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The metal content of galaxies provides a window into their formation in thefull context of the cosmic baryon cycle. In this study, we examine therelationship between stellar mass and stellar metallicity (${\rm MZ}_*{\rm R}$)in the hydrodynamic simulations Illustris, TNG, and EAGLE to understand theglobal properties of stellar metallicities within the feedback paradigmemployed by these simulations. Interestingly, we observe significant variationsin the overall normalization and redshift evolution of the ${\rm MZ}_*{\rm R}$across the three simulations. However, all simulations consistently demonstratea tertiary dependence on the specific star formation rate (sSFR) of galaxies.This finding parallels the relationship seen in both simulations andobservations between stellar mass, gas-phase metallicity, and some proxy ofgalaxy gas content (e.g., SFR, gas fraction, atomic gas mass). Since we findthis correlation exists in all three simulations, each employing a sub-gridtreatment of the dense, star-forming interstellar medium (ISM) to simulatesmooth stellar feedback, we interpret this result as a fairly general featureof simulations of this kind. Furthermore, with a toy analytic model, we proposethat the tertiary correlation in the stellar component is sensitive to theextent of the ``burstiness'' of feedback within galaxies.

Interplay of Stellar and Gas-Phase Metallicities: Unveiling Insights for Stellar Feedback Modeling with Illustris, IllustrisTNG, and EAGLE