Evolutionary Abundance-Ratio Effects

In Figure 12 our models for single stellar populations are displayed in the $H\beta$ vs. $<Fe>$ (upper panel) and $H\delta _F$ vs. $<Fe>$ planes. These indices illustrate very well the general effect of $\alpha$-enhanced isochrones on Balmer and metal lines. In both panels, black lines indicate models computed with the $\alpha$-enhanced Padova isochrones (Salasnich et al. 2000) and gray lines those with the solar-scaled isochrones (Girardi et al. 2000). The ages of the models displayed are, from top to bottom, 1.2, 1.5, 2.5, 3.5, 7.9, and 14.1 Gyr. For clarity, we restrict the comparison to those amongst the two sets of models computed with similar [Fe/H] values (2 through 4 and 6 through 8 in Table 24). Solid lines connect same-[Fe/H] models, and dotted lines connect same-age models. The models for 3.5 Gyr are plotted with a long-dashed line, for clarity.

The main difference between models computed with solar-scaled and $\alpha$-enhanced isochrones is that the latter tend to predict weaker Balmer lines and slightly stronger metal lines, for the same age and [Fe/H]. This is because $\alpha$-enhanced turn-off stars are cooler and fainter than their solar-scaled counterparts at fixed [Fe/H], due to increased opacity, especially due to oxygen, in the stellar interior (e.g., Vandenberg & Bell 2001). In particular, the mixture adopted by Salasnich et al. in their $\alpha$-enhanced tracks is enhanced in [O/Fe] by +0.5 dex relative to solar. As a combination of the temperature effects on Balmer and metal lines, the models based on $\alpha$-enhanced isochrones appear to ``slide'' relative to the solar-scaled models along same-[Fe/H] lines, towards weaker $H\beta$. The final effect is that, for a given data point, $\alpha$-enhanced models predict younger ages but, interestingly, essentially the same [Fe/H]. For the mixture adopted by Salasnich et al. (Table 24) the age effect is of the order of $\sim$ 1 Gyr at intermediate ages ($\sim$ 4 Gyr), and as large as $\sim$ 3 Gyr for the ages of the oldest globular clusters ($\sim$ 14 Gyr). This effect, together with our improvement to the fitting function of the $H\beta$ index, leads to significantly younger ages for old stellar populations, thus ameliorating a long-standing problem, namely, that stellar population synthesis models tend to predict too old ages for the oldest stellar systems (e.g., Cohen, Blakeslee & Rhyzov 1998, Gibson et al. 1999, Vazdekis et al. 2001, Papers I and II, Proctor, Forbes & Beasley 2004, Lee & Worthey 2005). This issue is addressed further in Section 5.

We also note that $H\delta _F$ is substantially less affected than $H\beta$ especially for the oldest models. Comparing the two models for 14 Gyr in the bottom panel of Figure 12 we see that the variation in $H\delta _F$ corresponds to less than $\mathrel {\copy \simlessbox }$ 1 Gyr, compared to $H\beta$, whose variation amounts to $\mathrel {\copy \simlessbox }$ 3 Gyr.

We would like to call the reader's attention to an important new development. After submission of the first version of this paper, Weiss et al. (2006) showed that there was an error in the opacity tables adopted in the calculation of the Padova $\alpha$-enhanced evolutionary tracks, by (Salasnich et al. 2000). This error is such that the temperatures at the red giant branch and turnoff were overestimated by 200 and 100 K, respectively, for solar metallicity. Even though new isochrones with the mixture adopted by Salasnich et al. are not available, we simulated the effect of the corrected opacity tables by artificially changing the temperatures of giant and turn-off stars uniformly by 200 and 100 K in Salasnich et al. isochrones with Z=0.04 (nearly solar [Fe/H]). As a result, Balmer lines get weaker and metal lines get stronger. The change in $H\beta$ ($H\delta _F$) is of the order of $\sim$ -0.15 (-0.1) ${\rm\AA}$. Because Balmer lines would tend to get weaker in the models, ages according to these ``corrected'' $\alpha$-enhanced isochrones would get younger, thus accentuating the differences seen in Figure 12. The effect would be of the order of $\sim$ 2.5 (1) Gyr for an 11 (3) Gyr-old stellar population, in the case of $H\beta$. Ages according to $H\delta _F$ would get younger by $\sim$ 1.2 (0.5) Gyr for 11 (3) Gyr-old stellar populations. The change in $<Fe>$ is of the order of $\sim$ +0.14 ${\rm\AA}$ and it is such that models change along a line of constant [Fe/H] in the $<Fe>$-$H\beta$ plane. More definitive numbers have to await publication of $\alpha$-enhanced theoretical isochrones computed on the basis of updated opacities.

According to Weiss (2006, private communication), adoption of new opacities has a less important impact for lower metallicities. For instance, in the case of the metallicity of 47 Tuc, changes in age would be of the order of $\sim$ 1.5 Gyr and essentially zero in [Fe/H], so that our discussion in Paper II remains entirely valid.