Description
The origin of chemical abundances has been studied in great detail for decades from observation surveys (such as APOGEE and LAMOST) to nucleosynthetic models of stellar structure and cosmic events. However, it can be difficult to differentiate the relationship between elements from chemical abundance patterns due to stellar migration and star misclassifications in surveys. In our present work, we create a dSph toy model (as seen in Alexander et al. 2024) to predict chemical abundances, star formation histories, age-metallicity relations and metallicity distribution functions. We predict the residuals of the chemical abundances and introduce correlation matrix maps which are used to predict the residuals of various chemical abundances as a function of metallicity. We find chemical abundance dispersion for Fe-peak elements is lower than $\alpha$-elements, and that the dispersion between Fe-peak elements and $\alpha$-elements is large due to them not sharing primary sources within stars. Similarly, [N/Fe] residuals are found to have little to no correlations with any other chemical abundance because they do not share primary nucleosynthesis. We also find [C/Fe] follows similar residual patterns to $\alpha$-elements at high metallicities. Finally, correlation matrix maps find little residuals between all elements in our sample at low metallicities, with some slight outliers in Fe-peak elements. These residuals are key to constraining hidden relationships between chemical abundances and are thus integral to discovering correlations between them.
