Interpretation of Abundance Ratios

In this paper we discuss abundance ratios and their relation to stellar nucleosynthesis and other parameters of chemical evolution models, reviewing and clarifying the correct use of the observed abundance ratios in several astrophysical contexts. In particular, we start from the well-known fact that abundance ratios depend on stellar yields, initial mass function, and stellar lifetimes, and we show, by means of specific examples, that in some cases it is not correct to infer constraints on the contributions from different supernovae types (Ia, II), and particularly on different sets of yields, in the absence of a complete chemical evolution model taking into account stellar lifetimes. In spite of the fact that some of these results should be well known, we believe that it is useful to discuss the meaning of abundance ratios in the light of several recent claims based upon an incorrect interpretation of observed abundance ratios. In particular, the procedure, often used in the recent literature, of directly deriving conclusions about stellar nucleosynthesis just by relating abundance ratios to yield ratios implicitly assumes the instantaneous recycling approximation. This approximation is clearly not correct when one analyses the contributions of supernovae type Ia relative to supernovae type II as functions of cosmic time. In this paper we show that the uncertainty which arises from adopting this oversimplified procedure in a variety of astrophysical objects, such as elliptical galaxies, the intracluster medium, and high redshift objects, does not allow us to draw any firm conclusion, and that the differences between abundance ratios predicted by models with the instantaneous recycling approximation and models with detailed stellar lifetimes is of the same order as the differences between different sets of yields. On the other hand, if one is interested only in establishing the global metal production (e.g. galaxies plus intracluster medium) over the lifetime of the Universe, then the adoption of simplified arguments can be justified.