Effective yields as tracers of feedback effects on metallicity scaling relations in the EAGLE cosmological simulations

Effective yields, $y_{\rm eff}$, are defined by fundamental galaxy properties (i.e., stellar mass -$M_{\star}$-, gas mass -$M_{\rm gas}$- and gas-phase metallicity). For a closed-box model, $y_{\rm eff}$ is constant and equivalent to the mass in metals returned to the gas per unit mass locked in long-lived stars. Deviations from such behaviour have been often considered observational signatures of past feedback events. By analysing EAGLE simulations with different feedback models, we evaluate the impact of supernovae (SN) and active galactic nuclei (AGN) feedback on $y_{\rm eff}$ at redshift $z=0$. When removing supermassive black holes (BH) and, hence, AGN effects, in simulations, galaxies are located around a plane in the $M_{\star} - M_{\rm gas} - {\rm O/H}$ parameter space (being O/H a proxy for gas metallicity, as usual), with such a plane roughly describing a surface of constant $y_{\rm eff}$. As the ratio between BH mass and $M_{\star}$ increases, galaxies deviate from that plane towards lower $y_{\rm eff}$ as a consequence of AGN feedback. For galaxies not strongly affected by AGN feedback, a stronger SN feedback efficiency generates deviations towards lower $y_{\rm eff}$, while galaxies move towards the opposite side of the plane (i.e., towards higher values of $y_{\rm eff}$) as SN feedback becomes weaker. Star-forming galaxies observed in the Local Universe are located around a similar 3D plane. Our results suggest that the features of the scatter around the observed plane are related to the different feedback histories of galaxies, which might be traced by $y_{\rm eff}$.