What Determines the Local Metallicity of Galaxies: Global Stellar Mass, Local Stellar Mass Surface Density, or Star Formation Rate?

Metallicity and its relationship with other galactic properties is a fundamental probe of the evolution of galaxies. In this work, we select about 750,000 star-forming spatial pixels from 1122 blue galaxies in the Mapping Nearby Galaxies at Apache Point Observatory survey to investigate the global stellar mass-local stellar mass surface density-gas-phase metallicity (M-*-Sigma(*)-Z) relation. At a fixed M*, the metallicity increases steeply with increasing Sigma(*). Similarly, at a fixed Sigma(*), the metallicity increases strongly with increasing M-* at the low-mass end, while this trend becomes less obvious at the high-mass end. We find the metallicity to be more strongly correlated to Sigma(*) than to M-*. Furthermore, we construct a tight (0.07 dex scatter) M-*-Sigma(*)-Z relation, which reduces the scatter in the Sigma(*)-Z relation by about 30% for galaxies with 7.8. <log(M-*/M-circle dot). <. 11.0, while the reduction of scatter is much weaker for high-mass galaxies. This result suggests that, especially for low-mass galaxies, the M-*-Sigma(*)-Z relation is largely more fundamental than the M-*-Z and Sigma(*)-Z relations, meaning that both M* and Sigma(*) play important roles in shaping the local metallicity. We also find that the local metallicity is probably independent on the local star formation rate surface density at a fixed M* and Sigma(*). Our results are consistent with the scenario that the local metallicities in galaxies are shaped by the combination of the local stars formed in the history and the metal loss caused by galactic winds.