To derive the calibration we used the sample of stars used by Beers et al. (1999) for the calibration of the KPindex. For all these stars UBV photometry and HP2 and KP indices are available. As calibrators we selected the stars with low reddening from Beers et al. (i.e. ). To make this criterion more stringent and thus to select a sample of truly unreddened stars, we searched the Hauck & Mermilliod (1998) catalog, through the interface of the General Catalog of Photometric Data (GCPD, Mermilliod et al. 1996) to find out stars of the Beers et al. sample with photometry. We then applied the Schuster & Nissen calibration to these data to obtain . Our final criterion was that both the estimate of E(B-V) of Beers et al. and the one derived from Strömgren photometry were less than or equal to 0.01 mag.
Out of the sample of Beers et al. (1999) 65 stars satisfy our criterion and they are reported in Table 1, the star name is given in Col. (1), Col. (2) gives the star type, according to Beers et al. (1999). Column (3) is [Fe/H] and Cols. (4)-(7) provide the Strömgren photometry extracted from the Hauck & Mermilliod (1998) catalogue. We performed a fit on this sample of stars for several functional forms. We computed the rms of the fit and we then discarded those stars whose residual was greater than rms. This was aimed at further cleaning the sample by rejecting stars which are either reddened or whose colours or line indices are affected by larger errors. Quite interesting only one star, CD 17504, was discarded, whichever functional form was used. This star is also the most metal-poor of the sample, in fact the only one below . Thus our fits were all performed on a sample totalling 64 stars.
We began with the assumption that both (B-V) and HP2strongly depend on temperature; we therefore fit a linear relation
The rms of the fit was 0.0153 mag and , i.e. , which indicates a good fit. In Fig. 1, panel a) we show a plot of (B-V)versus the right hand side of Eq. (1). Panels b) and c) display the residuals as a function of metallicity and (B-V) colour, respectively.
The range of validity of the calibration is
fixed by the properties of the calibrator stars. In our case
|Figure 1: a) The right hand side of Eq. (1) for the calibrators as a function of (B-V). The star CD 17504 appears to be an outlier and has not been used in the derivation of the calibration, and it is not drawn in panels b) and c), b) the residuals (B-V)-FIT as a function of metallicity, c) same as panel b) but as a function of (B-V)|
A matter of concern is wether the luminosity (gravity) dependence of the calibration is properly captured by the (U-B) colour. Inspection of Table 1 reveals that, although we did not impose any selection criterion on luminosity, most of our stars are dwarfs, only one is a giant, three sub-giants and one horizontal branch. This is a result of imposing a very tight criterion on reddening for the calibrators: all low-reddening stars are nearby and therefore most are dwarfs. So formally our calibration is valid only for dwarfs. In Fig. 2 we show the residuals of the fit as a box plot in the plane. There appears to be no obvious trend of the residuals with the luminosity of the stars, we may therefore expect that the calibration is in fact equally applicable to dwarfs and giants, as is the Schuster & Nissen calibration.
|Figure 2: The residuals (B-V)-FIT in the plane. The stars have been divided into 10 bins 0.01 mag wide. The size of the symbol is largest for the stars in the bins mag and decreases to the minimum size for stars in the bins with , as indicated in the scale plot shown below the figure. Negative residuals are shown with crossed squares, while positive residuals are shown with open squares. The star CD 17504 is drawn with an asterisk. The solid line represents the locus of points with for . The dashed line is the same but for|
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