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Modern yields per stellar generation: the effect of the IMF

Gaseous and stellar metallicities in galaxies are nowadays routinely used to constrain the evolutionary processes in galaxies. This requires the knowledge of the average yield per stellar generation, $y_{\text{Z}}$, i.e. the quantity of metals that a stellar population releases into the interstellar medium (ISM), which is generally assumed to be a fixed fiducial value. Deviations of the observed metallicity from the expected value of $y_{\text{Z}}$ are used to quantify the effect of outflows or inflows of gas, or even as evidence for biased metallicity calibrations or inaccurate metallicity diagnostics. Here we show that $\rm y_{\text{Z}}$ depends significantly on the Initial Mass Function (IMF), varying by up to a factor larger than three, for the range of IMFs typically adopted in various studies. Varying the upper mass cutoff of the IMF implies a further variation of $y_{\text{Z}}$ by an additional factor that can be larger than two. These effects, along with the variation of the gas mass fraction restored into the ISM by supernovae ($R$, which also depends on the IMF), may yield to deceiving results, if not properly taken into account. In particular, metallicities that are often considered unusually high can actually be explained in terms of yield associated with commonly adopted IMFs such as the Kroupa (2001) or Chabrier (2003). We provide our results for two different sets of stellar yields (both affected by specific limitations) finding that the uncertainty introduced by this assumption can be as large as $\sim0.2$ dex. Finally, we show that $y_{\text{Z}}$ is not substantially affected by the initial stellar metallicity as long as $\text{Z}> 10^{-3}~\text{Z}_{\odot}$.