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 \pm 0.6 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 .