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

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4. The abundance determination

The spectra used are [FORMULA] Å wide, centered around the Li I 6707.8 Å line. In this spectral region we have identified 13 Fe I lines with sufficient strength in the spectrum of the Sun to allow a direct determination of the solar [FORMULA] values. Unfortunately, no Fe II lines are present in the limited spectral region under analysis, making it impossible to check the effective temperature through a determination of the Fe ionization equilibrium.

Abundance analyses were performed with the WIDTH9 code, using a grid of stellar models computed with the ATLAS9 code (Kurucz 1993a ). For most of the stars in the sample no coherent multicolor photometry is available in the literature, and thus the surface gravity cannot be determined on an individual basis. We have therefore assumed that all stars are main sequence ones and adopted the value of surface gravity appropriate at each temperature for main sequence stars, based on the observed main sequence [FORMULA] -color relationship of Gray 1992 . This introduces a small additional uncertainty for the few slightly evolved hotter stars in the sample. For the micro-turbulence parameter [FORMULA] we have used the relationship of Edvardsson et al. 1993 , i.e.

[EQUATION]

assuming a constant [FORMULA] of 0.2 km/s for the cooler dwarfs for which the relationship predicts values smaller than 0.2 km/s.

An extensive grid of stellar models was computed, spaced by 25 K in [FORMULA], with temperature dependent [FORMULA] and [FORMULA] values, and using the [FORMULA] km/s, solar abundance grid of Kurucz 1993a . For each star, the equivalent width of the Fe I lines listed in Table 2 was measured from the spectra, using the splot routine from the IRAF software package, and de-blending nearby lines when appropriate and possible (in particular the 6696.30 Å Fe I line is blended with a nearby Al I line. See also Sect.  4.1). The measured equivalent widths, together with the model atmosphere from the computed grid with [FORMULA] closer to the actual photometrically determined value, were used as input to WIDTH9, which produces an abundance estimate for each line together with a mean abundance and a scatter. This mean abundance, together with the scatter, is reported in Table 1. Some of the lines could not be measured in some of the spectra, as in some case the radial velocity Doppler shift of the spectrum moved some of the lines outside the spectral region observed. Also, cosmic rays hits rendered, in a few cases, some lines unusable. Therefore in Table 1 we also report the number of Fe I lines contributing to the final abundance determination for each object.


[TABLE]

Table 2. The line list. Also reported in the last two columns, for comparison purposes, are the [FORMULA] values from Abia et al. (1988) and Balachandran and Lambert (1988), indicated as ARB+88 and BL88, respectively.


Line data were taken from the extensive lists of Kurucz 1993b . The [FORMULA] values were estimated from each line by using the WIDTH9 code together with the solar model atmosphere of Kurucz 1993b . Individual [FORMULA] values were varied until the computed equivalent widths for each line were found to be in agreement with the equivalent widths measured from a set of high signal-to-noise solar spectra taken with the same instrumental configuration as the stellar spectra. This procedure (which obviously will yield a differential abundance analysis with respect to the Sun) has the advantage of intrinsically allowing some correction for eventual spectrograph peculiarities (such as scattered light). The [FORMULA] values thus determined were found to be in reasonable agreement, as indicated in Table 2, with the values of Abia et al. and Balachandran & Lambert 1988 .

The larger error bars evident for the cooler stars in Fig. 1 are due to the often lower signal-to-noise in the spectra of these typically fainter objects, as well as to the difficulty of determining the continuum reliably in their more crowded spectra.

4.1. Blended lines

Three of the Fe I lines used in the analysis are blended and cannot be separated: Fe I 6705.10 Å is blended with a weak Fe I line at 6705.13 Å, Fe I 6713.05 is blended with a weak Fe I line at 6713.20 Å, and Fe I 6715.04 is blended with a weak Cr I line at 6715.41 Å. None of these blends can be resolved, and thus they have been measured as a single line. The [FORMULA] value determined from the solar spectrum is thus an "effective" [FORMULA] for the blend. This simplifying assumption, however, is only valid if the equivalent width of the two blended lines has the same temperature and abundance dependence. To verify this assumption we have generated a set of synthetic spectra, and determined the difference between the abundance determined by measuring the de-blended line (with an appropriately determined [FORMULA]) and the abundance determined by measuring the equivalent width of the blend (with the [FORMULA] value determined as above). An induced error of [FORMULA] % has been considered as acceptable. For the 6705.10-6705.13 Å Fe I blend, the induced error is [FORMULA] % across the whole temperature range while for the 6713.05-6713.20 Å Fe I blend the error is [FORMULA] % across the whole temperature range. For the 6715.04-6715.41 Å Fe I -Cr I blend the error is acceptable for [FORMULA] (where it is [FORMULA] %), but it becomes larger for [FORMULA]. Thus, the 6715.04-6715.41 Å Fe I -Cr I blend has not been used in the determination of the abundance of the objects cooler than 5000 K.

4.2. The difference between high- and low-excitation potential Fe lines

While the abundance values determined for hotter stars from all the Fe I lines are usually in very good agreement, with RMS scatters as small as 0.05 dex, for cooler stars the abundance values determined from the two low excitation Fe I lines in our line list (Fe I 6703.57 Å, with [FORMULA] eV, and Fe I 6710.32 Å, with [FORMULA] eV) are systematically lower by [FORMULA] dex than the abundance determined from the rest of the Fe I lines, which are all high excitation lines ([FORMULA] eV). Such difference in the behavior of high and low excitation Fe I lines in cool stars is already well known in the literature, and it is attributed to non-LTE effects (cf. for example Fig. 3 of Drake & Smith 1991 ). The study of Steenbock 1985 shows that NLTE effects are primarily due to over-ionization of Fe I rather than to non-thermal excitation effects, and that, as a consequence, NLTE effects will increase with increasing line strength and decreasing excitation potential, due to the different depth of formation of the core of these lines. Steenbock 1985 notes that weak, high-excitation Fe I lines are the ones which, in an LTE analysis, yield the abundance closest to the "true" value, with low-excitation lines yielding a much lower abundance (as we indeed observe in the cooler stars in our sample). Therefore we have only used the high-excitation Fe I lines, and discarded the abundance derived from the low-excitation lines for all the stars in the sample, even when it appeared to be in good agreement with the abundance of the high-excitation lines.

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© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

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