  We use photoionization models designed to reconcile the joint rest-UV-optical
spectra of high-z star-forming galaxies to self-consistently infer the gas
chemistry and nebular ionization and excitation conditions for ~150 galaxies
from the Keck Baryonic Structure Survey (KBSS), using only observations of
their rest-optical nebular spectra. We find that the majority of z~2-3 KBSS
galaxies are moderately O-rich, with an interquartile range in
12+log(O/H)=8.29-8.56, and have significantly sub-solar Fe enrichment, with an
interquartile range of [Fe/H]=[-0.79,-0.53], contributing additional evidence
in favor of super-solar O/Fe in high-z galaxies. Model-inferred ionization
parameter and N/O are strongly correlated with common strong-line indices (such
as O32 and N2O2), with the latter exhibiting similar behavior to local
extragalactic HII regions. In contrast, diagnostics commonly used for measuring
gas-phase O/H (such as N2 and O3N2) show relatively large scatter with the
overall amount of oxygen present in the gas and behave differently than
observed at z~0. We provide a new calibration for using R23 to measure O/H in
typical high-z galaxies, although it is most useful for relatively O-rich
galaxies; combining O32 and R23 does not yield a more effective calibration.
Finally, we consider implications for the intrinsic correlations between
physical conditions across the galaxy sample and find that N/O varies with O/H
in high-z galaxies in a manner almost identical to local HII regions. However,
we do not find a strong anti-correlation between ionization parameter and
metallicity (O/H or Fe/H) in high-z galaxies, which is one of the principal
bases for using strong-line ratios to infer oxygen abundance.

Astrophysics of Galaxies;Cosmology and Nongalactic Astrophysics