Abundance-Ratio Effects

Absorption-line strengths in the integrated spectrum of a single stellar population are affected by its abundance pattern for two main reasons: i) the effective temperatures and, potentially, the luminosities of two stars with same mass, age, helium abundance, and metallicity, but different abundance patterns, are different, and as a result the spectra of these two stars are different; ii) the spectra of two stars that occupy the same position on the HR diagram and have the same metallicity are different if they have different abundance patterns. The effect of the abundance mix on the effective temperature of a given star is due to the relative contribution of different elements to the overall opacity of the stellar interior. Oxygen is the most important metallic source of opacity at the high temperatures prevalent in the stellar interiors (Vandenberg & Bell 2001). In the outer layers, iron is the predominant metal source of opacity for FGK stars, which dominate the light of single stellar populations in the spectral region of relevance for this study. It is therefore fair to say that the effect of abundance ratios on the positions of stars in the HR diagram is dictated by the relative abundances of oxygen and iron. Line strengths, on the other hand, can be strongly affected by the individual abundances of elements which are not optically active enough to produce a substantial change in the star's structure. Two stars with the same mass, age, metallicity, and helium abundance, and whose abundance patterns are the same except, for instance, for their calcium abundances, have virtually the same temperature and luminosity, and their spectra will be essentially the same, except for differences in the strengths of lines due to atomic calcium or due to molecules involving calcium, such as calcium hydride.

Since the realization that the chemical composition of stars in giant early-type galaxies is enhanced in light elements (e.g., Peterson 1976, O'Connell 1980, Peletier 1989, Worthey et al. 1992), a great deal of effort has been invested into producing realistic models with an $\alpha$-enhanced abundance pattern. These efforts branch out in two major directions, aimed at accounting for the two major effects listed above: i) computation of stellar evolutionary tracks for metal-rich stars incorporating an $\alpha$-enhanced mixture (e.g., Weiss et al. 1995, Salasnich et al. 2000, Kim et al. 2002) in order to assess the impact of $\alpha$-enhancement on model predictions, and ii) estimating the effect of the abundance pattern onto stellar spectra and line indices (e.g., Barbuy 1994, Tripicco & Bell 1995, Paper I, Barbuy et al. 2003, Coelho 2004, Mendes de Oliveira et al. 2005, Korn, Maraston & Thomas 2005), using spectrum synthesis from model stellar atmospheres.

Before comparing model predictions with data in Section 5, it is interesting to discuss the impact of abundance ratios on model predictions. For simplicity, throughout this paper we refer to i) above as evolutionary abundance-ratio effects and to ii) as spectroscopic abundance-ratio effects. In Section 4.3.1, we examine evolutionary abundance ratio effects, which are those stemming from the influence of the abundance mixture on the luminosity and effective temperature of a star of given mass, metallicity and evolutionary stage. Spectroscopic abundance-ratio effects are considered in Section 4.3.2.