The Mass-Metallicity Relation with the Direct Method on Stacked Spectra
  of SDSS Galaxies
  The relation between galaxy stellar mass and gas-phase metallicity is a
sensitive diagnostic of the main processes that drive galaxy evolution, namely
cosmological gas inflow, metal production in stars, and gas outflow via
galactic winds. We employed the direct method to measure the metallicities of
~200,000 star-forming galaxies from the SDSS that were stacked in bins of (1)
stellar mass and (2) both stellar mass and star formation rate (SFR) to
significantly enhance the signal-to-noise ratio of the weak [O III] 4363 and [O
II] 7320, 7330 auroral lines required to apply the direct method. These
metallicity measurements span three decades in stellar mass from
log(Mstar/Msun) = 7.4-10.5, which allows the direct method mass-metallicity
relation to simultaneously capture the high-mass turnover and extend a full
decade lower in mass than previous studies that employed more uncertain strong
line methods. The direct method mass-metallicity relation rises steeply at low
mass (O/H ~ Mstar^{1/2}) until it turns over at log(Mstar/Msun) = 8.9 and
asymptotes to 12 + log(O/H) = 8.8 at high mass. The direct method
mass-metallicity relation has a steeper slope, a lower turnover mass, and a
factor of two to three greater dependence on SFR than strong line
mass-metallicity relations. Furthermore, the SFR-dependence appears monotonic
with stellar mass, unlike strong line mass-metallicity relations. We also
measure the N/O abundance ratio, an important tracer of star formation history,
and find the clear signature of primary and secondary nitrogen enrichment. N/O
correlates tightly with oxygen abundance, and even more so with stellar mass.
