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We investigate the relationships between stellar mass, gas-phase oxygenabundance (metallicity), star formation rate, and dust content of star-forminggalaxies at z$\sim$1.6 using Subaru/FMOS spectroscopy in the COSMOS field. Themass-metallicity relation at $z\sim1.6$ is steeper than the relation observedin the local Universe. The steeper MZ relation at $z\sim1.6$ is mainly due toevolution in the stellar mass where the MZ relation begins to turnover andflatten. This turnover mass is 1.2 dex larger at $z\sim1.6$. The most massivegalaxies at $z\sim1.6$ ($\sim 10^{11}M_\odot$) are enriched to the levelobserved in massive galaxies in the local Universe. The mass-metallicityrelation we measure at $z\sim1.6$ supports the suggestion of an empirical uppermetallicity limit that does not significantly evolve with redshift. We find ananti-correlation between metallicity and star formation rate for galaxies at afixed stellar mass at $z\sim1.6$ which is similar to trends observed in thelocal Universe. We do not find a relation between stellar mass, metallicity andstar formation rate that is independent of redshift; our data suggest thatthere is redshift evolution in this relation. We examine the relation betweenstellar mass, metallicity and dust extinction. We find that at a fixed stellarmass dustier galaxies tend to be more metal rich. From examination of thestellar masses, metallicities, SFRs and dust extinctions we conclude thatstellar mass is most closely related to dust extinction.

astrophysical journal/the astrophysical journal

The FMOS-Cosmos Survey of Star-Forming Galaxies at z~1.6 II. The  Mass-Metallicity Relation and the Dependence on Star Formation Rate and Dust  Extinction