Galactic Archaeology with [Mg/Mn] versus [Al/Fe] abundance ratios -- Uncertainties and caveats

The diagram depicting the abundance ratios [Mg/Mn] vs. [Al/Fe] has gained attention in recent literature as a valuable tool for exploring fundamental aspects of the evolution of the Milky Way and the Local Group. In particular, this combination of elements is supposed to be highly sensitive to the star formation history (SFH), unveiled by the imprints left on those abundances. Unfortunately, a complete discussion on the uncertainties associated is still missing, making it difficult to know how reliable the associated results are. In this paper we analyze, by means of detailed chemical evolution models, the nuclear uncertainties of Mg, Al, Mn and Fe to show how different yields can affect the trends in the [Mg/Mn] vs. [Al/Fe] plane. In fact, if different yield assumptions produce conflicting results, then the [Mg/Mn] vs. [Al/Fe] diagram does not represent a strong diagnostic for the SFH of a galaxy. We discuss the results on the [Mg/Mn] vs. [Al/Fe] diagram, as predicted by several Milky Way (MW) and Large Magellanic Cloud (LMC) chemical evolution models adopting different nucleosynthesis prescriptions. The results show that the literature yields require some corrective factors to reproduce the APOGEE DR17 abundances of Mg, Al and Mn in the MW and that the same factors can also improve the results for the LMC. In particular, we show that by modifying the massive stars yields of Mg and Al the behaviour of the [Mg/Mn] vs. [Al/Fe] plot changes substantially. In conclusion, by changing the yields within their error bars, one obtains trends which differ strongly, making it difficult to draw any reliable conclusion on the SFH of galaxies. The proposed diagram is therefore uncertain from a theoretical point of view and it could represent a good diagnostic for SFH if the uncertainties on the nucleosynthesis of these elements (Mg, Mn, Al and Fe) could be reduced by future stellar calculations.