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.