Do galaxy global relationships emerge from local ones? The SDSS IV MaNGA surface mass density-metallicity relation

We present the stellar surface mass density versus gas metallicity (Σ_*-Z) relation for more than 500 000 spatially resolved star-forming resolution elements (spaxels) from a sample of 653 disc galaxies included in the SDSS IV MaNGA survey. We find a tight relation between these local properties, with higher metallicities as the surface density increases. This relation extends over three orders of magnitude in the surface mass density and a factor of 4 in metallicity. We show that this local relationship can simultaneously reproduce two well-known properties of disc galaxies: their global mass-metallicity relationship and their radial metallicity gradients. We also find that the Σ_*-Z relation is largely independent of the galaxy's total stellar mass and specific star formation rate (sSFR), except at low stellar mass and high sSFR. These results suggest that in the present-day universe local properties play a key role in determining the gas-phase metallicity in typical disc galaxies.