The FMOS-COSMOS survey of star-forming galaxies at z~1.6. IV: Excitation
  state and chemical enrichment of the interstellar medium
  We investigate the physical conditions of ionized gas in high-z star-forming
galaxies using diagnostic diagrams based on the rest-frame optical emission
lines. The sample consists of 701 galaxies with an Ha detection at $1.4\lesssim
z\lesssim1.7$, from the FMOS-COSMOS survey, that represent the normal
star-forming population over the stellar mass range $10^{9.6} \lesssim
M_\ast/M_\odot \lesssim 10^{11.6}$ with those at $M_\ast>10^{11}~M_\odot$ being
well sampled. We confirm an offset of the average location of star-forming
galaxies in the BPT diagram ([OIII]/Hb vs. [NII]/Ha), primarily towards higher
[OIII]/Hb, compared with local galaxies. Based on the [SII] ratio, we measure
an electron density ($n_e=220^{+170}_{-130}~\mathrm{cm^{-3}}$), that is higher
than that of local galaxies. Based on comparisons to theoretical models, we
argue that changes in emission-line ratios, including the offset in the BPT
diagram, are caused by a higher ionization parameter both at fixed stellar mass
and at fixed metallicity with additional contributions from a higher gas
density and possibly a hardening of the ionizing radiation field. Ionization
due to AGNs is ruled out as assessed with Chandra. As a consequence, we revisit
the mass-metallicity relation using [NII]/Ha and a new calibration including
[NII]/[SII] as recently introduced by Dopita et al. Consistent with our
previous results, the most massive galaxies ($M_\ast\gtrsim10^{11}~M_\odot$)
are fully enriched, while those at lower masses have metallicities lower than
local galaxies. Finally, we demonstrate that the stellar masses, metallicities
and star formation rates of the FMOS sample are well fit with a
physically-motivated model for the chemical evolution of star-forming galaxies.
