Metal-enriched galactic outflows shape the mass-metallicity relationship

The gas-phase metallicity of low-mass galaxies increases with increasing stellar mass ($M_\ast$) and is nearly constant for high-mass galaxies. Theory suggests that this tight mass-metallicity relationship is shaped by galactic outflows removing metal-enriched gas from galaxies. Here, we observationally model the outflow metallicities of the warm outflowing phase from a sample of seven local star-forming galaxies with stellar masses between 10$^{7}$-10$^{11}$ M$_\odot$. We estimate the outflow metallicities using four weak rest-frame ultraviolet absorption lines, the observed stellar continua, and photoionization models. The outflow metallicity is flat with $M_\ast$, with a median metallicity of $1.0\pm0.6$ Z$_\odot$. The observed outflows are metal-enriched: low and high-mass galaxies have outflow metallicities 10-50 and 2.6 times larger than their ISM metallicities, respectively. The observed outflows are mainly composed of entrained ISM gas with at most 22% of the metals directly coming from recent supernovae enrichment. The metal outflow rate shallowly increases with $M_\ast$, as $M_\ast^{0.2 \pm 0.1}$, because the mass outflow rate shallow increases with $M_\ast$. Finally, we normalize the metal outflow rate by the rate at which star formation retains metals to calculate the metal-loading factor. The metal-loading factor inversely scales with $M_\ast$. The normalization and scaling of the metal-loading factor agree with analytic expressions that reproduce observed mass-metallicity relations. Galactic outflows fundamentally shape the observed mass-metallicity relationship.