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

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2. The solar neighbourhood single-star HRD

Completeness of the stellar sample, from which the solar neighbourhood HRD is constructed, is most important for any statistical approach. Hence, for any given volume, the minimum usable luminosity is defined by the magnitude down to which the observational sample is complete. HIPPARCOS coverage is anticipated to be fairly complete down to the sensitivity threshold of its "starmapper" detectors, which is about [FORMULA] (van Leeuven et al. 1992, Kovalevsky et al. 1995). For [FORMULA] pc, that would correspond to [FORMULA].

For an HRD of stars within [FORMULA] pc, completeness should consequently be expected further down, to about [FORMULA]. Hence, a comparison of the star counts between two samples and in different luminosity ranges is a good test of completeness, especially for the low luminosity end of the 100 pc HRD. It is also a good test, whether the stars are distributed evenly in space: Strikt homogeneity would yield a factor of 8 for all star counts. Any uniform ratio of respective star counts in so different volumes however is proof that neither HRD is dominated by specific local structure or star-burst events but is quite representative of the average galactic disk population. This point is of special relevance, when modelling the solar neighbourhood HRD with the simplification of a strictly random stellar age distribution.

Within statistical fluctuations, a uniform ratio of 7 is found between the respective star counts in all HRD regions with [FORMULA], except for the small number of higher mass MS stars (see Sect. 3.3). Here, the global galactic structure (the disk geometry) becomes evident: the finite scale height obviously reduces the stellar density in the polar regions of the 100 pc volume.

Between [FORMULA] 3.5 and 4, which includes stars within half a magnitude from the expected threshold, the 100 pc HRD appears to be incomplete by 10%: the respective star counts yield only a factor of 6.3. We therefore restricted the subsequent work to HRD regions with [FORMULA] brighter than 3.5.

Quality, i.e., the quality of the HRD positions, is the other important factor to consider here. The distances obtained from the HIPPARCOS catalogue have very non-uniform errors, depending on the already non-uniform parallax errors and increasing with the distance itself. The resulting error distribution function has the form of a main body of small errors plus two long tails of large errors.

Since large errors in parallax [FORMULA] result in an asymmetric error distribution in distance d, more stars are displaced to lower luminosities (smaller distances) than vice versa, i.e., there are many stars which in reality are from outside the sample volume. At [FORMULA] pc, displacements in [FORMULA] may reach [FORMULA] in extreme cases (standard deviation [FORMULA] 15 to 20mas), while for most stars [FORMULA] is known to within [FORMULA]. Sampling by a minimum quality parallax provides no improvement (rather the contrary), since it would introduce unwanted, non-uniform deviations from completeness in such a HRD.

Equally, the B-V colours become distorted in an asymmetric way: reddening becomes noticeable with larger distances, and photometry tends to be a bit less precise as well. However, we estimate both effects to be only of the order of [FORMULA], each.

Another source of confusion is non-resolved binaries of comparable brightness (including differences of up to an order of magnitude) which would occupy a false HRD position according to their composite colour and combined luminosity. We therefore removed all entries of spatially resolved binaries, which seem to cover already a large fraction of all binaries in the [FORMULA] pc sample. Of the remaining spectroscopic binaries, pairs with a cool giant and an early MS star would be the most obvious cases: they would falsly fill up the otherwise lowly populated Hertzsprung gap of the resulting HRD, therefore providing a worst-case test. The other HRD regions, however, are not over-proportionally filled in by binaries.

A check of the Herzsprung gap in the 50 pc HRD lead to the removal of two stars with [FORMULA], which were listed as spectroscopic binaries in the Bright Star Catalogue (BSC). Among 27 stars checked in the lower gap (i.e., HRD region HG in Table 1), three more binaries were found in the BSC and removed from the sample. In the 100 pc sample, 22 spectroscopic binaries were found among 48 checked gap stars ([FORMULA]), using the same criteria. Apart from the 7-times larger star counts, a larger fraction of spectroscopic binaries can indeed be expected there because fewer binaries are resolved spatially at larger distances. Stars in the lower Herzsprung gap of the 100 pc HRD are mostly not covered by the BSC and no further spectroscopic binaries were found. However, a few unknown binaries can be expected there.


[TABLE]

Table 1. Characteristic regions and star counts of evolved stars in the HRD: Hertzsprung gap (HG), lower giant branch (LGB), K giant clump (KGC) and "cool wind" region (CW).


Altogether, we count 1337 single stars in the solar neighbourhood for [FORMULA] pc and 8984 for [FORMULA] pc, for [FORMULA]. Visual inspection of the respective HRDs (Fig. 1 and Fig. 3) shows that well-defined features, such as the the zero age MS or the K giant clump (around [FORMULA], B-V = 1.0), are more smeared out in the 100 pc HRD. Obviously, its interpretation is more ambiguous - despite the 7 times larger star counts it provides. The situation is different, however, with the "cool wind" (B-V [FORMULA]) giants and the luminous blue loop giants. Both these giant groups cover larger areas of the HRD and therefore do not get so much confused with other, displaced stars. Since their numbers are too small in the 50 pc HRD, we here expect a definite advantage for the 100 pc HRD. In this way, both HRDs are nicely complementary in an analysis of evolved stellar population densities and we use both as reference samples for our computed HRDs (see Sect. 4.1 and Table 1).

[FIGURE] Fig. 1. The solar neighbourhood HRD for [FORMULA] pc, as observed by HIPPARCOS
[FIGURE] Fig. 3. The solar neighbourhood HRD for [FORMULA] pc, as observed by HIPPARCOS
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© European Southern Observatory (ESO) 1998

Online publication: June 2, 1998

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