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Astron. Astrophys. 350, 587-597 (1999)

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6. Resolving the metal-poor discrepancy

The most natural attempt to solve the discrepancy is by trying to adjust the "free" parameters, the helium content Y being the first target. However, for the stars in the metallicity bin [[FORMULA]], a [FORMULA] would be required, a cosmologically unacceptable value. A change in [FORMULA] does not help either, as it is producing a negligible effect in the low part of the main sequence under consideration here.

So, as noted in Lebreton et al. (1997) the discrepancy in the expected and actual positions of metal-poor stars needs either a drastic change in the zero-point of effective temperature (of the order of 200 K) or accepting the view that other processes must be included in the interpretation of the observations. It would be very difficult to plead a large correction in the effective temperatures at metallicity [FORMULA] and none at solar metallicity. So, we do not further consider this explanation and, now focus on the second one.

Two processes are considered in this section: (i) departures to LTE in the determination of [Fe/H] (ii) microscopic diffusion of helium and other heavy elements.

6.1. Non-LTE departures for iron

All the [FORMULA] values we have used were computed with the LTE approximation. Computing NLTE abundances for iron is a formidable task. However, it must be noted that Bikmaev et al. (1990) have claimed that a substantial overionisation occurs for Fe I in subdwarfs, and only Fe II lines should be used for determining iron abundances. Holweger and coworkers (private communication, 1993) found the same phenomenon in trying to compute departures from LTE for the very metal-poor star [FORMULA]. More recently, Nissen et al. (1997) found that spectroscopic gravities in subdwarfs were systematically lower than the gravities derived from Hipparcos distances. Finally, Thévenin & Idiart (1999) have undertaken NLTE computations of iron abundances in one hundred metal-poor stars, and found non-LTE corrections for several of our stars, of the order of 0.15 dex, for the mean metallicity ([FORMULA]) of our [FORMULA] subsample. Non-LTE corrections are negligible for stars with solar metallicities (same reference). The metallicity of isochrones to be compared to the set of stars with a mean LTE metallicity [Fe/H]=-0.72 is therefore the true NLTE metallicity [Fe/H]=-0.57. The situation is improved but a clear departure is still existing (Fig. 5).

[FIGURE] Fig. 5. This figure is a large scale HR diagram for the subsample of unevolved stars in the LTE metallicity range -1.05 [FORMULA] [Fe/H] [FORMULA] -0.45. The full line is a standard isochrone for the mean LTE metallicity of the sample [Fe/H] = -0.72. The dashed line is the standard isochrone corresponding to the NLTE mean metallicity of the sample [Fe/H] = -0.57. The dot-dashed line corresponds to an isochrone including microscopic diffusion of the elements for an age of 10 Gyr. The surface metallicity is the NLTE value [Fe/H]=-0.57, but the initial metallicity, which is very close to the mean interior metallicity was [Fe/H] [FORMULA]. The fit is now satisfactory. The tick marks show the value of the mass along the upper isochrone. The tick mark near 85 Peg A corresponds to 0.85 [FORMULA] (not labeled for clarity)

6.2. Sedimentation of heavy elements

The effects of sedimentation of heavy elements have recently been computed by Morel & Baglin (1999), for stars of metallicity [FORMULA], -0.9, -1.2,-1.7, and for 5 stellar masses, 0.85, 0.80, 0.75, 0.70, and 0.60 [FORMULA]. To produce significant effects in the HR diagram microscopic diffusion has to proceed on a sufficiently long timescale. This condition is fulfilled for the thick disk subsample under consideration here: the 10 Gyr isochrones of the Morel & Baglin paper are a suitable choice for our subsample. Two effects are present:

After a time of 10 Gyr, the stratification of the heavy elements translates the evolution point in both [FORMULA] and [FORMULA]. This effect is small: at 0.7 [FORMULA] and an initial metallicity of [FORMULA] the point is moved by [FORMULA] and [FORMULA]. But the surface metallicity of the star has dropped to [FORMULA]. Therefore, the theoretical position of a star of present metallicity [FORMULA], must be computed with a modified initial composition, leading after a 10 Gyr evolution, to the metallicity we observe now. This is the largest part of the correction, called the calibration correction by the authors. From their Table 2, and their Fig. 5 we have computed the corrections to be applied to a standard isochrone for the mean metallicity ([FORMULA]) of our sample in the range [FORMULA].

6.3. Cumulated effect

Applying these corrections to the dashed curve in Fig. 5 produces the dot-dashed isochrone. No systematic departure appears any more between the observations and the theoretical isochrone corresponding to the present surface metallicity of the stars. The initial discrepancy noted at the beginning of this section is then completely removed. The only star presenting a [FORMULA] discrepancy is the star HD 132142 at (3.707, 5.697). But there is a single spectroscopic determination of its metallicity and its photometry indicates a solar metallicity. So this exception is not a serious worrying.

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© European Southern Observatory (ESO) 1999

Online publication: October 4, 1999