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Figure 6.2. The predicted SN (Types II and Ia) rate in the Solar vicinity with the two-infall model. Figure from Chiappini et al. (1997).

Ia SN rate, and the Type II SN rate strictly follows the SFR, whereas the Type Ia SN rate is smoothly increasing.

Francois et al. (2004) compared the predictions of the two-infall model for the abundance ratios versus metallicity relations ([X/Fe] versus [Fe/H]), with the very recent and very accurate data of the project "First Stars" published by Cayrel et al. (2004). They adopted yields from the literature both for Type II and for Type Ia SNe and noticed that while for some elements (O, Fe, Si, Ca) the yields of Woosley & Weaver (1995) (hereafter WW95) reproduce the data fairly well, for the Fe-peak elements and heavier elements none of the available yields give a good agreement. Therefore, they varied empirically the yields of these elements in order to fit the data. In Figures 6.3 and 6.4 we show the predictions for a-elements (O, Mg, Si, Ca, Ti, K) plus some Fe-peak elements and Zn.

In Figure 6.4 we also show the ratios between the yields derived empirically by Francois et al. (2004), in order to obtain the excellent fits shown in the figures, and those of WW95 for massive stars. For some elements it was also necessary to change the yields from Type Ia SNe relative to the reference ones, which are those of Iwamoto et al. (1999) (hereafter I99).

In Figure 6.5 we show the predictions of chemical-evolution models for 12C and 14N compared with abundance data. The behavior of C gives a roughly constant [C/Fe] as a function of [Fe/H], although the amount of C seems to be slightly greater at very low metallicities, indicating that the bulk of these two elements comes from stars with the same lifetimes. The data in these figures, especially those for N, are old and do not concern very-metal-poor stars. Newer data concerning stars with [Fe/H] down to — -4.0 dex (Spite et al. 2005; Israelian et al. 2004) indicate that the [N/Fe] ratio continues to be high also at low metallicities, indicating a primary origin for N produced in massive stars. We recall here that we define as primary a chemical element that is produced in the stars starting from the H and He, whereas we define as secondary a chemical element that is formed from heavy elements already present in the star at its birth and not produced in situ. The model predictions shown in Figure 6.5 for C and N assume that the bulk of these elements is produced by low- and intermediate-mass stars (yields from van den Hoeck and Groenewegen (1997)) and that N is produced as a partly secondary and partly primary element. The N production from massive stars has only a secondary origin (yields from WW95). In Figure 6.5 we also show a model prediction in which N is considered to be a primary element in massive stars with the yields artificially increased. Recently, Chiappini et al. (2006) have shown that primary N produced by very-metal-poor fast-rotating massive stars can well reproduce the observations.

In summary, the comparison between model predictions and abundance data indicates the following scenario for the formation of heavy elements.

• 12C and 14N are mainly produced in low- and intermediate-mass stars (0.8 < M/Mq < 8). The amounts of primary and secondary N are still unknown and so is the fraction of C produced in massive stars. Primary N from massive stars seems to be required in order to reproduce the N abundance in low-metallicity halo stars.

• The a-elements originate in massive stars: the nucleosynthesis of O is rather well understood (there is agreement among authors); and the yields from WW95 as functions of metallicity produce excellent agreement with the observations for this particular element.

• Magnesium is generally underproduced by nucleosynthesis models. Taking the yields of WW95 as a reference, the Mg yields should be increased in stars with masses M < 20Mq and decreased in stars with M > 20Mq in order to fit the data. Silicon yields should be slightly increased in stars with masses M > 40Mq.

• Fe originates mostly in Type Ia SNe. The Fe yields in massive stars are still unknown; WW95 metallicity-dependent yields overestimate Fe in stars of masses < 30Mq . For this element, it is better to adopt the yields of WW95 for Solar metallicity.

• Fe-peak elements: the yields of Cr and Mn should be increased in stars of mass (10-20)Mq relative to the yields of WW95, whereas the yield of Co should be

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