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Astron. Astrophys. 347, 272-276 (1999)

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4. Conclusions

While it would be desirable to solve the solar lithium problem and to reduce the remaining solar model deficits (Fig. 1) simultaneously, it appears that the overshooting approach by Blöcker et al. (1998) is not able to do so. The arguments for this conclusion are that the overshooting parameter f (Eq. (1)) would have to be adjusted to different values both for the different phases of evolution (PMS and main-sequence) and for envelope and core overshooting. Since the seismic model leaves almost no room for overshooting from the transient convective core, which exists for some time during the PMS evolution, [FORMULA] is indicated. Second, overshooting from the convective envelope seems to be suppressed during the PMS evolution as well, because otherwise lithium would be destroyed too much (or completely) before the Sun has reached its ZAMS position. Recall that even the SSM model (without overshooting) is depleting lithium more efficiently than observed in the young open clusters ([FORMULA] Per or Pleiades). This requirement restricts f to be smaller than 0.016 in that phase, which is the value used by Herwig et al. (1997) to obtain a main-sequence width compatible with the observations for intermediate mass stars, and which resulted in significant third dredge-up in AGB stars. (Note that Herwig et al. 1997 keep the value of f constant during the evolution and for core and envelope overshooting.) However, for this value there is no further lithium depletion during the main-sequence evolution, which is in contradiction to the anti-correlation between lithium abundance and age for open clusters (such as Praesepe, NGC 752 and M67). Finally, the case presented by Blöcker et al. (1998) of [FORMULA] during the main-sequence evolution (only envelope) indeed solves the solar lithium problem. However, the resulting solar model shows an even stronger disagreement with the solar sound speed, such that the combined solution of both mentioned problems cannot be achieved with this approach.

To conclude, we consider the obvious need for a "variable" parameter in the overshooting approach and the failure to improve the solar model below the convective region as being discouraging. Rather, the turbulent diffusion approach (Chaboyer et al. 1995; Richard et al. 1996) seems to be more promising and should be investigated further. In this case, the solar lithium abundance can be reproduced and the sound speed profile improves slightly with respect to the seismic model. Whether our results allow negative conclusions for other situations, where the present overshooting approach has been used (main-sequence, AGB), is beyond the scope of the present paper. Actually, the non-constancy of f is an argument not to draw conclusions beyond the solar case. It would be highly useful to have 2d-hydrodynamical calculations available, which accomodate the whole convective region under consideration. This would also clarify, whether the overshooting description, which was derived from A-type stellar convective envelopes, is applicable at all to the solar case, where convection is much more effective than in the former stars.

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© European Southern Observatory (ESO) 1999

Online publication: June 18, 1999