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Astron. Astrophys. 331, 1011-1021 (1998)

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8. The case of open clusters

On the basis of the above discussion, our tentative explanation for the low solar Li-abundance is that it was achieved as a result of pre-MS depletion in a star left, in its first evolutionary phases, with a small rotation rate, possibly due to the formation of the planetary system. Only a small dynamo generated magnetic field could then counteract the "standard", large depletion suggested by our models for non rotating or slowly rotating stars, which should destroy lithium more efficiently than faster rotating stars. This is also consistent with the large spread of abundances found by King et al. (1997) among the Sun and the solar twins 16 Cyg A and B: the two components of this system differ in Li-abundance by a factor [FORMULA], bracketing the solar abundance and testifying that the solar surface Li-evolution is not an isolated anomaly. Although King et al. (1997) line of reasoning is very different from ours, we come to the same conclusion that the formation of a planetary system, with the associated loss of angular momentum from the star, could go together with larger Li-depletion.

We however know that some 1 [FORMULA] star in open clusters should maintain a large fraction of their [FORMULA], if we wish to reproduce the observed correlation [FORMULA] - [FORMULA] for the cluster stars. It is then important to understand which parameters influence this correlation, to get a consistent -though preliminary- framework of Li-evolution.

We show in Fig. 4 the [FORMULA] Per data by Balachandran et al. 1988 (as revised by Balachandran et al. 1996) compared with some "depletion curves". We show the [FORMULA] =15 and [FORMULA] =30G depletion lines for [FORMULA], which do not agree with the observations. In order to reproduce the average envelope of the [FORMULA] - [FORMULA] relation we need to reduce the metallicity to [FORMULA] (a reasonable choice) and to introduce a "variable" magnetic field, almost linearly increasing for decreasing mass (see Table 2). The fit of the observed data is thus "ad hoc", and indicates, as a zero order approximation, that the average [FORMULA] (or rotation rate?) must increase with decreasing mass. Note that, also for the largest values of [FORMULA], we always got in our models [FORMULA]. This latter result indirectly tells us also that an over (under) estimate of the true value of the adiabatic gradient by [FORMULA] would lead to orders of magnitude of under (over) estimate in the Li-depletion. This adds quantitative information to our previous discussion about the influence of thermodynamics through the adiabatic gradient.

[FIGURE] Fig. 4. Comparison of theoretical depletion seuqences with the [FORMULA] Per data by Balachandran et al. (1988, revised in 1996). The two solid lines are relative to magnetic fields increasing when decreasing the mass; the upper one corresponds to 5 G less than the lower one.

[TABLE]

Table 2. Input parameters for the models with varied [FORMULA]


The same holds for the Pleiades data by Soderblom et al. (1993a) and García Lopez et al. (1994) shown in Fig. 5: here we see more clearly that the low mass stars with larger abundances can be reasonably fitted by assuming that these stars had larger magnetic fields during their pre-MS evolution, probably due to higher rotation rates.

[FIGURE] Fig. 5. Comparison of theoretical depletion seuqences with the Pleiades data by Soderblom et al. (1993a) (open squares) and by García Lopez et al. (1994) (full squares).

As for the Praesepe (Soderblom et al. 1993b), we see in Fig. 6 that the data can be explained by larger metallicity and smaller rotation rates, corresponding to the two curves of [FORMULA] G and 30G. The metallicity of Praesepe is in fact close to the Hyades one, and larger than solar (Boesgaard & Budge 1988). Also notice that the low values of Li-abundances at [FORMULA] [FORMULA] are already affected by the depletion due to the presence of the "lithium dip" first found in the Hyades (Boesgaard & Budge 1988).

[FIGURE] Fig. 6. Comparison of theoretical depletion sequences with the Praesepe data by Soderblom et al. (1993b).

In conclusion, playing a little with magnetic fields, and recalling that part of the observed spread can be due both to observational problems and to the large sensitivity of Li-depletion on mass and chemical composition, the procedure here adopted seems to be able to provide sensible fits to the observations, spread included, even if we cannot claim "perfect" or "definitive" fits, in view of the several uncertainties still weighing on theoretical models.

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© European Southern Observatory (ESO) 1998

Online publication: March 3, 1998
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