luminosity function of 47 Tuc (King et al. 1985).

[FIGURE] Fig. 3. Log [FORMULA] against [FORMULA] for the program stars. The uncertainty in log [FORMULA] is estimated to be 0.2 dex except for Arcturus, for which it is probably 0.1 dex. The horizontal line indicates the position of the bump in the luminosity function of 47 Tuc (King et al. 1985).

The "abrupt" change in [FORMULA] ratio shortly after the luminosity-function bump occurs both at solar and at lower metallicities, although the final [FORMULA] ratio is lower in the more metal-poor stars. It is worth noting that the change in [FORMULA] ratio is "abrupt" only in terms of stellar luminosity. The LFB is caused by a slower rate of evolution for stars at this luminosity (that is, [FORMULA] is smaller there) owing to the H-burning shell contacting the H-rich, previously mixed, zone; of the time stars take to evolve from the beginning of the LFB to the tip of the giant branch, 15 - 20% of it is spent in the LFB. Consequently, the change in the [FORMULA] ratio may not be so abrupt in terms of time.

In order to enlarge our sample, we recomputed the absolute magnitudes from the HIPPARCOS parallaxes for the old disk giants with [FORMULA] ratios derived by SSP93. These stars also have moderate metal deficiencies (-1.0 [FORMULA] [Fe/H] [FORMULA] -0.3) . Due to the good luminosity determination, the complete data, which are presented in Fig. 2, can be reasonably viewed as an evolutionary sequence. We also show the [FORMULA] ratios previously derived by Cottrell & Sneden (1986) for the stars which belong to the SSP93 sample.

The SSP93 isotope ratios tend to be systematically higher than the Cottrell & Sneden values for stars with high [FORMULA], but this is easily understood as being due to SSP93's superior spectral resolution. The higher spectral resolution allows detection and better measurement of the very weak [FORMULA] features. This highlights a general problem in the determination of [FORMULA] ratios: three effects operate to make [FORMULA] detection difficult for low-luminosity stars. First, at lower luminosities the [FORMULA] proportion is lower due to their unmixed state. Second, model atmosphere effects operate so that higher-gravity, lower-luminosity stars have weaker CN lines even for constant chemical composition in the atmosphere. Third, the lower stellar luminosity makes it more difficult to obtain the requisite S/N to detect the weak lines.

Despite the uncertainties, it is clear that in the present complete sample, no star with [FORMULA] shows a carbon isotopic ratio lower than the one predicted by standard dilution models. Fig. 2 is strong evidence that extra mixing begins at a luminosity of about [FORMULA]. This limit in luminosity corresponds to the approximative value for [FORMULA] observed in clusters of the same [Fe/H] as the present stars (Fusi Pecci et al. 1990). The cutoff region appears broader here than in our restricted sample, mainly due to a probable scatter in the stellar masses in SSP93 data. Indeed, a [FORMULA] difference corresponds approximatively to a shift of 0.2 in [FORMULA] for the position of the bump (Fusi Pecci et al. 1990).

We show the observed [FORMULA] ratios plotted against [FORMULA] in Fig. 3. [FORMULA] Ori presents a ratio consistent with standard post-dredge-up predictions. The [FORMULA] ratio decreases simultaneously with the [FORMULA] ratio between [FORMULA] = [FORMULA] 1.0 and [FORMULA] 0.5 by about 0.3 dex, revealing that the extra-mixing process also slightly affects the N abundance. Arcturus, for which the data is by far the best due to its brightness, stands however above the curve for the other stars (which really means above [FORMULA] Leo A, at the same luminosity, by 0.3 dex). 3 This difference was recognized easily 15 years ago by Lambert & Ries (1981), who found a difference of 0.47 dex. The 47 Tuc stars, at [FORMULA], present [FORMULA] ratios lower than those in the less evolved objects.

In the M67 data (Brown 1987), a change in the C/N ratio at and above the luminosity of the RGB bump is not clear. This is probably due to errors, both random and systematic, in the abundances derived from the synthetic spectrum fits, and aggravated by the sparseness of the cluster RGB. A systematic offset in the nitrogen abundance was found in that study, and an attempt was made to calibrate this out in a post hoc way. The result, however, is that any slow trend in C/N with luminosity in the Brown (1987) data must be interpreted with caution. It is more secure, however, to note that the total change in the C/N ratio between stars at the base of the giant branch and those at the RGB tip and in the post-helium core flash clump is larger than predicted in standard models, so that the most luminous M67 giants again have also engaged in some extra mixing.

In our sample, the Li abundance drops between [FORMULA] Ori and [FORMULA] And (in terms of luminosity) after which it is below detectability. It is difficult however to argue for the luminosity onset of extra-mixing from this data. Indeed, lithium destruction on the main sequence may lead to a dispersion of the abundances on the red giant branch which could explain the difference between [FORMULA] Ori and [FORMULA] And. In any case, the lithium abundances in the more evolved stars from our sample clearly indicates that an extra-mixing mechanism transports lithium from the convective envelope down to the region where it is destroyed by proton capture after the end of the dilution phase. In a large sample of evolved halo stars, Pilachowski, Sneden & Booth (1993) also showed that the lithium abundance continues to decrease after the completion of the first dredge-up.

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© European Southern Observatory (ESO) 1998

Online publication: March 10, 1998