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

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3. Steps towards a clean sample

A number of corrections was applied to the sample to ensure that it is as free of contaminants as possible.

3.1. Accuracy & errors

It is of prime importance to study the accuracy of the calculated masses. Nissen (1994) made a study of the calibration of the Strömgren system for F and G stars. In this study he finds among other things the standard scatter in [FORMULA], [FORMULA] and [Fe/H] determined from Str"omgren photometry. These results can then be used to estimate the accuracy of the mass as found by the method described above. Nissen finds that the error in photometric distance is about 15%, which corresponds to 0.3 mag. For disk stars the error in effective temperature lies around 100 K. The error in [Fe/H] is estimated to 0.15 dex from Olsen (1984). This is a conservative value as for most stars (those above [Fe/H] =-0.6) the scatter in the calibriation was 0.13, furthermore for the F stars the scatter is between 0.08 and 0.11 dex.

A grid of calculated masses running from [Fe/H]=0.00 to [Fe/H]=-1.05 in steps of alternately 0.07 and 0.08, from [FORMULA] = 1.5 to [FORMULA] = 9.9 in steps of 0.15, and from [FORMULA] (8000 K) to 3.477 (3000 K) in steps of 50 K, was constructed. This is then a `double resolution' grid, i.e. the step length is half the scatter. Using the next nearest neighbour it is possible to estimate the average scatter as a function of mass. It is obvious that the grid points outside the theoretical sets give nonsensical results. To avoid using these points in the estimation of the scatter, any points with a calculated mass below [FORMULA] or above [FORMULA] were not used. In addition only calculated masses within [FORMULA] of any of the interpolation points were used. The results are shown in Fig. 2.

[FIGURE] Fig. 2. Average scatter in the mass determinations. The solid line is the scatter from [FORMULA], the dashed line is the scatter from [FORMULA], the dash-dotted line is the scatter from [Fe/H] and the dash-dot-dot-dot line is the combined scatter. Only stars within [FORMULA] of an interpolation point have been used and invalid neighbours have been removed.

The mass is determined with an average scatter of [FORMULA]. There is a slight increase with increasing mass, but this is explainable. This increase is mostly derived from [FORMULA], and as the distance in [FORMULA] between tracks is larger on the lower main sequence, a "step" in mass up or down in the HR diagram will influence the calculated mass less. It is interesting to note that the average scatter is comparable to the difference between using the old and the new models.

3.2. Binaries & subgiants

To correct for any possible contamination of the sample by multiple stars or subgiants, the sample has to be examined closely to remove any such stars. To do this the remaining stars were all checked in several catalogues. The catalogues used were:

  • The Washington Double Star Catalogue (Worley & Douglass 1996) This catalog contains 78100 known visual double stars.

  • The SIMBAD online database was checked to find MK-classifications for the stars in the sample. It was also used as a source to find multiple stars, generally spectroscopic binaries.

  • The Hipparcos catalogue (ESA 1997) was used to check the photometric parallaxes. In general the photometric parallaxes was verified, although a few subgiants were discovered in this way.

Using these catalogues, the stars were classified into several categories:

  • Visual binaries. The visual binaries in the sample were split in two. The systems with a separation greater than [FORMULA] were regarded as single stars as the photometry of the individual components should be unafected by the other component. For the remaining visual binaries there are three possibilities. If the magnitude difference, [FORMULA], is larger than 5.0 the primary star dominates, and the system is regarded as a single star. If [FORMULA] is below 0.2 the two stars are regarded as identical, and the system is counted twice if the photometric parallax places the system within 29 pc to account for the extra luminosity. If [FORMULA] is between 0.2 and 5.0 the photometry is regarded as corrupted and the stars are discarded.

  • Spectroscopic binaries. There were eight stars that SIMBAD categorized as spectroscopic binaries. These stars were removed as their photometry may be unreliable.

  • Variable stars. These stars were removed from the sample.

  • Eclipsing binaries. The four eclipsing binaries in the sample were removed.

  • Alpha Centauri was in the sample, but it was removed as the photometry was of both [FORMULA] Cen A & B combined, and as their [FORMULA], they were discarded.

  • Giants. A few giant stars were still in the sample. They were removed.

  • Subgiants. Although a lot of the subgiants in the sample were already removed by the interpolation program several remain. These stars were removed here. The removal process was stepwise. First the MK classifications from the SIMBAD database were examined. If there were more than three sources that all agreed on the luminosity class, the star was either accepted or rejected on that basis. If that was not enough, the position of the individual star in the [FORMULA], [FORMULA] and [FORMULA] diagrams were examined. Finally, the distances to all the remaining stars were checked with Hipparcos data. Here a conservative limit of 60 pc (corresponding to 40 pc + 3[FORMULA]) was adopted. Stars with larger Hipparcos distances were discarded.

  • CORAVEL spectroscopic binaries. CORAVEL data was used to remove 15 spectroscopic binaries.

  • Halo stars. One halo star (HD 113083) was found from the velocity data described below.

  • Single main sequence stars. These stars were accepted and used.

The sample should now be reasonably free of disturbing double stars and subgiants, and it now contains 497 stars.

3.3. Chromospheric activity

Chromospheric activity may affect the photometric metallicities, through an influence on the Strömgren [FORMULA] index (e.g. Giampapa et al. 1979; Morale et al. 1996). To examine whether this has any effect on the current sample, the Henry et al. (1996) survey of HK line emission in solar-like stars (between G0 and K2) south of [FORMULA] and with HD magnitude [FORMULA] was used. For a G2V star this corresponds to a distance of [FORMULA]. This sample contains 650 stars. Comparing with stellar densities they expect their sample to contain about 50% of the stars present within [FORMULA].

Of the 1141 stars in the current sample within [FORMULA], 399 were also present in the Henry et al. sample. This is perhaps a bit low as Henry et al.'s sample extends to [FORMULA], thus having almost twice the volume, but the current sample also includes a fair amount of F stars and giants etc. This is a sufficiently large sample that an investigation of the effect on the photometric [Fe/H] can be made. Using Henry et al.'s limit of [FORMULA] to divide the sample into active and inactive stars, two subsamples are made which can then be compared. The effect suggested by Morale et al. and Giampapa et al. should lead to quite different metallicity distributions, with the high activity part considerably more metal poor than the low metallicity part. But as can be seen in Fig. 3, no real difference can be seen.

[FIGURE] Fig. 3. Comparison of the metallicity distribution of 399 stars classified as active and inactive by Henry et al. (1996). The solid line is inactive stars, the dotted line is active stars.

Even when limited to the stars that are accepted after all tests there are still 235 stars left, enough for these investigations. When the sample is limited to these stars, the result does not change, as seen in Fig. 4. This leaves a significant discrepancy between these results and the predictions of others. In an attempt to understand this phenomenon, the distribution of [Fe/H] versus [FORMULA] (Fig. 5) was examined.

[FIGURE] Fig. 4. Comparison of the metallicity distribution of stars classified as active and inactive by Henry et al. (1996), using only the 235 stars accepted after all tests. Again the solid line is inactive stars, the dotted line is active stars.

[FIGURE] Fig. 5. [Fe/H] versus [FORMULA] for the 399 stars from Fig. 3. Active stars, with [FORMULA] are predicted to have lower photometric metallicities.

As can be seen, there is little indication that low metallicity stars are seriously polluted by active stars. There is a clear relation between metallicity and activity to around [FORMULA], as expected from the activity - age - metallicity connection. Around solar metallicity there is a range of activity levels. Only those stars categorized as very active by Henry et al. (1996) ([FORMULA]) show a tendency to have underestimated metallicities. These stars form a very small part (2.6% according to Henry et al.) of the G dwarfs, so even without any attempt to remove such stars from a sample they would not affect it greatly. Among the active stars there are a few stars below [Fe/H] [FORMULA], but the great majority lies around solar [Fe/H]. Even among the few highly active stars with low [Fe/H] only one was present after all the other tests. It was removed.

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© European Southern Observatory (ESO) 2000

Online publication: December 5, 2000