In this study we present detailed calculations of absorption line indices on the Lick System based on the new stellar models by ( ) incorporating the enhancement of \alpha -elements both in the opacity and in the chemical abundances .
The models span large ranges of initial masses , chemical compositions , and ages , and are calculated for both solar and enhanced abundance ratios [ X _ { el } / Fe ] of \alpha -elements .
With these models and the so-called Response Functions of ( ) , we calculate the indices for Single Stellar Populations ( SSPs ) of different age , metallicity and degree of enhancement .
Starting from the widely accepted conviction that { H _ { \beta } } is a good age indicator , that [ MgFe ] is most sensitive to metallicity , and indices like { Mg _ { b } } , { Mg _ { 2 } } and others are most sensitive to metallicity and degree of enhancement , we made use of the triplet { H _ { \beta } } , { Mg _ { b } } and { \langle Fe \rangle } , and Minimum-Distance Method proposed by ( ) to estimate the age , metallicity and enhancement degree for the galaxies of the ( ) 
sample , and compare the results with those by ( ) and ( ) .
Since very large differences are found , in particular as far as the age is concerned , ours are systematically older than those of ( ) and ( ) , we analyze in a great detail all possible sources of disagreement , going from the stellar models and SSPs to many technical details of the procedure to calculate the indices , and finally the pattern of chemical elements ( especially when \alpha -enhanced mixtures are adopted ) .
Each of the above aspects of the problem bears on the final result : amazingly enough , at increasing complexity of the underlying stellar models and SSPs , the uncertainty increases .
However , the key issue of the analysis is that at given metallicity Z and enhancement factor , the specific abundance ratios [ X _ { el } / Fe ] adopted for some elements ( e.g .
O , Mg , Ti , and likely others ) dominate the scene because with the ( ) Response Functions they may strongly affect indices like { H _ { \beta } } and the age in turn .
In brief , with the ratio [ Ti/Fe ] =0.63 adopted by ( ) , { H _ { \beta } } at old ages turned out to be larger than the mean observational value , and therefore the age was forced to very old values in order to recover the observations .
In contrast , the results by ( ) and ( ) are immediately recovered if their [ Ti/Fe ] ratios are adopted , i.e .
[ Ti/Fe ] =0.0 or 0.3 , respectively .
We have also analyzed how the galaxy ages , metallicities and degrees of enhancement vary with the triplets of indices in usage .
To this aim we turn to the Trager “ IDS Pristine ” sample which contains many more galaxies and a much wider list of indices than the González sample .
The solution is not unique in that reflecting the poor ability of most indices to disentangle among the three parameters .
Finally , at the light of the above results and points of uncertainty , we have drawn some remarks on the interpretation of the distribution of early-type galaxies in popular two-indices planes , like { H _ { \beta } } vs . { [ MgFe ] } .
We argue that part of the scatter along the { H _ { \beta } } axis observed in this plane could be attributed instead of the age , the current explanation , to a spread both in the degree of enhancement and some abundance ratios .
If so , another dimension is added to the problem , i.e .
the history of star formation and chemical enrichment in individual galaxies .
The main conclusion of this study is that deriving ages , metallicities and degree of enhancement from line indices is a cumbersome affair whose results are still uncertain .