Results

The fitting functions obtained according to the procedure delineated above are presented in Tables 7-22 and displayed in Figures 6-6. In the Figures we adopt a cosine-weighted interpolation to represent the plots in the boundaries between the different plotting regions, following Cenarro et al. (2002). The reader should keep in mind that the plots shown in Figures 6-6 are limited representations of the fitting functions presented in Tables 7-22. Most indices depend on three variables, $T_{\rm eff}$ , [Fe/H], and $\log g$ through most of the parameter space. Yet, the plots only allow us to display the index variations as a function of the two most important parameters, $T_{\rm eff}$ and [Fe/H]. Therefore, we must assume a $\log g$ value for the indices that do depend on this parameter, which can vary by as much as 5 orders of magnitudes in the sample considered here. We did so by adopting a $T_{\rm eff}$ $\log g$ relation interpolated in the isochrones from Girardi et al. (2000) for 5 Gyr and solar metallicity.

From the Figures and Tables it can be seen that the fits look fairly robust for G-K giants, and F-G dwarfs, which are the stellar types that are best represented in the spectral library. For these stars, reliable estimates of the behavior of the indices as a function of effective temperature, metallicity and surface gravity could be achieved. Outside these regions of parameter space, the low density of the spectral library (especially in the case of the very cool stars) and uncertainties in the stellar parameters made it very difficult to obtain estimates of the response of spectral indices to metallicity and surface gravity. Therefore, our fitting functions for all indices, except Fe5270 and Fe5335, are solely dependent on effective temperature for K-M dwarfs, M giants and B-A dwarfs. For those two indices we could not obtain fitting functions that would extend into the K-M dwarf regime without a moderately strong dependence on [Fe/H].

The boundaries listed in Tables 7-22 are the ones adopted to produce the fits. Those attempting to reproduce our polynomial fits in Tables 7-22 should adopt those boundaries as input in their programs. The latter boundaries should not be confused with those provided in Table which specify the regions of parameter space within which the various fitting functions should be applied. Those are meant to be used by stellar population synthesis modelers wishing to adopt our fitting functions for the various Lick indices. The reader will notice that the boundaries in Table  are in general contained within those of Tables 7-22, for a given index and stellar family. This is to ensure that application of our fitting functions be restricted to regions of parameter space where they are well constrained by the input stellar data. We strongly caution the reader against trusting extrapolations of the fitting functions away from the boundaries given in Table , as in many cases the functions behave in a strongly non-physical way outside the fitting region. In the case of the CN indices, we could not find polynomial functions capable of describing index behavior as a function of $T_{\rm eff}$and [Fe/H] in a satisfactory fashion in the metal-poor regime. Therefore we caution readers against trusting either the fitting functions or the single stellar population models for those indices below [Fe/H]=-1.0.

Blue indices tend to display a marked sensitivity to $\log g$ in stars hotter than $\sim$ 8000 K and for very low gravities ( ). All Balmer lines tend to be considerably weaker in the spectra of B-A super-giants than in that of dwarfs and giants of the same $T_{\rm eff}$. At such high $T_{\rm eff}$s Balmer lines are very strong, and their wings tend to be stronger for higher gravities. In the spectra of B-A dwarfs, the wings of the Balmer lines are so strong that they dominate the absorption at K and have an impact on all other absorption line indices in that spectral region. As a result, indices like CN$_1$, CN$_2$, Ca4227, and G4300 present a dependence on $\log g$ that is similar in strength to that of the Balmer lines, but with opposite sign. Because the spectral library has just a handful of B-A super-giants, this effect could not be modelled in a reliable fashion, and we decided to exclude these very low surface gravity stars from our fits. Therefore, the fitting functions for hot stars should only be applied to stars with , for which no dependence of Balmer lines (and the other spectral indices) on $\log g$ could be perceived in our data.