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

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1. Introduction

It is well known how much stellar evolutionary theory has learnt from the HRDs of clusters - so far much more than from the stars of the solar neighbourhood. Partly, the explanation lies with the special kind of sample - stars all of (about) the same age - which only clusters can provide. However, another reason is simply technical: before HIPPARCOS, only the very nearest stars had precise enough parallaxes to qualify for a well-defined HRD. Therefore, rarer and interesting types of stars like luminous late-type giants, e.g., mostly remained out of reach.

Now that the HIPPARCOS mission and catalogue has been completed, precise absolute magnitudes have become available for thousands of stars, some of which even form a volume-limited complete sample. Therefore, the resulting new solar neighbourhood (single stars) HRD can compete with the best cluster HRDs in terms of precise positions. Moreover, it includes large numbers of stars of a whole range of ages. That has made it a different and interesting kind of high quality sample. Its potential goes far beyond quantitative comparisons of evolutionary models with many individual stars - the solar neighbourhood HRD now qualifies for statistical tests as well. This includes a check of the mass function for the stars within 50 to 100 pc. Important for evolutionary theory, however, is another new option: to study various evolutionary time scales, including some briefer stages.

So far, evolutionary theory has mainly been tested by a comparison of isochrones with cluster HRDs (e.g., Meynet et al. 1993, Pols et al. 1998), or comparing evolutionary tracks with precise binary data (e.g., Andersen 1991, Schröder et al. 1997, Pols et al. 1997) or with log g and [FORMULA] from model atmospheres of bright main sequence (MS) stars in clusters (Schönberner & Harmanec 1995). The main purpose of all those tests has been an empirical quantification of effects from convective mixing in the H-burning cores of MS stars. In most codes, this is still approximated by a simple mixing length approach. As a consequence, extended mixing (i.e., beyond the Schwarzschild instability), often called "overshooting", had to be introduced in an ad hoc way and requires an empirical quantification, which is usually given in terms of an "overshoot length" [FORMULA]. Also, more empirical tests are needed to determine, what is the lowest mass of a MS stellar model for which overshooting is required.

The onset of overshooting on the MS might tell us something about the nature of that extended mixing. Is it strictly coupled to the onset of core convection, which takes place in ZAMS stars of about [FORMULA]? Or is it coupled to (core) rotation (Flieger & Langer 1995, Talon et al. 1997)? Or is it mainly an overshooting (literally) of convective elements into the convectively stable regions? In the last case, a marginally convective core might not be sufficient and a threshold convection (and MS stellar mass) has therefore been suggested and discussed by several authors, from both an empirical and a theoretical point of view (e.g., Roxburg 1992, Alongi et al. 1993, Umezu 1995).

Previous evidence for overshooting has mostly been gathered from the width of the MS. However, the significance of this approach diminishes towards the suspected onset of overshooting. Cluster and binary data suggest an onset somewhere between 1.1 to [FORMULA] (e.g., Meynet et al. 1993, Pols et al. 1998). An overview of other than MS-related effects of overshooting and a new sensitive test was published by Schröder & Eggleton 1996. They employed the luminosity of the He-core burning phase, using giants in well-studied binaries, i.e., [FORMULA] Aur systems. However, suitable binary candidates for that approach are presently restricted to stellar masses of more than 2.5 [FORMULA]. That leaves a gap of sensitive tests just in the critical mass range (1.1 to about [FORMULA]), which contains a large fraction of stars and late-type giants (see Sect. 4.3).

With this work, we want to demonstrate that the use of stellar population densities in various characteristic regions of the local HRD can sensitively test evolutionary time scales and also complements existing tests of stellar evolution. In particular, the number of stars counted in the Hertzsprung gap (HG) - and to some extent also the giant branch (GB) and K giant clump (KGC) - is a sensitive indicator of overshooting in the critical mass range around [FORMULA]. The lifetime of those H-shell burning phases depends strongly on the mass of the He-core, which would be larger if overshooting took place during the preceding H-core burning MS phase.

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© European Southern Observatory (ESO) 1998

Online publication: June 2, 1998