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

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