In the previous sections, some examples of the uncertainties affecting the predictions of chemical evolution models have been presented. Part of these uncertainties are due to the lack of complete and homogenous sets of stellar yields for various initial metallicities. To compute adequate chemical evolution models of whatever galaxy, we need homogeneous chemical yields for all the major isotopes, for the whole range of stellar masses, for many initial compositions and taking into account all the most relevant processes occurring in the stellar interiors until the final evolutionary phases. Such optimal grid of yields is far from existing. The results from stellar nucleosynthesis are steadily improving with time, with most of the processes occurring during stellar evolution being treated with increasing precision. However, the yields available to the community are still very heterogeneous and incomplete and not one single set of nucleosynthesis predictions exists taking properly into account all the processes in all the phases of stars of all masses (say from 0.8 to 100 M) and at least 2-3 different metallicities (from metal poor to solar and, possibly, super solar). This circumstance not only prevents the computation of detailed self-consistent chemical evolution models for a number of key elements, but can even lead to misleading results. The potential risk can be visualised by comparing with each other the yields provided by different authors and the corresponding normalizations through an IMF.
The left-hand panel of Fig. 4 shows a subset of the solar yields presented by [Portinari, Chiosi, & Bressan 1998] for massive and quasi-massive stars and by [Marigo 2001] for low and intermediate mass stars. This is the best case in literature of self-consistent yields for all masses, based on the same stellar evolution models and input physics. What is normally available in the literature is a collection of yields for partial mass ranges, each computed under different assumptions and often for different metallicities. A typical case is shown in the right-hand panel of Fig. 4, where the solar yields by [Marigo 2001] for low and intermediate mass stars are now combined with those by [Woosley & Weaver 1995] for massive stars. Two problems are immediately apparent. First, stars in the mass range 5 < M / M < 11 have not been computed by either Marigo or Woosley & Weaver, which implies that to use this combination of yields one must interpolate over this mass interval. Second, massive stars do not go beyond 40 M and to higher masses one must therefore extrapolate. The latter issue might not have overwhelming consequences in the modelling of the recent chemical evolution of the Milky Way, since any reasonable IMF predicts very few stars more massive than 40 M, but can be extremely relevant for very early epochs, when the most massive stars were the only polluters. The former problem has very serious implications because stars in the 5 - 11 M range are the most effective contributors to the ISM chemical enrichment. In Fig. 5 the yields of Fig. 4 have been weighted with Tinsley's (1980) IMF. The linear interpolation performed to cover the 5 - 11 M interval absent in the Marigo/Woosley & Weaver combination results in a bump (right-hand panel) in the contribution of these stars to the enrichment of He, N and O which is totally absent in the left-hand panel, where the homogeneous sets of yields are shown. This enhanced contribution is most likely spurious and can lead to a significant overprediction of the elements mostly produced by stars of these masses.
Figure 4. Stellar yields: ejected mass of newly synthesized element as a function of the stellar initial mass. Left-hand panel: the case of the homogeneous sets of solar yields by [Marigo 2001] and [Portinari, Chiosi, & Bressan 1998] covering the whole mass range. Right-hand panel: the standard case of incomplete coverage with inhomogeneous sets [Marigo 2001, Woosley & Weaver 1995] which do not consider initial masses with 5 < M/M < 11 (the lines plotted in this mass range are linear interpolations) and beyond 40 M.
Figure 5. Fractional ejected mass of newly synthesized element weighted with [Tinsley 1980] IMF. Left-hand panel: the case of the homogeneous sets of solar yields by [Marigo 2001] and [Portinari, Chiosi, & Bressan 1998]. Right-hand panel: the case of the inhomogeneous, non adjacent sets by [Marigo 2001] and [Woosley & Weaver 1995].
To overcome these problems, we strongly encourage the community of stellar nucleosynthesis experts to provide homogeneous yields for all stellar masses, computed up to the final evolutionary phases and for several initial metallicities.
Acknowledgments. Some of the results described here have been obtained thanks to pleasant and recurrent collaborations with A. Aloisi, D. Galli, F. Matteucci, F. Palla, D. Romano and L. Stanghellini. I am grateful to Corinne Charbonnel for many useful conversations on the stellar yields and to Donatella Romano for her invaluable help. Part of these researches was funded through INAF-PRIN-2005.