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Astron. Astrophys. 335, 855-866 (1998)

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5. Discussion and conclusions

In this paper we have discussed the relation between metallicity indices, such as [FORMULA] and [FORMULA], and total mass in nuclei of ellipticals and its implications in terms of models of formation and evolution of elliptical galaxies.

In order to do that we have transformed the average abundance of Fe in the composite stellar population of the galaxy, as predicted by different models of chemical evolution, into [FORMULA] and [FORMULA] indices by means of the available calibrations.

We have shown the results of classic wind models for ellipticals, such as those discussed by Arimoto and Yoshii (1987) and Matteucci and Tornambè (1987), as well as the results of models with variable IMF from galaxy to galaxy and with galactic winds occurring first in the more massive systems, implying that these systems are older than the less massive ones. We have found that it is not possible to establish clearly which kind of model should be preferred, first of all because of the large spread present in the data.

Moreover, little difference is found in the predicted indices of models which predict a [FORMULA] either increasing or decreasing with galactic mass, although the data seem to suggest an increase of this ratio with galactic mass larger than predicted by any of the models.

On this basis, the classic wind model can not be considered worse than the other models. Actually, the classic wind model with a flat constant IMF seems to be the only one which can reproduce the whole range of the observed indices. However, if we isolate the data from Gonzalez (1993) and do not consider the others, then in order to reproduce the flat slope of the [FORMULA] versus [FORMULA] relation, as given by the best-fit of the data, one should assume that Fe among the nuclei of ellipticals is almost constant whereas Mg increases from less massive to more massive nuclei. This is not achieved by any of the models presented here since it would require quite "ad hoc" assumptions especially concerning the type Ia SNe.

From the numerical experiments performed in this paper we can say that a model which explains at the same time the mass-metallicity and the iron-magnesium relation requires an inverse wind situation, with a strong increase of the star formation efficiency with galactic mass (i.e. Model VI), rather than a variable IMF from galaxy to galaxy, and an IMF with a slope [FORMULA]. However, a model of this type is not able to reproduce the observed ranges of [FORMULA] and [FORMULA]. We have also calculated models where amount and concentration of dark matter increases, compatibly with the formulation of the potential energy of the gas, with decreasing galactic luminous mass (see Persic et al. 1996), with the net result of obtaining an "inverse wind" situation. The results are very similar to those of Model III. Therefore, to obtain a better agreement with observations one should invoke also in this case an increase of the star formation efficiency with galactic mass. This would certainly flatten the [FORMULA] vs. [FORMULA] relation but it would further shrink the ranges of the predicted indices. In fact, both an increasing star formation efficiency and a decreasing importance of dark matter with increasing luminous galactic mass can be viable solutions to achieve the situation of more massive ellipticals being older than less massive ones.

In conclusion, it is quite important to establish the value of [Mg/Fe] from the observational point of view since abundance ratios, such as [Mg/Fe], represent an important diagnostic to infer ages in galaxies, due to the different timescales for the Mg and Fe production. Generally, a high [Mg/Fe] is interpreted as a young age and the upper limit for the age is given by the time at which the chemical enrichment from type Ia SNe starts to become important. This timescale depends not only on the assumed progenitors of type Ia SNe but also on the star formation history of the galaxy considered (see Matteucci 1997) and for giant elliptical galaxies this timescale is of the order of [FORMULA] years and in any case it can not be larger than 1 Gyr also for smaller systems. This is at variance with what stated by Kodama and Arimoto (1997) who claim, on the basis of results concerning our Galaxy (Yoshii et al. 1996), that this timescale is of the order of 1.5-2.5 Gyr. This is indeed true for our Galaxy where the star formation history has been quite different than in ellipticals and it had been already pointed out in Greggio and Renzini (1983) and in Matteucci and Greggio (1986). This is a quite important point, both for the galactic chemical enrichment and for the predictions about SN rates at high redshift.

Therefore, an enhanced [Mg/Fe] indicates that the process of galaxy formation must have been very fast thus favoring a monolithic collapse scenario rather than a merging scenario. In this framework, a [Mg/Fe] ratio higher in more massive ellipticals than in less massive ones could be interpreted as due to their faster formation and evolution (see Matteucci 1994; Bressan et al. 1996).

An independent way of estimating the ages of ellipticals, where for ages we intend the time elapsed from the last star formation event, is to study the [FORMULA] index. This index is, in fact, related to the age of the dominant stellar population, since it gives a measure of the turn-off color and metallicity. It can therefore be used to solve the age-metallicity degeneracy. Bressan et al. (1996), by analyzing the [FORMULA] and other physical parameters in the sample of ellipticals observed by Gonzalez (1993), concluded that massive galaxies should have stopped forming stars before less massive ones, in agreement with the results of the inverse wind model discussed here. Finally, we would like to point out that both models with a Salpeter IMF and a variable IMF have a potential problem in reproducing high [[FORMULA]/Fe] ratios in the intracluster medium (ICM), as shown by their low average [FORMULA] ratios (see Tables 7-12). Therefore, in agreement with MG95 and Gibson and Matteucci (1997) we conclude that a flat IMF is required to explain the high [[FORMULA]/Fe] ratios, as found by ASCA observations (Mushotzsky 1994).

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© European Southern Observatory (ESO) 1998

Online publication: June 26, 1998