The Abundance Pattern of the Library Stars

As stressed in the Introduction, one can only use a stellar population synthesis model to estimate the abundance patterns of galaxies if the abundance pattern of the input model is known. The latter is dictated by the abundance pattern of the stars used in the construction of the models. The latter probably mirrors the abundance pattern of the solar neighborhood and as such it should vary as a function of [Fe/H] (e.g., Edvardsson et al. 1993). This so-called ``bias'' of stellar population synthesis models was pointed out, and accounted for, by Thomas et al. (2003a). In this section we try to characterize the abundance pattern of our models. This information will make it possible to use these models to infer accurate abundance ratios from integrated spectra of galaxies through the method developed by Trager et al. (2000) and Thomas et al. (2003a).

We searched the literature for abundance determinations of our library stars. We found data for roughly one third of the entire library and assume that these stars are representative of the whole sample. The results are plotted in Figure 5, where abundance ratios of some key elements are plotted against [Fe/H]. The sources of the abundances plotted are as follows: Calcium abundances come from Thévenin (1998), Gratton et al. (2003), and Reddy et al. (2003). Magnesium abundances come from the latter works and also from Carretta, Gratton & Sneden (2000). Oxygen comes from Luck & Challener (1995), Thévenin (1998), Reddy et al. (2003), Gratton et al. (2003), Carretta et al. (2000), and Israelian et al. (2004). Titanium abundances were taken from Thévenin (1998) and Gratton et al. (2003). Most of the carbon abundances come from Carretta et al. (2000), but we also include data from Shi, Zhao & Chen (2002), Carbon et al. (1987), and Reddy et al. (2003). Nitrogen abundances were drawn from Shi et al. (2002), Israelian et al. (2004), Ecuvillon et al. (2004), Reddy et al. (2003), Carretta et al. (2000), and Carbon et al. (1987).

In Figure 5, giant stars are plotted as open squares and dwarfs as small dots. As expected, the abundance ratios of some elements do present a significant variation as a function of [Fe/H]. From this figure it is also clear that there are two groups of elements in terms of the behavior of their abundances as a function of evolutionary stage. For magnesium, calcium, titanium, and oxygen, the abundances in giants and dwarfs seem to be similar. The same is not true for carbon and nitrogen, though. The abundances of carbon are much lower in giants than in dwarfs. Nitrogen, on the other hand, is more abundant in giants than in dwarfs. These trends are not unexpected. They result from contamination, during the first dredge-up, of the atmospheres of giant stars by fresh material processed by the CNO-cycle (e.g., Iben 1964, Brown 1987, Carretta et al. 2000, Thorén, Edvardsson & Gustafsson 2004). As a consequence, the giant abundances for these elements do not reflect their original values, so that they will not be considered here. For the other elements, the data on giant stars are consistent with, but more scattered than, those of dwarfs, so that we decided to eliminate the giant abundances in the following derivation.

In order to estimate mean values for the abundance ratios of the various elements as a function of [Fe/H], we fitted low order polynomials to the relations [X/Fe] vs. [Fe/H]. The results are presented in Table 6 for a number of reference values of [Fe/H]. The 1-$\sigma$ error bars come from the r.m.s. of the polynomial fits at different [Fe/H] bins and probably reflect a combination of measurement errors and intrinsic spread. We chose to present these data in fine [Fe/H] bins, in spite of the relatively large error bars in the abundance ratios, in order to facilitate interpolation in the table values.

A few caveats need to be kept in mind when using these numbers. The first one concerns the oxygen abundances of metal-poor stars, which are still very controversial (see the review by Kraft 2003). Different abundance analysis methods, relying on the forbidden lines at $\sim$ 6300 ${\rm\AA}$, the triplet at $\sim$ 7770 ${\rm\AA}$ or synthesis of OH bands in the near-UV and near-IR, yield abundances differing by up to 0.5 dex at [Fe/H] $\sim$ -1.5. Probably because our abundances were compiled from works employing different methods, our mean [O/Fe] values for [Fe/H] $\mathrel {\copy \simlessbox }$ -1.0 fall right in the middle of the range of current determinations (see Figure 1 of Fulbright & Johnson 2003). While that may leave us in a relatively safe position, we caution the reader that these values might need to be revised once oxygen abundances from different groups reach agreement.

There also is disagreement in the literature in determinations of carbon abundances of field stars. On one side, Shi et al. (2002) and Reddy et al. (2003) find carbon to be overabundant relative to iron in metal-poor stars and increasingly so with decreasing [Fe/H]. On the other hand, Carbon et al. (1987) and Carretta et al. (2000) found [C/Fe] $\sim$ 0 and essentially invariant as a function of [Fe/H]. Finally, Shi et al. (2002) agree with Carretta et al. for [Fe/H] $\mathrel{\copy\simgreatbox}$ -0.7, but find carbon overabundances for more metal-poor stars. The [C/Fe] values displayed in Figure 5 and Table 6 are solar and constant with [Fe/H] because most of the carbon abundances come from Carretta et al. (2000). As for nitrogen, Shi et al. (2002), Ecuvillon et al. (2004), and Israelian et al. (2004) all find [N/Fe] $\sim$ 0 and constant within a very large [Fe/H] range. On the other hand, Reddy et al. (2003) find [N/Fe] $\sim$ +0.2, in a much smaller range of [Fe/H].

There are three separate issues that should be highlighted here. The first is related to the uncertainties mentioned above. While we are not in a position to choose among the various abundance determinations, we alert the reader for the obvious fact that the numbers provided in Table 6 might need to be revised when future improvements in abundance determinations come about. The second regards the degree to which the spectral library in use here, and any other spectral library for that matter, can be safely assumed to replicate the abundance pattern of the solar neighborhood in detail. The selection of targets involved in the production of such spectral libraries is dictated by criteria that are very different from those involved in standard surveys of the abundance pattern of Galactic field stars. Therefore, it is not unlikely that the abundance pattern of the stars in the spectral library might be biased in different ways. An obvious example of a way in which this can happen is the inclusion of cluster stars (Worthey et al. 1994), whose detailed abundance patterns often differ from those found in the field. Last, but not least, there is the issue of whole regions in the stellar parameter space where detailed abundances (and sometimes even just [Fe/H]!) are unknown. That is the case in both ends of the $T_{\rm eff}$ spectrum, and is especially worrisome in the case of bright stars such as M giants and hot stars in general. Fortunately, we are working in a spectral region where the former contribute little light and are mostly concerned with an age/metallicity regime where the latter are not very important. But that should be a reason for concern for work on stellar populations younger than $\sim$ 1 Gyr, and for any attempt at studying stellar populations of any age longward of $\sim$ 6000 ${\rm\AA}$.