The Physical Conditions of a Lensed Star-forming Galaxy at z=1.7

We report rest-frame optical Keck/NIRSPEC spectroscopy of the bright lensed galaxy RCSGA 032727-132609 at z=1.7037. From precise measurements of the nebular lines, we infer a number of physical properties: redshift, extinction, star formation rate, ionization parameter, electron density, electron temperature, oxygen abundance, and N/O, Ne/O, and Ar/O abundance ratios. The limit on [O III]~4363 A tightly constrains the oxygen abundance via the "direct" or electron temperature method, for the first time in an average-metallicity galaxy at z~2. We compare this result to several standard "bright-line" O abundance diagnostics, thereby testing these empirically-calibrated diagnostics in situ. Finally, we explore the positions of lensed and unlensed galaxies in standard diagnostic diagrams, and explore the diversity of ionization conditions and mass--metallicity ratios at z=2.