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

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5. Thermodynamics and convection theory

Before entering the discussion of the possible explanations for both the presently observed solar [FORMULA] abundance and abundances observed in young open clusters, let us warn the reader about uncertainties still weighing on the main micro/macro-physical inputs. This should help understanding the degree of reliability of the present generation of theoretical models, and avoiding trivial mistakes when rising conclusions from comparisons between observational and theoretical data.

First we will discuss the effect of the thermodynamic treatment on Li-depletion in pre-MS, mainly through the value of the adiabatic gradient which, in the end, determines the thickness of the convective envelope. In Fig. 1 we show the standard track compared to a track (MIHEOS) computed assuming, as the only difference, the Mihalas et al. (1988) equation of state in place of the OPAL one. Remember that in DM94 the Mihalas et al. EOS was adopted.

The MIHEOS track shows lower Li-depletion than the STD one by a factor 4. In order to understand the reason for this apparently large difference between results arising from two apparently equally updated thermodynamic treatments, we computed several tracks by increasing from 5000 K (as in the standard track) to larger and larger values of T the point at which we switch from the Mihalas et al. to the OPAL EOS. The final Li-abundances were the same as for the STD track as long as the Mihalas et al. EOS was substituted only up to relatively low T's (that is: below H and He-ionization, [FORMULA] K). When, on the contrary, it was adopted also to describe the H and He-ionization region, the resulting Li-depletion suddenly decreased and never changed any longer, also increasing the transition temperature to [FORMULA] K, well past Li-burning.

The difference is then in the treatment of the partial ionization regime, namely in the value of the adiabatic gradient in those regions which largely influence the convective envelope thickness. It is presently hard to say which of the two EOS' is more physically sound: we chose the OPAL one both for consistency with the opacities and because extensive tables are provided for several H-abundances at a given Z. However, a warning immediately arises: since pre-MS Li-depletion is largely affected by the value of the adiabatic gradient in partial ionization regime, no interpolation between pure-H and pure-He compositions can be adopted in these computations, since pure element compositions do not include the reciprocal influence of ionization, which is instead dominant for the effect under scrutiny (Saumon et al. 1995). An indirect proof of the importance of having a correct treatment of the adiabatic gradient will result at the end of Sect. 8, where we discuss the computations including a variable magnetic field.

Next test deals with the influence of the convection model on Li-depletion. In Fig. 1 we show the difference between the standard track and an MLT one (MLT track) computed with the value of the free parameter fitting the present sun, that is: [FORMULA]. Pre-MS Li-depletion is orders of magnitude lower, as expected since the MLT fluxes are too low, and they require in the average larger values of superadiabaticity than any FST treatment. The convective envelope is then shallower and Li-burning stops at an earlier phase.

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© European Southern Observatory (ESO) 1998

Online publication: March 3, 1998