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Astron. Astrophys. 364, 102-136 (2000)

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8. Abundances

8.1. Abundances from KPNO and ESO-CAT spectra

Our first estimate of the abundances (using the mean stellar parameters given in Table 7) was made by fitting the measured equivalent widths ([FORMULA]) of the apparently unblended lines to the computed ones. In the case of the spectra observed at Kitt Peak 9, we tried to determine the microturbulent velocity ([FORMULA]) by assuming that, for a given element, the abundance is independent of the equivalent widths. The uncertainty, however, both in the equivalent widths of the weak lines and in the [FORMULA] values (especially for the lines of Ti II , which are the most numerous) severely limits this method of obtaining [FORMULA]. We therefore, in addition, determined [FORMULA] by comparing the observed spectra against a series of synthetic spectra in which [FORMULA] was sampled in steps of 1.0 km s[FORMULA]; in a few cases an intermediate step of 0.5 km s[FORMULA] was used.

In the case of BD +00 0145 and HD 14829 and for the stars observed at ESO we assumed a microturbulent velocity [FORMULA] of 2.0 km s[FORMULA], since there were too few lines in their spectra to allow us to derive [FORMULA].

In computing the synthetic spectra, we used either the mean abundance derived from the equivalent widths for species with more than one measured line (e.g. Fe I , Fe II , and Ti II ) or the abundance computed from a single line if only one line of a species was available (e.g. Ba II [FORMULA]4554).

The synthetic spectra were computed at a resolving power of 500 000 and then were degraded to 15 000 (the nominal resolution of the Kitt Peak spectra) using a gaussian instrumental profile. The computed spectra were then broadened by the rotational velocity ([FORMULA]) that is given in Column 2 of Table 15. This [FORMULA] was derived by fitting the observed profile of the Mg II  4481 Å to the computed profile assuming the Mg abundance that had been derived from the measured equivalent width. No macroturbulent velocity was considered.

The comparison of our observed spectra with the synthetic spectra showed that some of the lines in our original list should be discarded either because they were blended or because they were too weak. The WIDTH program was now used to recompute new abundances from the equivalent widths ([FORMULA]) of the remaining lines using the value of [FORMULA] that had been determined from the synthetic spectra. We made several iterations using both the comparison of the observed and the computed [FORMULA] and the comparison of the observed and synthetic spectra until the abundances obtained by the two methods were consistent. In the course of the successive iterations we changed the [FORMULA] and the metallicity of the models so that they were as close as possible to the values that we derived from the abundance analysis.

The measured equivalent widths ([FORMULA]), the adopted [FORMULA], their sources, and the logarithmic abundances relative to the total number of atoms are given for the individual lines for each star in Table 4 for the KPNO spectra and in Table 5 for the ESO-CAT spectra. Table 9 lists, for each star, the model parameters, the microturbulent velocity and the average abundances derived from the measured equivalent widths of the individual lines. We derived the barium abundance from the Ba II  4554.033 Å line. For a few stars, we used only the synthetic spectra, while for some others we used the equivalent width method in addition. Both values are given in Table 9 (that from the synthetic spectra is identified with the superscript S). The slight systematic difference between the abundances obtained by the two methods may be related to the placement of the continuum level which was fixed independently by Kinman for the measurement of the KPNO equivalent widths and by Castelli for the normalization of the whole observed spectrum.


[TABLE]

Table 9. Abundances derived from the KPNO and CAT spectra.



[TABLE]

Table 9. Abundances derived from the KPNO and CAT spectra.
Notes:
S) Abundances derived from the synthetic spectrum analysis
1) RR Lyrae variable CS Eri at phase 0.42. A further discussion is given in Sect. 10.7


Table 10 summarizes the abundances relative to the solar values together with the [Mg/Fe] and [Ti/Fe] ratios. The solar abundances, relative to the total number of atoms, are taken from Grevesse et al. (1996). Their logarithmic values are -4.46 for Mg, -5.68 for Ca, -8.87 for Sc, -7.02 for Ti,-6.37 for Cr, -4.54 for Fe, and -9.91 for Ba. A few of them are also given in the last line of Table 10 for reference.


[TABLE]

Table 10. The adopted parameters and abundances relative to the solar values.
Notes:
K): KPNO spectra; [FORMULA]: CAT spectra a) Derived from Mg II  [FORMULA] 4481 (see text).


The ESO-CAT abundances, although based on only a few lines, show excellent agreement with those derived from the KPNO spectra for the non-variable stars HD 31943, HD 130095, HD 139961 and HD 180903 and for the low-amplitude variable HD 202759. The case of the larger amplitude type-c variable HD 16456 (CS Eri) is discussed in Sect. 10.7.

For the stars whose [FORMULA] exceeds about 8 500 K (or about half the stars in our sample), the He I [FORMULA] 4471 line is visible in our spectra. Its strength agrees with that predicted by the synthetic spectrum for a solar helium abundance.

8.2. The [Fe/H] abundance as a function of the equivalent width of Mg II  [FORMULA]4481 line and the colour index [FORMULA]

In most halo stars, [Mg/Fe] can be assumed either to be constant or a slowly-varying monotonic function of [Fe/H] (see Sect. 10.5). If we have the photometric information, we can derive the stellar parameters and then determine [Mg/H] from the equivalent width of the Mg II  [FORMULA]4481 line even in quite low resolution spectra; [Fe/H] can then be derived by assuming an appropriate value for [Mg/Fe]; in this paper we assume [Mg/Fe] = 0.43.

Even if only [FORMULA] is available, one can estimate [Fe/H] from the the equivalent width W of the Mg II  [FORMULA]4481 doublet and the intrinsic colour. Using the data and [Fe/H] abundances that we derived from our KPNO spectra we found the following expression:

[EQUATION]

where [FORMULA] was obtained by using the mean extinctions given in boldface in Column 3 of Table 7 10. [Fe/H] derived from the above equation is listed in the last column of Table 10. The rms difference between our measured [Fe/H] and those obtained from this equation is [FORMULA]0.12 for the range -0.05[FORMULA][FORMULA][FORMULA]0.17. Systematic differences can occur between equivalent widths measured at very different spectral resolutions. Our relation strictly applies only to spectra whose resolution is comparable to those discussed in this paper; it may be less accurate if used with equivalent widths derived from lower resolution spectra.

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Online publication: December 15, 2000
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