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Astron. Astrophys. 355, 299-307 (2000)

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4. Atomic diffusion and subdwarfs ages

The age of field subdwarfs is, together with the age of stellar clusters, an important piece of information needed for understanding time scales and formation mechanism of the Galaxy. As repeatedly stressed before, the isochrones used for studying field subdwarfs of a certain surface metallicity are different from the ones to be employed when dealing with GC with the same observational value of [Fe/H]. This is clearly at odds with the usual procedure, when using standard isochrones, to use the same models for field and GC MS stars.

In Fig. 7 (upper panel) we display, as an example, standard and C isochrones with [Fe/H]=-2.3 and selected ages ([FORMULA]8,12,13 Gyr in the case of standard models, while for C isochrones [FORMULA]8,12 Gyr). It appears clear how the influence of diffusion is extremely relevant for the derived subdwarfs ages. The TO absolute V brightness for a standard isochrone with [FORMULA]13 Gyr is coincident with the TO brightness of a C isochrone of only 8 Gyr; both the TO [FORMULA] and [FORMULA] differences corresponding to an age between 8 and 12 Gyr are strongly reduced (by [FORMULA]50%) when passing from standard to C isochrones. This undoubtedly causes a strong reduction in the derived subdwarfs age, and has an important effect also on the determination of the age dispersion.

[FIGURE] Fig. 7. Upper panel: Colour Magnitude Diagram of the TO region of standard (solid lines) and C isochrones (dotted lines) for the displayed value of [Fe/H]; the ages are 8,12,13 Gyr for the standard isochrones, 8 and 12 Gyr for the C ones. Lower panel: as in the upper panel, but for D (dashed lines) and C (dotted lines) isochrones with [FORMULA]8,12 Gyr.

The reason for such a big difference with respect to standard calculations is that the C isochrone is basically an isochrone of much larger initial metal abundance than the standard one (by how much larger depends on the age) and with diffusion. It is well known that for a fixed age the effect of diffusion at a fixed initial metallicity is to decrease the TO luminosity (and colour); in the case of C isochrones, there is in addition the effect of the larger initial abundance which further lowers the TO luminosity (and colour); the amount of the cumulative effect depends on the selected age and initial metallicity.

In the lower panel of Fig. 7 a comparison between the TO region of C and D isochrones with [Fe/H]=-2.3 and [FORMULA]8,12 Gyr is shown. The use of the D isochrones (suitable for GC) for deriving subdwarfs ages does not introduce a too large error for [FORMULA]12 Gyr, while the difference with respect to C isochrones is very large for [FORMULA]8 Gyr. This is due to the fact that, due to the lower age, the TO-mass is higher and therefore the depth of the convective envelope is smaller in TO stars, with the consequent larger depletion (and increase of the initial metallicity for the calibrated models) of the metal and helium abundances due to diffusion.

Diffusion has further important consequences when trying to determine the age-metallicity relation for old Halo subdwarfs. We have already seen that the use of diffusive C isochrones in place of standard ones strongly reduces the derived subdwarfs ages. Once the age of a sample of subdwarfs is obtained, one can study the age-metallicity relation for deriving information about Galactic formation mechanism and time scales. Of course the relevant quantity is the relation between the age of the stars and the metallicity from which they formed, which, in case of diffusion, is different from the actual one. The difference between initial and surface [Fe/H] at the TO is always within 0.1-0.3 for ages of about 10 Gyr or larger. But if one derives subdwarfs ages of the order of 6-8 Gyr (using the appropriate C isochrones), the observed [Fe/H] of TO stars must be increased by [FORMULA]0.2-1.0 (somewhat larger corrections are found for the most metal poor models with [Fe/H]=-2.3) for obtaining the initial value. This has to be taken into account in the analysis.

It is interesting to notice that if, for example, TO very metal poor subdwarfs with [Fe/H] around -3.0 (a sample of them can be found in Schuster et al. 1996) are found to be relatively young ([FORMULA]8 Gyr) when employing the appropriate [FORMULA]-enhanced diffusive C isochrones, their initial metallicity had to be [Fe/H][FORMULA]2.2, very similar to the initial metallicity of the most metal poor GC.

By considering the fact that the [Fe/H] depletion is larger at lower ages (at least for ages larger than [FORMULA]6 Gyr), it is interesting to notice that if one finds in a given observed metallicity range that metal poor subdwarfs are younger than metal rich ones, this could correspond - for a particular combination of ages and width of the metallicity range - to an age spread at a constant value of the initial metallicity.

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© European Southern Observatory (ESO) 2000

Online publication: March 17, 2000