Both Stellar Mass and Gravitational Potential Shape the Gas-Phase Metallicity

The relation between metallicity and galaxy mass (the so-called mass-metallicity relation) is the strongest and most prominent among scaling relations between chemical enrichment and galactic properties. However, it is unclear whether this relation primarily traces metal retention or the integrated production of metals, as past studies have obtained contrasting results. We investigate this issue through an extensive Random Forest and Partial Correlations analysis of spectral cubes of 4,500 galaxies from the MaNGA survey. We find that stellar mass ($\rm M_*$) and baryonic gravitational potential ($\rm \Phi_* = M_*/R_e$) are the two most important quantities determining gas metallicity in galaxies. However, their relative roles strongly depend on the galactocentric radius -- the metallicity within 0.7~$\rm R_e$ depends primarily on the stellar mass, while the metallicity at radii beyond 0.9~$\rm R_e$ depends primarily on the gravitational potential. This finding can be interpreted in terms of metals in the central region ($\rm R\leq 0.7~R_e$) being mostly bound, regardless of the global gravitational potential and, therefore, the metallicity is determined primarily by the cumulative production of metals (hence the integrated star formation history, i.e. $\rm M_*$); by contrast, in the galactic peripheries the retention of metals depends more critically on the gravitational potential, hence the stronger dependence of the metallicity on $\rm \Phi_*$ at large radii. Our finding reconciles apparent discrepancies between previous results. Finally, we find that the Star Formation Rate is the third most important parameter (after $\rm M_*$ and $\rm \Phi_*$) in determining the metallicity, as expected from the Fundamental Metallicity Relation.