1. T.P. Idiart  and J.A. de Freitas Pacheco   Universidade de São Paulo (Brasil)  Observatoire de la Côte d’Azur (France) Introduction Elliptical galaxies are usually think as old, complex stellar systems, whose the stellar population bulk was formed from an interstellar medium enriched in heavier elements produced mainly by massive stars (  9M  ). The chemical clocks used to date the stellar population are basically the yields of type II and Ia supernovae. Type II supernovae (SNII) ejecta are rich in  elements like Mg, Ca, Ti, O and Si, whereas type Ia supernovae (SNIa) contribute to enrichment of the interstellar medium mainly in the elements of the iron peak. The high iron content and the mean non-solar [  /Fe] ratio in E galaxies indicate that most of the stars were formed very rapidly. We developed a multi-population model taking into account stellar evolutionary tracks with non-solar [  /Fe] ratios. These produce a more adequate scaling between  -elements and iron abundances, mainly at high metallicities. In our scenario is included the possibility of a two phase interstellar medium produced by SN explosions. This model is applied to study the chemical and photometrical evolution of E galaxies. Our picture provides a natural way to stop the star formation after the wind onset, when the remaining gas is only in the hot and ionized phase. A two-phase one-zone model with wind outflow Main hypotheses:  the interstellar medium contains hot (T  50000 K) and cold gas  hot gas mass ≈ ionized gas mass  the gas is heated by type II and Ia explosions  winds are originated from the SN events  stars are not formed in hot gas conditions The model Evolution of the Elliptical Interstellar Gas conservation of total gas mass Basic equations fraction of formed stars f star fraction of ejected gas mass f eject fraction of hot (ionized) gas f G (t) = total gas mass fraction f HOT (t) = hot gas mass fraction  (m) = initial mass function M R = mass of remanent star k = star formation efficiency t W = time parameter of the wind C 1 = function of ionizing energy C 2 = function of physical properties of the gas (hot gas) SN = supernova frequency Database for stellar population synthesis of E galaxies The evolutionary tracks for  -enhanced stars MetallicityReferences Z=0.0001 ([Fe/H]=-2.66)Girardi et al.(2000) Z=0.0004([Fe/H]=-2.01)Girardi et al. (2000) Z=0.008 ([Fe/H]=-0.75)Salanich et al. (2000) Z=0.019 ([Fe/H]=-0.34)Salanich et al. (2000) Z=0.040 ([Fe/H]=+0.07)Salanich et al. (2000) Z=0.070 ([Fe/H]=+0.36)Salanich et al. (2000) The conversion from Z to [Fe/H] for an  -enhanced mixture of +0.4 can be estimated directly from the expression by Salaris et al. (1993), using the correction by Yong-Cheol et al. (2002) for higher values of metallicity. This relation is scaled to the solar abundances by Anders & Grevesse (1989), which are compatible with the abundance catalog by Thévenin (1998). Lick spectroscopic indices for  -enhanced stars As a stellar atmospheric database, we used Thévenin’s (1998) catalog, which has a set of homogeneous parameters: effective temperature, surface gravity and chemical abundances of various nuclear species determined by a detailed spectral analysis. The  -elements considered for non- solar [  /Fe] classifications were: O, Mg, Si, Ca and Ti. At least three different elements were used to classify stars with an  -enhanced abundance pattern ([element/Fe]  0.2). In these conditions a total of 62 stars with observed spectroscopic indices were selected. The figure shows the relationship between atmospheric parameters and spectroscopic indices for the selected  -enhanced stars. For comparison, a sample of solar [  /Fe] ([element/Fe] < 0.1) stars are overplotted. Calibration of the free parameters: star formation efficiency and initial mass function using the M V × (U-V) diagram for Virgo-Coma ellipticals Fiducial models at zero redshift Initial E mass M  K (Gyrs -1 )  Mean pop age (Gyrs) mean [Fe/H] mean [Mg/Fe] U-VMg 2 (mag) H  (Å) 2×10 12 0.801.89 ±0.13 13.45 ±0.07 +0.24 ±0.12 +0.53 ±0.06 1.67 ±0.06 0.313 ±0.011 1.63 ±0.02 7×10 11 0.532.00 ±0.08 12.91 ±0.02 +0.19 ±0.08 +0.47 ±0.04 1.59 ±0.05 0.301 ±0.010 1.66 ±0.02 2×10 11 0.402.11 ±0.04 12.41 ±0.01 +0.12 ±0.04 +0.41 ±0.02 1.47 ±0.05 0.2 8 4 ±0.006 1.70 ±0.01 5×10 10 0.402.32 ±0.05 12.48 ±0.00 -0.10 ±0.06 +0.27 ±0.04 1.32 ±0.04 0.251 ±0.009 1.79 ±0.02 2×10 10 0.402.42 ±0.07 12.53 ±0.05 -0.21 ±0.07 +0.18 ±0.06 1.24 ±0.06 0.236 ±0.009 1.84 ±0.04 K = star formation efficiency  = coefficient of IMF These models show that the most massive galaxies have higher star formation efficiency, flatter IMF, higher mean stellar population ages, more metallic stars and higher non-solar [  /Fe] ratio. The predicted observed stellar absorption indices Mg2 and H  at z=0 are also shown. RESULTS This figure shows the evolution of the hot and cold gas for galaxies of distinct initial masses M GAL. The ordinate shows the mass fraction of hot and cold gas in units of M GAL, and the abscissa the time evolution in units of age of the galaxy  UNIV. Note that only the cold gas component is available to form stars, implying that the vast majority of stars is already formed in early times of galaxy evolution. The high efficiency of star formation and the existence of a hot gas component limits drastically the number of stars formed more recently. This is crucial to achieve the M V × U-V relation for E galaxies, because the U-V color is very sensible to the existence of younger population of stars. As show in histograms, more than 90% of the stars are formed in the first 4 Gyrs of E galaxy evolution. The number of younger stars increases as the initial galaxy mass M GAL decreases. This happens because a lower star formation efficiency implies in a lower quantity of hot gas and hence an extented star formation period. Model predictions for different redshifts The stellar population at zero redshift The graphs show the behavior of Lick indices as a function of the central velocity dispersion (a mass indicator) for different redshifts. According to the parameters of the fiducial models, the indices show significant variations in this redshifts range. Project supported by IAG/USP, FAPESP and CNPq