3. Abundance determination
For the reduction of the spectra, we used the Inter-Tacos software of Geneva Observatory 1. The spectra were divided by an average of six flat-field exposures, after the background had been fitted by 2-d polynomials and subtracted. Then, they were extracted using a simple addition of the intensities along a virtual slit of 15 pixels. The wavelength calibration was performed with the same software, using Th-Ar spectra taken in the afternoon preceding the night. The rms scatter of the residuals around the fitted dispersion relation was 3.1 mÅ, which is quite good for this resolution. After rebinning to a constant wavelength step of 0.03 Å, which is over-sampled, we filtered all spectra by eliminating the high frequencies of their Fourier Transform. For that purpose, we used a FFT with a window of 65% of (/R). The 55 orders were individually normalized to the continuum, using an interactive Supermongo procedure which interpolates between the continuum points by a 3rd degree spline.
3.1. Abundance determination
The list of lines and oscillator strengths used for our abundance determinations is the same as that adopted by Boyarchuk et al. (1996). The photospheric lines are chosen in wavelength zones avoiding the telluric absorption lines. The equivalent widths below 10 mÅ are rejected because they are too sensitive to noise and normalization. Table 3 (available only in electronic form) summarizes the line parameters and measured equivalent widths. For Mg i, not included in the list of Boyarchuk et al., we adopt the values of Thévenin (1989 , 1990).
The abundances are determined using the MOOG code (C. Sneden, Texas University) in the "abfind" mode, combined with atmospheric models of Kurucz (1996). The Kurucz models are interpolated by cubic splines in the and plane (solar abundances are assumed as far as the atmospheric structure is concerned). For some lines for which we have reasons to suspect that blends would make the equivalent width method risky (oxygen and europium), we compute a synthetic spectrum including a large number of neighboring lines, and determine the abundance of the considered element by best fitting the synthetic spectra to the observed one (the `best' fit being evaluated by eye estimate). In that case, the MOOG code is used in its "synth" mode and the lines are taken from the VALD database (Piskunov et al. 1995).
The measurement of abundance deviations as small as 0.15 dex requires good spectra with signal-to-noise (S/N) ratios above 100. Such a S/N is reached at almost all wavelengths in all our spectra, except near the [O i] line in three stars in NGC 2360 (star numbers 7, 50 and 62). No O abundance is presented for those stars.
3.2. Atmospheric parameters
The determination of the atmospheric parameters (gravity), (effective temperature) and (microturbulent velocity) is crucial for a good abundance estimation. The fact that the distance to the open clusters and the masses M of the individual stars are known provides a relation between and given by
where M is expressed in solar mass, is the absolute visual magnitude in V and BC is the bolometric correction. We assume , and take the bolometric corrections from Flower (1977) (which are very close to the theoretically derived ones of Bessell et al. 1998).
The atmospheric parameters and of each star are estimated from an iterative procedure based on the method used by Boyarchuk et al. (1996), but modified to take into account the known bolometric magnitudes of the stars.
Let us consider a given star. Starting with an initial guess of km s-1, we construct a diagram (Fig. 1) plotting the abundances of the iron-peak elements computed by MOOG from our observed spectrum, as a function of the effective temperature ( is computed for each value through Eq. 1). If all iron-peak elements had a solar abundance distribution, then there should be a value of at which their abundances (normalized to solar) are identical. In practice, we choose (by visual estimate) the value of at which the spread of abundances is minimal. Then, for this value, the usual diagram showing the Fe i abundances versus equivalent widths is used to adjust the best velocity of microturbulence . Finally, the whole procedure is reiterated in order to get mutually consistent parameters.
The value of found after the convergence of the iterative procedure differs by no more than 0.15 km s-1 with the first guess, which is consistent with the formal standard deviation of 0.11 km s-1 for that parameter, obtained from the uncertainty on the regression line of Fe i abundances versus equivalent widths.
This iterative procedure is applied to each of our stars. The resulting atmospheric parameters are summarized in Table 4. The derived effective temperatures agree to better than 100 K with the classical one based on the lack of correlation between abundance and excitation potential, the agreement improving with S/N ratio.
Table 4. Fundamental parameters of the 7 red giants and mean abundances relative to the Sun. For each species, the second line gives the rms standard deviation of the abundances obtained from individual lines. N is the number of lines measured. The oxygen abundances and [O/Fe] are derived from the equivalent width neglecting the possible contribution of the Ni i line, while [O/Fe]* is computed from a synthetic spectrum including the Ni i line (with the gf value from Kurucz 1994). [Fe/H] is an average weighted by the number of Fe i and Fe ii lines. [M/H] is a similar average, but on all iron-peak elements from Ca to Ni.
Finally, the sensitivity of our abundance determinations to the adopted atmosphere models is tested by recomputing some abundances with the models of Bell et al. (1976). They lead to similar results, in the sense that abundances given by individual lines are the same within dex after allowance for a slight systematic offset: the models of Bell et al. systematically lead to a 0.04 dex underabundance compared to Kurucz's models (for lines with an equivalent width mÅ; the offset is larger for stronger lines). In view of the relatively good agreement between both sets of models, we chose the Kurucz ones because they are more recent and easier to use.
The surface abundance of a given element is determined by adjusting the equivalent width(s) of its line(s) predicted by synthetic spectra to those measured in the observed spectra. Actually the MOOG program computes an abundance for each line of a given element, and derives a mean abundance value by averaging the abundances associated to each of those lines. In computing the synthetic spectra, the formation of a dozen molecules (among them C2, CH, CN, CO, MgH, TiO) is considered.
In the case of Eu, the only usable line is blended. We therefore determine its abundance by a visual match on a synthetic spectrum which includes all possible blends. This element is marked with an asterisk in Table 3. The same technique is used for oxygen, discussed in Sect. 6. The Eu ii line does not seem to be significantly affected by hyperfine structure, since its equivalent width in the Sun provides an abundance perfectly consistent with the meteoritic one, using precise experimental oscillator strengths (Biémont et al. 1982). Our value adopted for this line is only 0.03 dex below the one used by Biémont et al., so it would lead to a solar Eu abundance of 0.53 instead of 0.50 dex, while the meteoritic abundance is dex (Grevesse & Noels 1993).
The elemental abundances found in this work are listed in Table 4.
For information, we plot in Fig. 2 (filled circles and triangles) the microturbulence velocity deduced for our stars as a function of the surface gravity, together with the measurements of Boyarchuk et al. (1996) for five G7-K0 field giants (open circles, their sixth star is not considered because it is much cooler, of M0 type) and those of Luck (1994) for clusters' supergiants and giants with K (open triangles). The combined data reveals a positive correlation between and .
Considering only our seven points, the usual correlation coefficient gives a t-test value of only -2.17, implying a significance level of about 90 percent, while the Spearman rank correlation coefficient gives a slightly better t-test of -2.84 and a significance level of 96 percent. For the usual LSQ fit assuming no error on the abscissa and a constant error on the ordinate, we find
with an rms scatter of the residuals of 0.083 km s-1. For a fit where errors are assumed to be the same on both axes, the relation would be
with an rms scatter of the residuals of 0.088 km s-1. The scatter of the residuals is entirely compatible with the internal standard deviation of given above. It is smaller than that of the data from Luck (1994) and from Boyarchuk et al. (1996), partly due to the better homogeneity in metallicity and effective temperature.
© European Southern Observatory (ESO) 2000
Online publication: August 17, 2000