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Astron. Astrophys. 334, 901-910 (1998)

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5. Discussion

With the exception of the luminous blue-loop giants, there is a remarkable quantitative agreement between the best parameterized computed HRD and the observed solar neighbourhood HRD (see Table 1), even for critical stellar number counts such as in the HG region. Furthermore, the parameterization required for the best match is the same as demanded by previous empirical tests, i.e., with cluster isochrones and evolved eclipsing binaries.

The new kind of empirical test presented here is based on the dependence of star counts in the lower Hertzsprung gap on overshooting in stellar models with masses around 1.6 [FORMULA]. The number of HG stars, when computed on the basis of grid 2 (using overshooting for all stars, lower masses included) becomes strikingly out of range with the oberved number. It is too small by more than a factor of 2. The LGB, following in the evolution, is also underpopulated, but the HG region provides a more unambiguous evidence because its counts are independent of the low-mass cut-off choice (not so the LGB region).

Computations without any overshooting, as with grid 1, noticably overestimate the number of KGC giants (see Table 1 again). The main reason is a larger ratio of core He-burning over core H-burning lifetimes and an increase of the superior mass limit for undergoing a He-flash - i.e., 2.5 [FORMULA] with grid 1, versus [FORMULA] with grid 3 and [FORMULA] with grids 2 and 4.

It is surprising that, already in a volume of only 50 pc radius, the assumption of a stricly random and otherwise constant stellar birthrate is good enough to reproduce the local HRD so well. Major star burst events would show up as a higher stellar density in the HRD along the respective isochrone, but that cannot be seen in Fig. 1. Hence, all our characteristic regions cover a large range of stellar age. Diffusion and mixing of the local stellar population in the course of galactic rotation may well be a reason for that. Any star-burst-related effects on the star counts (Table 1) are therefore well supressed. That is also true for smaller displacements in luminosity and colour of those stars, which have undetected fainter companions.

In summary, only the hybrid grids (3 and 4) give a good model of the stellar number counts in all characteristic regions. Overshooting (on the MS) is started with stellar masses of 1.7 [FORMULA] and reaches its full extent between 2 [FORMULA] (grid 4) and 2.5 [FORMULA] (grid 3) - representing the results of earlier empirical tests (Schröder et al. 1997, Pols et al. 1997). The HRD stellar population densities turn out to be insensitive to that subtle difference, while the HG population agrees sensitively with the non-overshooting models for [FORMULA] (and solar-like abundances). Some ambiguity, however, remains: Pols et al. (1998) require overshooting for their best isochrone fit of the metal-poor cluster NGC 2420, which has a turn-off mass as low as 1.5 [FORMULA]. Therefore, more work is needed to empirically quantify stellar evolution in this mass range.

Based on our empirically tested evolutionary tracks (such as in grid 3), we can finally compute various characteristic properties of evolved stellar stages in the HRD - the mass distribution functions for the KGC, the upper GB and AGB (as shown in Figs. 7 to 9) are only examples.

An interesting application is a comparison of stellar evolutionary history to stellar activity, which is now widely observed over the HRD in terms of coronal X-ray emission (see Hünsch et al 1996, Hünsch & Schröder 1996). It is surprising how far stellar activity can reach into late stellar evolution (Hünsch et al. 1997) and more work will be published soon.

Another application of more general interest aims at galactic physics, i.e., on an estimate of the combined stellar mass-losses (gas and dust) on a galactic scale. Such gas and dust injection rates are important figures in modelling the chemical evolution of a galaxy (e.g., Dwek, 1997). When we use the solar neighbourhood as a probe of the galactic disk, our computed, empirically constrained stellar samples yield the fraction of relevant AGB giants, which is 0.3%. The computations also yield the distribution function of initial masses and the whole evolutionary histories. That includes the respective He core masses, which are a main factor for the subsequent AGB life times.

In a future paper we will focus on those final stages. Then, mass-losses become a significant factor in stellar evolution - which, at the same time, drives the giant into a dramatic increase of mass-loss and dust-formation towards the end of its stellar life (see, e.g., Dominik et al. 1990, Lafon & Berruyer 1991). Therefore, computations require a combined and selfconsistent treatment of both processes. A grid of such tracks, based on this work (an empirically derived PDMF and evolutionary history), will then yield the integrated injection rate of processed gas and dust back into the galactic interstellar medium.

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© European Southern Observatory (ESO) 1998

Online publication: June 2, 1998