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Astron. Astrophys. 323, 809-818 (1997)

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3. The effective temperature scale

There is still no widespread agreement neither on the absolute calibration of the effective temperature scale of cool dwarfs nor on the relationship between the photometric and spectroscopic (i.e. ionization balance) effective temperature scales. Given the dependence of the derived metallicity on the assumed effective temperature, and therefore on the final results of the present work, we review the process of derivation of [FORMULA] in detail.

When dealing with a sample of stars of different metallicity, the [FORMULA] index is not an appropriate [FORMULA] indicator, as for the range of metallicity observed in our sample stars, the [FORMULA] derived on the assumption of solar metallicity can be in error by as much as [FORMULA] K (see Buser & Kurucz 1992 ). The [FORMULA] versus [FORMULA] calibration is also sensitive to interstellar reddening. The [FORMULA] index is a much better choice, as it has very little sensitivity to metallicity effects at least down to [FORMULA], and, the sensitivity to reddening is very small (although, even for nearby stars, as shown by Gray 1995 , reddening induced effects can yield errors on [FORMULA] derived [FORMULA] as large as 20 K).

The most uncertain issue is the calibration of photometric indices in terms of "absolute" [FORMULA]. As discussed in detail by Bessel 1979 , for more luminous stars absolute determinations of the effective temperature are based on interferometric stellar diameter measurements, which, when coupled with bolometric magnitude measurements, allow for the effective temperature to be derived from first principles, independent from any stellar atmosphere modeling. However, interferometric stellar diameter measurements are not available for the fainter stars, i.e. for late G and K dwarfs. Alternative approaches are possible. The one adopted by Bessel 1979 is to assume, supported by reasonable theoretical assumptions, that the atmospheres of lower gravity stars (giants) behave, from the point of view of the color- [FORMULA] relationship, identically to the atmospheres of dwarfs. The [FORMULA] versus [FORMULA] calibration of Bessel 1979 for dwarfs is, for objects cooler than the Sun, essentially the one derived for giant stars.

The calibration of Bessel 1979 has recently been challenged by Taylor 1992 , who determined a [FORMULA] versus [FORMULA] calibration for G and K dwarfs, using effective temperatures determined both from model atmosphere analysis of Balmer line wings and from infrared flux modeling. While both methods incorporate some degree of model dependence, they have the advantage of being explicitly calibrated on dwarf stars. The Taylor 1992 calibration differs, for cooler dwarfs, from the Bessel 1979 one. While both appear to have essentially the same sort of linear relationship between [FORMULA] (usually using the variable [FORMULA]) and [FORMULA] the difference in slope is large (see Fig. 1 of Taylor 1992 ), with redder K stars being hotter by as much as 250 K in the Taylor 1992 calibration.

We have determined the abundance for the present sample using both temperature scales. The upper envelope of the scatter plot of [Fe/H] versus [FORMULA] derived using the Bessel 1979 calibration has a strong slope, with cooler stars having higher abundances with respect to hotter ones by about 0.2 dex. This indicates that the [FORMULA] scale adopted is not coherent with the one of the model atmospheres used for the abundance analysis. Such a slope is not present in the data analyzed with the Taylor 1992 [FORMULA] scale (see Fig. 1), which is therefore used in the following.

[FIGURE] Fig. 1. The Fe abundance, plotted against effective temperature, for the whole sample studied in the present work. The vertical error bars are the formal error on the abundance determined by the spread of the values derived from the individual Fe lines.

For most of the stars in the sample homogeneous [FORMULA] photometry is available (Bessel 1990 ). For some of the stars however only [FORMULA] or [FORMULA] data are available (see Favata et al. 1996 ), for which Taylor 1992 does not offer a calibration. For these objects we have used the Bessel 1979 color-temperature calibration for the [FORMULA] and [FORMULA] colors and converted it to the Taylor 1992 absolute [FORMULA] scale.

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© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998