Astron. Astrophys. 325, 535-541 (1997)

4. Discussion

4.1. The spread

As outlined in the introduction, the main aim of the present work was to establish whether a real spread in Li abundances exists among main sequence stars in a solar-age, solar-metallicity cluster like M 67. The most appropriate way of investigating this issue, is first to look at the distribution of stars in a colour-equivalent width diagram; these are measured quantities and thus much less affected by errors than effective temperatures and Li abundances.

In Fig. 1 (upper panel) the Li equivalent widths are shown as a function of (B-V) colour. In the figure stars observed by us are represented with filled squares, while stars taken from the literature are indicated by open squares. Circles identify those stars for which radial velocity measurements indicate duplicity, variability, or possible variability (cf. Tables 1 and 2). We caution that some of the sample stars were not included in the Mathieu and Latham (1996) survey, therefore the number of possible binaries has to be considered as a lower limit.

Fig. 1. (upper panel) Li Equivalent widths vs. B-V colour for M 67. Filled squares, our observations. Open squares, data taken from literature. Circles indicate known binaries or radial velocity variables. (lower panel) Colour-magnitude diagram for the same stars as in the upper panel. Symbols are as above. Stars with upper limits in Li are marked with arrows.

From Fig. 1 it is clear that a large spread in the measured equivalent widths is present at each colour, well above the uncertainty of the equivalent width measurements. The spread is seen at all colours, indicating therefore that the observed spread is neither limited to the warmer stars (where it could indicate the presence of Li-gap stars, Boesgaard and Tripicco 1986, if these stars have not yet evolved off the main-sequence, contrary to what expected, cf. Balachandran 1995), nor to the cooler ones.

On the other hand, we know that the colour-magnitude diagram (CMD) of M 67 shows a large spread in magnitudes at each colour. It is therefore necessary to investigate whether the Li spread is related to the spread in the CMD. If, for example, the spread were caused by contamination from binaries, low equivalents widths could be due to dilution from the continuum of the secondary star: Li poor stars therefore should be located, on average, above the cluster main sequence.

Fig. 1 (lower panel) shows the V vs. B-V colour-magnitude diagram for the stars in Tables 1 and 2. Both upper limits and detections have been included in the figure. Known binaries are indicated. The figure clearly shows that the stars with upper limits in Li are uniformly distributed in the CMD, indicating that the spread is not linked to the stellar magnitude, at least not in a straightforward way. Fig. 1 also shows that no trend in Li is present among the binaries, and that the number of Li-poor binaries is basically the same as that of the Li-rich ones.

Fig. 2 is the same as Fig. 1, but for the (V-I) colour. The same pattern as in Fig. 1 is seen, leading to the same conclusions.

Fig. 2. (upper panel) Li equivalent widths vs. V-I colour for M 67. Filled squares, our observations. Open squares, data taken from literature. Circles indicate known binaries or radial velocity variables. (lower panel) Colour-magnitude diagram for the same stars as in the upper panel. Symbols are as above. Stars with upper limits in Li are marked with arrows.

To conclude, the presence of binaries cannot fully explain the observed scatter in Figs. 1 and 2. As an example, in Fig. 3 the spectra of two pairs of supposedly single stars having similar colours but different Li lines are plotted. Clearly, the Li abundances are different, while no major difference is seen for the other lines, indicating that the scatter in Li is real.

Fig. 3. CASPEC spectra in the Li region of pairs of stars with similar colours but different Li abundances. In each panel, the continuum of one of the star is shifted vertically with respect to the other for clarity reasons.

Standard models, where the depletion of Li is due only to convective mixing, are unable to explain this spread, since for a given age, effective temperature, and metallicity, the Li abundance should be the same. Clearly this is not the case and other processes must affect Li depletion for solar-type stars in M 67.

For instance, rather than by convection, Li depletion could be caused by mixing mechanisms which depend on the stellar angular momentum, as suggested, among others, by Pinsonneault et al. (1990), Michaud & Charbonneau (1991) and Charbonnel et al. (1994). These mechanisms add an extra parameter -either rotational velocity or the initial angular momentum- and since this parameter is likely to be different from one star to the other, a spread in Li abundances can easily be produced. Alternatively, Li depletion in Pop I stars could basically follow the standard models (as suggested by Spite and Spite 1982) and the Li-rich stars at each colour could be the ones in which the standard convective mixing operates. In the Li-poor stars, an extra depletion occurs, It is unclear, however, what this mechanism might be.

It is also possible, at least in principle, that small differences exist in the interior of otherwise similar stars, leading to different amounts of Li depletion. For instance, Swenson et al. (1994) have pointed out that Li depletion may strongly depend on the abundance of certain key elements, like oxygen, which can modify stellar atmospheric opacities and thus lead to different amounts of convective mixing. One could hyphotesize that the spread in Li among solar-type stars in M 67 is produced by differences in the abundances of other elements. It is difficult to understand how these differences could be present in a cluster; on the other hand, differences in CN-CH have been observed among main sequence stars belonging to the globular cluster 47 Tuc (Briley et al. 1994) which suggests that some chemical inhomogeneities may originate before the ascent of the red giant branch.

At the moment we cannot discriminate between these different hypotheses. We can broadly estimate the fraction of Li-rich vs. Li-poor solar-type stars in M 67: this fraction may approach 40 , a percentage very similar to that observed among field G dwarfs (Pasquini et al. 1994).

We think that it is quite worrying that the CMD of M 67 is so scattered. Binaries can only partially explain the spread in magnitude of the CMD of this cluster. Even in our subsample, stars exist that have similar colours, but large differences in magnitude, and they are most likely single. It seems that in this old cluster it is hard to find two stars that are real "twins".

4.2. S1045

One of our sample stars, S1045, is worth to be discussed separately, since this star is a known double-lined spectroscopic binary with similar components and a 7.6 day orbital period (Latham et al. 1993).

Li observations of S1045 were reported by Deliyannis et al. (1994) (hereafter we refer to these observations as CTIO), who found in both components a Li abundance of N(Li) , higher than the average Li abundance of M 67 stars. They interpreted this result as a strong support to the theory of rotationally induced mixing.

Deliyannis et al. (1994), however, do not seem to have taken in full account in their analysis the binary nature of this star: the spectra of the two components in fact were separated by 2.6 Å, making the Li line of one component (star 1) blended with the Fe 6705 Å line of the other component (star 2) and the Li line of star 2 blended with the 6710Å  Fe line of star 1. Since they attributed the measured equivalent widths only to Li, their abundances are expected to be overestimated.

The CTIO digitized spectrum of S1045 was re-analysed by us using the same spectral synthesis code used by Randich et al. (1993) in their study of RS CVn binaries. By fitting this spectrum with two equal stars with K and N(Li) = 2.96 (the first case in Table 2 of Deliyannis et al.), we obtained the synthetic spectrum shown in Fig. 4, which is clearly a non acceptable fit to the observed spectrum. In the same figure, the separate contributions of the two stars are also plotted, to show the severe blending of the Li and Fe lines. Note that, under the assumption of equal stars, each of the two components contribute to half of the total flux: the continua are therefore at the 0.5 level. A good fit of the CTIO spectrum was obtained assuming two equal stars with =6100 K and N(Li)=2.6. The latter value is significantly less than estimated by Deliyannis et al., while the temperature is the one adopted by us from the B-V calibration (cf. Table 1) and it is within the range of models considered by Deliyannis et al. (see their Table 2). The lower Li abundance derived by us from the CTIO spectrum is not significantly higher than for other stars in M 67.

Fig. 4. CTIO spectrum of the SB2 binary S1045 (solid line) with overplotted the results of a spectral synthesis fit (dotted line) using the parameters of case 1 of Deliyannis et al. (i.e. two equal stars with K and N(Li)=2.96). The fit is clearly unacceptable. The separate contributions of the two stars to the fit are also shown. Each star contributes to half of the total flux: the continua are therefore at the 0.5 level. Note the strong contamination of the Li line of both stars by Fe lines of the other star.

To check this point further, we have reobserved S1045 at ESO on February 23, 1995. The results from our best fit are given in Tab. 1: a Li abundance of for both stars was derived, a result quite different from that obtained by fitting the CTIO spectrum. Our CASPEC spectrum together with the best fit is shown in Fig. 5.

Fig. 5. ESO spectrum of the SB2 binary S1045 (solid line) with overplotted our best fit listed in Table 1 (dotted line).

Why did we obtain different results from the CTIO and ESO spectra ? From a direct comparison of these spectra (which have similar resolution and similar separation between the two components), the reason from the discrepancy is clear (see Figs. 4 and 5): the CTIO spectrum shows a strong filling-in of all lines with respect to our CASPEC spectrum. The reasons for this filling-in remain unclear: either some scattered light was present in the CTIO spectrum, or some physical process makes the stellar continuum varying. Migrating spots are unlikely, because they should be exceptionally large, and such strong variations are not observed even in the most active stars (Pallavicini et al. 1993). The existence of a third companion cannot be excluded, although it is unlikely that this hypothetical companion contributes only to the continuum, with no other spectral signature.

In summary, the case of S1045 is puzzling. The two existing high quality, high resolution spectra are inconsistent.

The high abundance inferred from our spectrum would indicate that the initial Li abundance in M 67 should have been at least as high as N(Li) 3. This value is close to the initial Li abundance in the solar system and is close to the maximum abundance measured in young clusters like the Pleiades, the Hyades and Praesepe. Thus, S1045 must have suffered very little depletion (if any!) during its main sequence lifetime.

4.3. Comparison with other clusters

In Fig. 6 Li abundances for M 67 stars are plotted (filled squares), together with the Li abundances for the Hyades (open stars) and for the 2 Gyr old cluster NGC752 (starred), as compiled by Balachandran (1995). The Sun is also shown in the plot. The stellar effective temperature scales used by Balachandran (1995) and in this work are the same, thus the abundances are on the same relative scale and should not be affected by major systematic uncertainties.

Fig. 6. Li abundances vs. effective temperatures for solar type stars in clusters of different ages: M 67 (4.7 Gyr, filled squares), Hyades (0.8 Gyr, stars), NGC752 (2 Gyr, starred). The position of the Sun is also indicated.

The fact that we have been able to prove the presence of a scatter in Li abundances among the stars of M 67 allows us to investigate the evolution of Li with age under a novel perspective. For sake of simplicity we refer to the M 67 stars with a low Li content as "overdepleted" (but equivalently we could consider the M 67 stars with high Li content at each colour as "underdepleted").

Fig. 6 shows that:

• The upper envelope of the M 67 stars follows closely the Hyades distribution, with only 0.25 dex offset (this difference may be larger for cooler stars).
• Although the NGC752 sample consists of only seven stars, no significant difference is evident between the distribution of Li abundances in M 67 and in NGC752.
• If the high abundance measured in S1045 is representative of the initial abundance of M 67, the initial solar system abundance (N[Li]=3.31, Grevesse et al. 1996) is not exceptional for the solar age and metallicity, but is shared by other coeval systems in the Galaxy. In addition, this would imply that a depletion of at least a factor 4 occurred for the other stars of M 67.
• The Li abundances among the M 67 stars cover a range of more than one order of magnitude, from values comparable to the present solar value (N[Li]=1.1), up to N[Li] 2.5. The fact that the Sun lies on the lower envelope of the M 67 distribution suggests that the Sun represents a quite normal case of "overdepleted" star 4 Gyrs old. Considering the M 67 sample and the sample of field G stars of Pasquini et al. (1994), the same behaviour is shared by 40 of the solar metallicity, solar age stars.

  Among the observed stars very few have Li abundances with intermediate values. In other words, the distribution of Li abundances in M 67 stars could be bimodal (although our statistics is not sufficient to prove it). A similar behaviour was observed among field G stars by Pasquini et al. (1994). If the low Li abundances are produced by a mechanism of extra depletion, this mechanism must be very efficient, when in force.

The observational evidences summarized above clearly show that Li abundance is not a good tracer of stellar age, at least for stars older than the Hyades. Different Li depletion mechanisms seem to operate for different stars of the same mass, which makes the interpretation of Fig. 6 in terms of evolution of Li abundance with age not straightforward.

The similarity between the Hyades curve and the M 67 upper envelope shows that for some stars Li depletion depends very weakly on age during most of their main sequence lifetime: their Li content does not substantially change between an age of 0.8 Gyr and 4.7 Gyr. This result is also supported by sparse observations of the 6 Gyr old cluster NGC188 (Hobbs and Pilachowski 1988), in which several stars were found with a Li content as high as N[Li]=2.3. This suggests that Li depletion is not very efficient for many stars during main sequence lifetime. This conclusion assumes that the initial Li content of M 67 was as high as suggested by our analysis of S1045, i.e. N(Li) 3, a value comparable to the initial Li abundance in the Hyades and in the solar system. This conclusion would not be correct only in case the initial Li abundance in M 67 was much higher than in the Hyades, a possibility which at the moment is not supported by any observational evidence.

Conversely, for about 40 of the stars, a drastic Li depletion occurs. This depletion seems to start only after the first Gyr of permanence on the main sequence. G stars strongly depleted in Li are in fact not observed in the Hyades and in the coeval Praesepe cluster (Soderblom et al. 1993b), while they are present in M 67 and possibly in the 2 Gyr old cluster NGC752. Is this depletion produced by mechanisms related to rotation and/or angular momentum loss, or by some other, yet unknown, extra depletion mechanism ? As mentioned in Sect. 4.1, we cannot yet discriminate between the various possibilities. The fact that S1045 has the highest Li abundance of any star in M 67 may indicate that rotation is relevant in the Li evolution, but the present data cannot firmly demonstrate it. The observed separation between "overdepleted" and "underdepleted" stars may, on the other hand, be of not easy interpretation in the framework of rotational theories, if this separation is as sharp as suggested by the presently available data (but the statistics is too low to be sure that the distribution is really bimodal). In fact, if different levels of Li depletion are produced by different amounts of angular momentum loss (and associated rotation-induced turbulence) one would expect to observe a continuous distribution of Li abundances rather than a bimodal distribution, unless the initial stellar angular momenta were unevenly distributed. Also, the absence of a spread in the Hyades argues against this mechanism.

© European Southern Observatory (ESO) 1997

Online publication: April 28, 1998

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