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

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4. The "standard" model and the Lithium-mass relation

The main results are shown in Table 1 and in the Figs. 1 - 3. We will consider as "standard" track the solar model obtained by assuming chemical composition [FORMULA], [FORMULA]. The helium abundance is obtained by requiring the fit of the present solar luminosity at the solar age of 4.6 [FORMULA] yr. The metallicity adopted is at the top of the range allowed for the solar model. A metallicity of [FORMULA] is probably more adequate (Grevesse 1984, Grevesse & Noels 1993) but, since we already know that, the larger Z the larger Li-depletion (D'Antona & Mazzitelli 1984), we chose the upper limit for [FORMULA] as it amplifies the effect of the different parameters on pre-MS Li-burning.


Table 1. Input parameters for the computed sequences

The standard track shows a much larger Li-depletion than in DM94 (present depletion about three orders of magnitude larger). Part of the difference is due to the different value of Z (0.019) adopted in DM94 since, as we already know and are going to better elucidate, around the solar metallicity, Li-depletion for a star of solar mass is a strong function of Z. Another fraction of the difference is due to the update in the opacities, which are now somewhat larger than in the first OPAL release just at the temperatures of [FORMULA] burning (Iglesias et al. 1992), leading to slightly deeper convective envelopes. Also the thermodynamics conspired (see later) in increasing Li-depletion. Finally, the update of the FST convective fluxes from those by Canuto & Mazzitelli (1991) to the CGM ones (which are in the average larger, thus leading to lower superadiabaticities and deeper convective envelopes) again worked in the direction of increasing pre-MS Li-depletion (D'Antona & Mazzitelli 1997).

The present situation is then that, with the most updated physical inputs, we have a reverse problem with solar [FORMULA] with respect to a few years ago. In fact, the predicted pre-MS depletion is presently too large to explain observations. Not only there is no need to introduce slow mixing mechanisms acting during the MS to further deplete the still large abundance of [FORMULA] left after pre-MS; we now have the opposite problem of understanding if some plausible physical mechanism acting in pre-MS can counteract Li-burning.

We checked the variation in Li-depletion for a small variation in the total mass of the star. The [FORMULA] final abundance is a growing function of the mass as expected, since more massive stars have shallower convective envelopes in pre-MS. In Fig. 1 we show the huge difference in the final Li-abundance (three orders of magnitude) between the models of 0.95 (M095 track) and 1.05 [FORMULA] (M105 track). This result unambiguously shows that enormous care has to be taken when reducing observations from the [FORMULA] - [FORMULA] plane to a [FORMULA] - [FORMULA] one through [FORMULA] relations or, even more, to a [FORMULA] -mass relation.

[FIGURE] Fig. 1. Comparison between the standard model lithium depletion as a function of log age and models differing in mass (0.95 and 1.05 [FORMULA]), or in the EOS, or in the convection treatment. The depletion with the Mihalas et al. thermodynamics is smaller by a factor [FORMULA], due to the different behaviour of the adiabatic gradient in the partial ionization regions. The MLT model leads to lower pre-MS Li-depletion than the FST model, due to the lower convective fluxes, large superadiabaticity and narrower convective regions.

Namely, a small observational uncertainty in the MS value of [FORMULA], or small errors in the theoretical [FORMULA] and MS [FORMULA] -mass relations would turn out in associating to a given star, of observed [FORMULA] abundance, a value of [FORMULA] (or mass, almost linear with [FORMULA] in the MS region of interest) slightly different from the real one. The very steep relation [FORMULA] -mass would then amplify the difference between the theoretically predicted Li-depletion for that "observational" mass and the actual [FORMULA] abundance. It is worth noting that exact knowledge of the chemistry of the observed sample of stars is required, since both [FORMULA] and [FORMULA] -mass relations are a function of Z.

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© European Southern Observatory (ESO) 1998

Online publication: March 3, 1998