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

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1. Introduction

Elliptical galaxies do not show the presence of HII regions and it is not possible to resolve single stars in them in order to measure photospheric abundances. Therefore, most of the information on these objects is obtained from their integrated properties: abundances are derived either through colors or integrated spectra and in both cases the derived information is a complicated measure of metallicity and age (the well known age-metallicity degeneracy). The most common metallicity indicators are [FORMULA] and [FORMULA], as originally defined in Faber et al. (1977; 1985). Population synthesis techniques are adopted to analyze the integrated properties of ellipticals and to derive an estimate of their real abundances. Unfortunately, they contain several uncertainties residing either in incomplete knowledge of stellar evolution or in deficiencies in stellar libraries, as discussed in Charlot et al. (1996). In recent years more and more population synthesis models (Bruzual and Charlot, 1993; Buzzoni et al., 1992; Bressan et al., 1994; Gibson, 1997; Bressan et al., 1996; Gibson and Matteucci, 1997; Tantalo et al., 1998) have appeared but the basic uncertainties still remain. In this paper we want to focus our attention about the comparison between theoretical model results and metallicity indicators. In this framework we will analyze the relationship between [FORMULA] and [FORMULA] and its implications for the mechanism of galaxy formation.

Several authors (Faber et al. 1992; Worthey et al. 1992; Carollo et al. 1993; Davies et al. 1993; Carollo and Danziger 1994a,b), from comparison of the observed indices with synthetic indices, concluded that the average [FORMULA] in giant ellipticals must be larger than the solar value. This result was also confirmed by the analysis of Weiss et al. (1995) who made use, for the first time, of stellar evolutionary tracks calculated under the assumption of non-solar ratios.The same authors found that the [FORMULA] versus [FORMULA] relation among nuclei of giant ellipticals is rather flat and flatter than within galaxies. From the flat behavior of [FORMULA] vs. [FORMULA] the same authors inferred that the abundance of Mg should increase faster than the abundance of Fe among nuclei of giant ellipticals. This conclusion is at variance with the predictions of supernova-driven wind models of ellipticals (Arimoto and Yoshii, 1987; Matteucci and Tornambè 1987). In fact, Matteucci and Tornambè (1987) showed that, in the framework of the classic wind model for ellipticals, the [Mg/Fe] ratio is a decreasing function of the galactic mass and luminosity. The reason for this behavior is clear: if Fe is mostly produced by the supernovae of type Ia, as it seems to be the case in our Galaxy (Greggio and Renzini 1983; Matteucci and Greggio 1986), whereas Mg is mostly originating from supernovae of type II, then the iron production is delayed relative to that of Mg and its abundance should be larger in more massive galaxies which develop a wind later than the less massive ones. All of this is valid under the assumption that after the onset of a galactic wind star formation should stop or should be negligible, which is a reasonable assumption for elliptical galaxies. Faber et al. (1992) proposed alternative scenarios to the classic supernova driven wind model, as originally proposed by Larson (1974). They suggested three different scenarios all based on the assumption that Mg is produced by type II supernovae and Fe is mostly produced by type Ia supernovae: i) a selective loss of metals, ii) a variable initial mass function (IMF) and iii) different timescales for star formation. These hypotheses were discussed by Matteucci (1994), who tested them in the context of chemical evolution models. In the hypothesis of the different timescales for star formation Matteucci (1994) suggested that the more massive ellipticals might experience a much stronger and faster star formation than less massive ellipticals leading to a situation where the most massive objects are able to develop galactic winds before the less massive ones. She called this case "inverse wind model". On the other hand, in the classic wind model of Larson (1974) the efficiency of star formation was the same for all galaxies thus leading to the fact that the galactic wind in more massive systems occurs later than in less massive ones, due to their deeper potential well. In the models of Arimoto and Yoshii (1987) and Matteucci and Tornambè (1987) the efficiency of star formation was a decreasing function of galactic mass, based on the assumption that the timescale for star formation is proportional to the cloud-cloud collision timescale which, in turn, is proportional to the gas density. Therefore, since in this monolithic collapse picture the gas density decreases with the galactic mass, the galactic wind was even more delayed for the most massive systems. Matteucci (1994) proposed, as an alternative, a star formation efficiency increasing with the galactic mass and she justified this assumption by imagining that giant elliptical galaxies, instead of forming through a monolithic collapse of a gas cloud, form by merging of gaseous protoclouds. The merging process can, in fact, produce higher densities for increasing galactic mass and/or higher cloud-cloud collision velocities resulting in a faster star formation process. In such a model the galactic wind occurs earlier in massive than in smaller ellipticals thus producing the expected trend of an increasing [Mg/Fe] as a function of galactic mass. Matteucci (1994) also showed that a variable IMF with the slope decreasing with increasing galactic mass and luminosity can produce the same effect without an inverse wind situation. The reason for that resides in the fact that a flatter IMF slope favors massive stars relative to low and intermediate masses, thus favoring Mg production over Fe production. However, Matteucci (1994) could not translate the predicted abundances into [FORMULA] and [FORMULA] since there were no available calibrations for [Fe/H] versus [FORMULA] but only calibrations for [FORMULA] vs. [FORMULA]. Therefore she did not compare the predicted abundances with observations.

Recently, calibrations for the iron index have become available (Borges et al., 1995; Tantalo et al., 1998) and therefore in this paper we revisit the whole problem of inferring trends on the real abundances by metallicity indices and we discuss the influence of the calibration relationships, which allow us to pass from indices to abundances, and we show that the inferred trend of Mg/Fe with galactic mass is not so clear when interpreted in terms of real abundances, thus warning us from drawing any firm conclusion on galaxy formation processes just on the basis of the observed behavior of [FORMULA] versus [FORMULA]. indices. The reason for that resides partly in the large spread present in the observational data and partly in the fact that metallicity indices depend not only on the abundances of single elements but also on the ages and on the metallicity distribution (Tantalo et al. 1998) of the different stellar populations present in elliptical galaxies.

In Sect. 2 we will discuss the chemical evolution model, in Sect. 3 we will define the average abundances of a composite stellar population, in Sect. 4 we will describe the model results and transform the predicted abundances into indices by means of the most recent metallicity calibrations. Finally in Sect. 5 some conclusions will be drawn.

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© European Southern Observatory (ESO) 1998

Online publication: June 26, 1998