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

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6. Chemistry, magnetic field, diffusion and overshooting

As anticipated, Z=0.02 is likely to be an upper limit for the solar metallicity. In Fig. 2 we present our results obtained by varying the chemical composition of a solar mass star. A relatively large change in [FORMULA] abundance causes small variations in the [FORMULA] final abundance, while a [FORMULA] decrease in the value of Z makes the [FORMULA] abundance to vary by almost two orders of magnitude. The higher Z track results in a larger depletion, as in that case we know that opacity is larger and the convective envelope gets deeper. The assumption [FORMULA] might give a value for the final [FORMULA] abundance which is in excellent agreement with that presently observed. However, we are not claiming that this solves the problem of the sun, both since Z=0.017 is only a lower limit for the solar metallicity, and because of the still unknown effect possibly due to other physical inputs (see later).

[FIGURE] Fig. 2. Effects of different chemical abundance on solar pre-MS Li depletion. A reduction of Z within values still acceptable leads to a decrease of two orders of magnitude in depletion, and to the observed abundance. Also the results obtained with a diffusive algorithm coupling nuclear burning and turbulent mixing are shown. Li-depletion is decreased by a factor 3; this is to be kept in mind, since diffusion is a more physically sound approximation than instantaneous mixing.

In this framework, it is interesting to speculate that even small chemical inhomogeneities in a cloud giving birth to an open cluster might be responsible of a fraction of the observed [FORMULA] abundances spread detected in young clusters.

We then discuss the results obtained for the solar model when including the effect of the magnetic field as discussed in Sect. 4.4. As already mentioned, the magnetic field forces larger convective temperature gradients, thus leading to a minor penetration of the convective envelope and to less [FORMULA] depletion. We therefore expect higher [FORMULA] abundances for higher values of [FORMULA], which is actually what we observe from Fig. 3. We see that a value of the solar magnetic field of [FORMULA] G might lead to the observed Li abundance in the Sun with no need of further hypotheses.

[FIGURE] Fig. 3. Effects of different magnetic fields on solar pre-MS Li depletion. The larger is [FORMULA], the lower is Li depletion. Note that the value of [FORMULA] (extra-gradient) for all the tracks shown never reached up [FORMULA].

This result, although only semi-quantitative as above noted, is to be taken seriously. At present, the debate about the mechanisms generating magnetic fields in stellar structures (including fossil magnetic fields) is still open, and even in the presence of rotating stellar models it would not be so easy to give sound quantitative estimates of the internal profiles of B starting from first principles. Nevertheless, hints about the solar internal constitution and measurements of surface magnetic fields (and rotation periods) of pre-MS stars do not exclude at all -not to say suggest- the presence of internal magnetic fields of magnitude even larger than those adopted in the present computations. As an example, the track [FORMULA] =20 G would require, at the base of the convective envelope and at the end of the pre-MS Li-burning phase, [FORMULA] G.

We also tested the diffusive algorithm for coupled Li-burning and mixing. Although the nuclear lifetimes of lithium at the bottom of convection turned out relatively long with respect to mixing times, a profile of [FORMULA] was indeed detected inside the convective region, and this led to a not negligible cumulative effect at the end of pre-MS burning: Li-depletion turned out to be 3 times less than with instantaneous mixing.

Although this result cannot yet be assumed as definitive, since it depends on the approximations adopted to model the diffusive coefficient, it is nevertheless instructive. A "sensible" model for diffusion, which is already likely to be more physically sound than instantaneous mixing, does affect pre-MS Li-depletion and has to be included in all the future computations if absolute, quantitative results are to be looked for. We recall the reader's attention on the fact that, like in the case of Li-production in the convective envelopes of asymptotic giant stars (Sackmann et al. 1974), nuclear depletion and mixing are to be treated together. Separately applying nuclear evolution and then diffusive mixing would lead nowhere.

Overshooting too may influence the amount of lithium which is burnt: this is because it carries [FORMULA] inside deeper regions, where it is destroyed: models computed with overshooting will necessarily have smaller residual abundance of Li. D'Antona & Mazzitelli (1984) found that an overshooting distance [FORMULA] was necessary to fit the Hyades [FORMULA] curve; yet this extra-mixing was not enough to reproduce the solar observed value. Vandenberg & Poll (1989), adopting more recent (and larger) opacities (LAOL: Huebner et al. 1977), showed that a lower extra-mixing ([FORMULA]) was required to fit the same cluster.

These attempts to increase Li-depletion were justified by the large values of residual Li-abundances found in low mass stars with solar metallicity, with the opacities of the epoch and by adopting the MLT to describe turbulent convection. As we have seen, the problem is now reversed. And yet overshooting can be present, and we better study also the effect of this feature on pre-MS Li depletion.

The effect of an overshooting [FORMULA] from the base of the convective envelope in our models can be seen in Table 1 in the model OV01B00. Li-depletion is increased by more than six orders orders of magnitude; this effect, however, can be more than completely reset by a magnetic field of [FORMULA] G only (model OV01B30). It seems then reasonable that a balance between metallicity, magnetic field and overshooting can play a key-role in determining the real extent of pre-MS [FORMULA] depletion inside the stars.

A possible reasonable metallicity for the solar model might be [FORMULA] (Grevesse & Noels 1993). Together with an overshooting of [FORMULA], model OV005B15 shows that the current solar situation may be easily reproduced if we hypothesize that a magnetic field [FORMULA] G was present in the Sun during the pre-MS phase, and working with diffusive mixing. This is our present reasonable guess for the pre-MS evolution of the Sun. With [FORMULA] G (model OV005B20), room is left for some MS depletion associated with slow mixing mechanisms.

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© European Southern Observatory (ESO) 1998

Online publication: March 3, 1998