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

The metal content of galaxies provides a window into their formation in the full context of the cosmic baryon cycle. In this study, we examine the relationship between stellar mass and stellar metallicity (${\rm MZ}_*{\rm R}$) in the hydrodynamic simulations Illustris, TNG, and EAGLE to understand the global properties of stellar metallicities within the feedback paradigm employed by these simulations. Interestingly, we observe significant variations in the overall normalization and redshift evolution of the ${\rm MZ}_*{\rm R}$ across the three simulations. However, all simulations consistently demonstrate a tertiary dependence on the specific star formation rate (sSFR) of galaxies. This finding parallels the relationship seen in both simulations and observations between stellar mass, gas-phase metallicity, and some proxy of galaxy gas content (e.g., SFR, gas fraction, atomic gas mass). Since we find this correlation exists in all three simulations, each employing a sub-grid treatment of the dense, star-forming interstellar medium (ISM) to simulate smooth stellar feedback, we interpret this result as a fairly general feature of simulations of this kind. Furthermore, with a toy analytic model, we propose that the tertiary correlation in the stellar component is sensitive to the extent of the ``burstiness'' of feedback within galaxies.