Do galaxy global relationships emerge from local ones? The SDSS IV MaNGA
  surface mass density-metallicity relation
  We present the stellar surface mass density {\it vs.} gas metallicity
($\Sigma_*-Z$) relation for more than 500,000 spatially-resolved star-forming
resolution elements (spaxels) from a sample of 653 disk 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 four in metallicity. We show that this local relationship can
simultaneously reproduce two well-known properties of disk galaxies: their
global mass-metallicity relationship {\it and} their radial metallicity
gradients. We also find that the $\Sigma_* - Z$ 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 disk galaxies.
