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Astron. Astrophys. 363, 947-957 (2000)

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2. The sample

2.1. Observations

This work is based on observations obtained with the Danish 50cm and 1.54m telescopes on La Silla. All stars from the Michigan Spectral Catalogue (Houk & Cowley 1975; Houk 1978, 1982) in the spectral range F to K2, and below [FORMULA] were included. This spectral range was used to ensure that all stars in the G dwarf mass interval were included, as different age and metallicity spread stars of a given mass over a wide spectral range.

The sample has varying magnitude limits based on color. That can be seen in Table 1. [FORMULA] is the absolute photographic magnitude and [FORMULA] is the established apparent photometric limit in the corresponding color interval. For the F stars the limit was [FORMULA] which is more than adequate.


Table 1. The sample limits as a function of spectral type.

All stars of luminosity class V, IV or undertermined class are included. The sample consists of 5561 stars.

Strömgren four color photometry was obtained for all stars. The [FORMULA] index was measured for F and early G-type stars. The observations are more fully described by Olsen (1983, 1993, 1994).

The calibrations used are split in two parts; the G dwarfs and the F dwarfs, for which separate calibrations were used. In the zone where these groups overlap the F dwarf calibration was used. The F dwarf group used the Crawford (1975) calibration for [FORMULA], the Nissen (1981) calibration for [Fe/H], the Magain (1987) calibration for [FORMULA] and the Olsen (1988) calibration for [FORMULA]. In the G dwarf group the calibration by Olsen (1984) was used.

2.2. Distance limit

To ensure that the sample is reasonably volume complete a distance limit must be established. This is done by comparison with a homogeneous distribution. For [FORMULA] the sample is reasonably complete to [FORMULA]. For the F stars in the sample the limit is beyond [FORMULA], causing a lot of them to be removed when the sample is reduced to stars within [FORMULA]. The distance limit leaves 1141 stars in the sample.

2.3. Mass derivation

The masses of the stars in the sample were determined by linear interpolation in the evolutionary models by VandenBerg et al. (2000). These models are brand new, and include an improved equation of state with non-ideal corrections, updated nuclear reactions, neutrino cooling rates, and modern opacites. The new models are so superior compared to the older models (VandenBerg 1985) that the older models should be considered obsolete. Even so the old models were used for comparison to gauge the effect of different models on the resulting masses. The models agree within 0.05 to [FORMULA], with a small trend, where the old models give slightly lower masses for low metallicity stars.

In referring to these models, the following definitions are used: A point is the data describing a single model star of a given mass and metallicity at one age in its evolution. A track is the collection of points describing the evolution of a model star of a given mass and metallicity. A set is the collection of tracks describing stars of a given metallicity.

This is an interpolation in three dimensions. The dimensions involved are: [FORMULA], [FORMULA] and [Fe/H]. The interpolation is split in three parts to match these dimensions. For each of the two sets nearest to the star in [Fe/H], the two tracks nearest to the star is found. Temporary points are then found on these tracks by interpolating along the track, so that the temporary points have the same [FORMULA] as the star. It is then possible to find a temporary mass for the star in each set. A final interpolation (between the two sets) gives the mass of the star. As a test this mass is compared with the four masses used to derive it. If the resulting mass is within [FORMULA] of any of these points the result is accepted. This leaves 749 stars in the sample. If the sample is restricted to stars where no extrapolation is used to derive their mass, the number of stars is reduced to 550. In both cases this is still a fairly large sample.

A total of 392 stars were discarded by the interpolation program. It is of course very interesting to examine these stars. The Olsen (1984) calibration is only valid for luminosity class V stars. In general, subgiants will get a too low [Fe/H]. To test for subgiants, the Olsen [Fe/H] was compared to the calibrations of Schuster & Nissen (1989), as their calibration does include subgiants. Of the 392 rejected stars, 206 were outside the calibration limits of Schuster & Nissen. 116 had [FORMULA]. This indicates that they are subgiants. Looking at the [FORMULA] diagram (Fig. 1) it is obvious that the 116 stars with conflicting [Fe/H] lie in the area where subgiants normally are found (see Olsen 1984). It is also obvious that the stars outside the calibration range are mostly giants and stars on the lower main sequence (K-dwarfs etc.).

[FIGURE] Fig. 1. [FORMULA] diagram for the discarded stars. The diamonds are stars outside the calibration ranges of Schuster & Nissen (1989), the crosses are stars with conflicting [Fe/H] and the triangles are the rest. The solid line is the preliminary standard relation for dwarfs of Hyades metallicity. The dashed line is for giants.

Of the remaining 70 discarded stars, 14 were close binaries according to the Hipparcos catalogue (ESA 1997). In addition, one was found to be chromospherically active according to the EMSS survey (Einstein Observatory Extended Medium Sensitivity Survey, see Sect. 3.3). It is not clear why the remaining stars are discarded, but their small number justifies simply accepting that they did not fit in some way.

2.4. The mass interval

The range of colors included in the sample corresponds to a mass interval, within which the sample is reasonably complete. The lower mass limit is established by comparion to the lowest temperature for each metallicity in the theoretical models by VandenBerg et al. (2000). This establishes the lower mass limit to between [FORMULA] and [FORMULA]. As stars with high metallicity has lower [FORMULA] than comparable low metallicity stars, a limit at [FORMULA] will lead to high metallicity stars being under-represented. The upper mass limit must be established so that all stars below the mass limit have main sequence lifetimes longer than the age of the disk. As this age is still controversial this limit is subject to some uncertainty. The limit is established by comparing the age of a model star 0.02 dex (in [FORMULA]) past the bluest point of the evolutionary track. This extra distance is chosen so that a [FORMULA] star with solar metallicity has a main sequence lifetime of 10.7 Gyr, and to allow for the observational scatter. The resulting ages are shown in Table 2.


Table 2. Main sequence lifetimes at different [Fe/H].

As the region below [Fe/H] = -1.0 is only marginally relevant for the purposes of this paper, as there are very few stars in the sample below this limit, it is safe to assume that the limit is somewhere between 0.9 and 1.0 [FORMULA]. This does represent a rather narrow range when compared with the color limit.

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Online publication: December 5, 2000