Two important caveats are worthy of mention. First of all, one of the single most important parameters influencing the integrated properties of stellar populations has been left out of the procedure outlined above: the abundance of oxygen. Oxygen abundances affect the stars' interior opacities, thus having a strong impact on their structure and evolution. In our case, the abundance of oxygen therefore affects the choice of theoretical isochrones adopted in the model synthesis. Unfortunately, oxygen abundances for non-resolved, old and intermediate-age, stellar populations are unknown and very difficult to constrain. It has become standard practice in the literature to address this problem by adopting not only the assumption that oxygen tracks magnesium, but also the more far-reaching corollary that [Z/H] can be determined once Fe and Mg indices (or a combination therefrom) are matched by the models. The former, more fundamental, assumption, while grounded on the theoretical expectation that magnesium and oxygen have a similar nucleosynthetic origin (e.g., Matteucci & Tornambé 1987, Wheeler et al. 1989, Woosley & Weaver 1995) has recently been challenged by the finding that metal-rich Galactic bulge stars, which have strongly super-solar [Mg/Fe], appear to have [O/Fe] below or around solar (Fulbright, Rich & McWilliam 2005, Cunha & Smith 2006). Therefore, we emphasize that, while the assumption of oxygen tracking magnesium might be, if not entirely reasonable, the only possible way out of this quandary, it is no more than an assumption, which still awaits confirmation from a compelling observational result. For the time being, any results coming from the method proposed here should be taken with caution. A good way of dealing with this uncertainty would be to adopt two widely different values of [O/Fe] and carrying out the procedure to the end, so that the final impact of an [O/Fe] assumption on the final results can be assessed.
Another important caveat regards the uncertainties in the outputs
of this method. Except for age and [Fe/H], error propagation should
lead to very large error bars in the abundances of the elements at the
bottom of the hierarchy devised above. Therefore, the uncertainty in the
abundance of calcium, for instance, should be the highest, as the Ca4227
index is strongly influenced by the abundances of carbon and nitrogen,
whose uncertainties in turn depend on the uncertainties in [Fe/H]
and age. The case of magnesium is less serious, as the Mg
index is
strongly affected only by age, [Fe/H], besides the output parameter,
[Mg/Fe]. Nitrogen stands in between those two cases, as the CN band is
affected by age, [Fe/H], and [C/Fe], besides [N/Fe]. In view of these
difficulties, we strongly recommend the reader to restrict application
of this method to only very high S/N data, so as to prevent the very
large uncertainties inherent to the method from rendering the results
meaningless.
This method has been implemented by G. Graves, from Lick Observatory, as an IDL routine which will soon be made available publicly. The routine, called ``EZ_Ages'', and the mathematical algorithm used to search the best solutions for a given set of index measurements are described in detail in Graves & Schiavon (2006, in preparation).