Beyond the Fundamental Metallicity Relation: galaxy sizes encode the link between inflow and metallicity
Gas-phase chemical abundances are key observable consequences of galaxy evolution, being intrinsically tied to galaxy formation histories. Gas metallicity rises with increasing stellar mass ($\mathrm{M_*}$), forming the well-known mass-metallicity relation (MZR). MZR residuals have separately been shown to anti-correlate with star-formation rate (the ``fundamental'' metallicity relation), with gas mass and with optical size, but no single analysis has considered all trends together. We thus perform a combined analysis of all three trends, utilizing optical MaNGA integral field spectroscopy, HI-MaNGA gas masses, and MaNGA DynPop dynamical masses. We estimate inner gas masses for $\sim$1500 star-forming galaxies, finding this to be the most important parameter after $\mathrm{M_*}$ in predicting gas metallicities. We obtain equivalent results for stellar metallicities and gaseous N/O, suggesting that current inner gas masses are intrinsically linked to long-term chemical evolution histories. We show that more compact galaxies have lower dynamical masses, challenging suggestions that deeper gravitational potentials confer higher metallicities. We find a strong correlation between inner gas mass and galaxy size, meaning that short term inflow fluctuations cannot be responsible for the MZR residuals. With chemical evolution models, we show that our results can instead be explained by differences in long-term inflow histories. The earlier inflow histories of compact galaxies lead to lower gas masses and more rapidly declining gas reservoirs at late times, leading to higher metallicities. At fixed stellar mass, galaxy size therefore encodes the link between halo assembly histories, long-term gas inflow histories, current gas reservoirs and metallicity.