5 Discussion

As a summary of the results presented in the two previous sections we conclude that: 1) G-type stars in NGC 188 are no more Li depleted than Li-rich stars in M 67 and are at most a factor of two more Li depleted than their Hyades counterparts; 2) M 67 remains so far the only cluster showing a clear spread in Li among solar-type stars. In other words, the evolution of the upper envelope of the Li vs. $T_{\rm eff}$ distribution past the age of the Hyades, as well as the evolution of the spread from the age of M 67 to that of NGC 188, further challenge our understanding of the Li destruction in solar-type stars.

5.1 The upper envelope

Figure 5: Average Li abundance vs. age for five open clusters. The average $\log n$(Li) values have been computed considering stars in the temperature range $5750\leq T_{\rm eff}\leq 6050$ K. Error bars denote $1\sigma$ standard deviations. NGC 752 is not included in the plot since only two stars in the considered $T_{\rm eff}$ range have available Li measurements. Note however that for these two stars we derive Li abundances $\log n$(Li)= 2.32 and 2.43 (as for the other clusters, we have re-analyzed the original data of Hobbs & Pilachowski 1986).

As we mentioned in the introduction, Randich et al. (2000), on the basis of a comparison of the Hyades, of the intermediate age clusters IC 4651, NGC 3680, and NGC 752, and of the solar age cluster M 67, concluded that the mechanism that drives Li depletion appears to stop in the late phases ($\geq$2 Gyr) of MS evolution, unless different conditions/parameters lead to different Li depletion timescales. In Fig. 5 we plot the average Li abundance as a function of age for stars in the 5750-6050 K temperature range. The Hyades, IC 4651 and NGC 3680, M 67, and NGC 188 are considered in the plot; for M 67 we included only stars lying on the upper envelope ( $\mbox{$\log n$ (Li)}\ge 2$). Error bars represent $1\sigma$ standard deviations from the average. The figure evidences a plateau in Li abundances for ages older than $\sim$2 Gyr and, except for Li-poor stars in M 67, there seems to be no additional evolution of Li abundances beyond 2 Gyr. This result suggests three alternative scenarios: i) the clusters have all the same initial abundance, but solar-type stars have not undergone additional Li depletion beyond $\approx$2 Gyr, i.e., if a star has not severely depleted Li at that age, it will not deplete it afterwards (except again for Li-poor stars in M 67) until first dredge-up and dilution occur; ii) the clusters have all the same initial abundance, but different initial conditions and/or different parameters led to different Li depletion rates, with NGC 188 being characterized by the longest Li depletion timescale. Since on theoretical grounds metallicity, and more in general $\alpha$-element abundances, are thought to affect both standard and non-standard mixing processes (e.g., Chaboyer et al. 1995; Swenson & Faulkner 1992; Piau & Turck-Chièze 2002), a difference in chemical composition could be a possible cause for different timescales of Li depletion; iii) the clusters have different initial Li abundances; in particular, the very old cluster NGC 188 might have had, because of its age, a lower Li abundance than the younger clusters. In this case, it must have also undergone considerably less Li depletion than the other clusters to end up with the same average Li abundance.

At present we have no definite clues to discern between these three possibilities; hypothesis i) is the simplest one, but requires a physical mechanism that is not efficient at ages older than about 2 Gyr. None of the Li depletion processes so far proposed has these characteristics. As to the second scenario, we note that no Li depletion - metallicity relation is found for solar-type stars up to the Hyades age (e.g., Jeffries 2000 and references therein). Furthermore, Pasquini et al. (2001) found [Fe/H $]=-0.17 \pm 0.11$ for NGC 3680, while Bragaglia et al. (2001) measured [Fe/H]=+0.16 for IC 4651; the two clusters hence differ in metallicity by a factor of 2, yet they have the same average Li abundance. This suggests that overall metallicity has little effects on Li depletion also at old ages, at least when the rather narrow range of [Fe/H] values covered by Pop.  I stars is considered. In any case, our analysis confirms that NGC 188 has solar metallicity and solar metallicity has also been reported for M 67 (e.g., Jones et al. 1999 and discussion therein); thus, even if metallicity would affect Li depletion, it is not plausible that the two clusters had different Li histories due to different overall metallicities. Besides iron, the abundance of $\alpha$-elements and in particular of oxygen significantly affects stellar opacities, the depth of convective zone, and in principle mixing (e.g., Swenson & Faulkner 1992; Piau & Turck-Chièze 2002). With the exception of the Hyades, a detailed $\alpha$-element abundance analysis for the clusters shown in Fig. 5 has so far not been carried out and thus we are not able to investigate whether the flat $\log n$(Li) vs. age distribution after 2 Gyr is the result of different heavy element abundances; given the old age of NGC 188, it is well possible that the relative abundance of metals in this cluster may differ from the solar distribution. However if Li evolution in the four clusters of Fig. 5 older than 1 Gyr is driven by heavy element abundances, it would be surprising that these abundances are precisely tuned to give the same average Li abundance in all clusters. The same argument applies to the third possible scenario; whereas lower initial Li abundance for NGC 188 cannot be excluded (although the inferred solar metallicity of NGC 188 together with the observed Li vs. Fe Galactic enrichment argue against this possibility), this assumption would imply that NGC 188 has also suffered throughout its lifetime a much lower Li depletion than the younger clusters. We concur with Hobbs & Pilachowski (1988) that the possibility that NGC 188 was characterized by a different initial Li abundance seems very unlikely.

As a final remark, we note that the average abundance of the 13 NGC 188 members in our sample is very close to the value of the Li plateau for Pop.  II halo stars with [Fe/H $] \leq -1.4$and turn-off stars in globular clusters (e.g., Bonifacio et al. 2002). This point may be a coincidence and Pop.  II stars on the Spite's plateau cover a wider range of temperatures; thus, we do not intend to draw any conclusion from it. However, we regard this coincidence as very intriguing and worth of further investigation.

5.2 The dispersion

Randich et al. (2000) from the lack of dispersion in Li abundances among solar-type stars of the intermediate age clusters IC 4651 and NGC 3680, concluded that the dispersion must have developed after $\sim$2 Gyr; if this is indeed the case, any cluster older than that age should exhibit a dispersion. Our results for NGC 188 suggest instead that M 67 might be a peculiar cluster and that solar-type stars in clusters normally do not develop a dispersion in Li. A larger number of intermediate-age/old clusters is obviously needed, as well as new observations of NGC 752, to investigate whether M 67 is really unique and to put this conclusion on firm basis. We recall however that a spread in Li is also present among old stars in the field (e.g., Duncan 1981; Pallavicini et al. 1987; Pasquini et al. 1994): in particular, we mention that several field stars as old as the Sun, but with much higher Li content exist. The simultaneous presence of Li-rich and Li-poor stars in M 67 and in the field implies that, depending on a parameter that is neither age nor mass, Li destruction can be either rather slow or very fast. Various hypothesis have been proposed in the literature to explain the star-to-star scatter in M 67; for example, the co-existence of two sub-clusters (e.g. García López et al. 1988), a scatter in initial rotation rates (e.g., Jones et al. 1999) or, more recently, a scatter in heavy element abundances (e.g., Piau et al. 2003).

As discussed by Randich et al. (2000), if the dispersion observed in M 67 is due to different initial rotation rates and angular momentum evolutions, the lack of a dispersion in other old clusters and in particular in NGC 188, would imply that solar-type stars in these clusters arrived on the ZAMS with very similar initial rotation rates; this is quite unlikely since a dispersion in initial rotation rates is indeed observed in all the young clusters so far surveyed for rotational periods and/or velocities (e.g., Stauffer et al. 1997; Barnes 2000 and references therein). We also mention that, according to current models including mixing driven by angular momentum, a scatter in Li abundances at the age of M 67 would imply a scatter in Be abundances. Randich et al. (2002) instead measured the same Be abundances for M 67 stars with a different Li content.

On the other hand, we do not have observational evidences to proof or dis-proof the other two possibilities, i.e., whether the scatter is due to differences in heavy element abundances among M 67 stars or if the cluster results from two different subclusters. We note however that both hypotheses would imply that the population of M 67 is not homogeneous, confirming that M 67 is a peculiar cluster. This would also be in agreement with the fact that a dispersion in Li is observed among field stars, i.e., within a very inhomogeneous sample.