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.
