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Astron. Astrophys. 334, 953-968 (1998)

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6. Comparisons with previous evolutionary tracks

Among the several authors having provided in the past evolutionary sets of intermediate mass stars, the more recent ones are Chin & Stothers 1990, 1991; Schaller et al. (1992), Brocato & Castellani (1993), Schaerer et al. (1993), Mowlavi et al. (1994), Deng et al. (1996a,b). It is worth comparing our results with previous models computed with analogously updated micro-physical inputs, although an FST coupled-diffusive mixing and overshooting has not yet used by other authors. We then excluded from our comparisons the models by Chin & Stothers (1990, 1991) and by Brocato & Castellani (1993), since they adopted radiative opacities quite different from the updated OPAL ones present in our models. More reasonable are the comparisons with the results by Schaller et al. (1992, hereafter SSMM), Mowlavi & Forestini (1994, hereafter MF), Deng et al. (1996a,b,, hereafter DBC), since their input micro-physic is much closer to the one in ATON 2.0 code. Of course, all the above quoted authors used the Mixing Length Theory (even if DBC worked out some corrections to the plain MLT) to deal with convection. In Fig. 8 we show the variation with mass of the hydrogen burning times computed by ourselves and by the authors mentioned above.

[FIGURE] Fig. 8. Comparison of our results with those of other authors

Before performing more detailed comparisons, we evaluated first-approximation transformations of luminosity and [FORMULA] to slightly different chemistries, to better compare our results to the ones obtained in Zero Age Main Sequence (ZAMS) with different ([FORMULA]) values. They turned out:

[EQUATION]

[EQUATION]

First we considered the models by SSMM, for (Y, Z)=(0.30, 0.020), in which instantaneous overshooting of [FORMULA] is present. Given the chemistries, we must add to their ZAMS points the values [FORMULA] and [FORMULA]. The Zero Age Main Sequence locations turn out very similar; our ZAMS structures are in the average slightly more luminous and hotter, the maximum differences being however only [FORMULA] in [FORMULA] and [FORMULA] in [FORMULA]. This similiarity is not surprising, since the physical inputs are very close both in SSMM and in our models.

This is not yet, however, a test on overshooting, which only affects the width of the MS. For the range of mass [FORMULA], also the width is similar in the present models with diffusive overshooting ([FORMULA]) and in SSMM. The average discrepancy is again of [FORMULA] in [FORMULA]. For larger masses ([FORMULA]) the width of our MS band is slightly, sistematically larger ([FORMULA] in [FORMULA]). Closely related to the amplitude of MS is also its duration. In Fig. 8 we see that the lifetimes of stars in core H -burning phase in SSMM models are very similar to ours up to [FORMULA], while SSMM get faster H -exhaustion for larger masses. At [FORMULA], our lifetime in MS is [FORMULA] longer than for SSMM. As already seen, half of the difference is due to our coupled-diffusion (Sect. 4.1) evolutionary scheme; the remaining [FORMULA] can be attributed to the non exact identity of diffusive and instantaneous overshooting, and to residual differences in the physical and chemical inputs between the two sets of models.

Analogous results are found when comparing our models with those by MF, where instantaneous mixing and overshooting with [FORMULA] =0.20 are applied to models with M =2.5, 5, 10, 15 [FORMULA], and (Y, Z)=(.275,.020). Small differences in lifetime of H-burning ([FORMULA]) are found; the width of our MS is slightly smaller than in MF by [FORMULA] (that is: almost negligible) in [FORMULA] for the whole range of masses considered. Also the MS lifetimes are very close in both cases.

Interesting comparison can be made also with the DBC models, since they adopt a diffusive algorithm to deal with overshooting. For completeness, in Fig. 8 we also plot their models obtained with a classical instantaneous mixing scheme. The most outstanding result when comparing models obtained with diffusive overshooting is the similarity between our times of hydrogen burning with theirs over the whole range of masses spanned, our lifetimes being larger than their at [FORMULA] just by [FORMULA], that is: the difference due to coupled-diffusion evolutionary scheme. We conclude then that, apart for this latter feature, the two overshooting algorithms used by DBC and by ourselves have almost the same effect, at least when dealing with main sequence stars of intermediate mass.

In the end, we want to stress what we already claimed, that is:

-this first test confirms that, on quantitative grounds, diffusive overshooting with [FORMULA] gives results consistent with those obtained with instantaneous overshooting, [FORMULA], without having to care of setting overshooting to zero at [FORMULA] and having a more physically sound description of the occurrences at the convective boundaries;

-the differences due to the use of the coupled-diffusion scheme instead of the instantaneous mixing one are of the same magnitude of other differences due to physical and chemical inputs; they must be accounted for in updated generations of stellar models.


[TABLE]

Table 4. Lifetime H-burning (in unit of [FORMULA] yr) DBC1 stands for classical mixing, while DBC2 for diffusive process


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© European Southern Observatory (ESO) 1998

Online publication: June 2, 1998

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