We present a combined analysis of rest-frame far-UV (1000-2000 A) and rest-frame optical (3600-7000 A) composite spectra formed from very deep observations of a sample of 30 star-forming galaxies with z=2.4+/-0.1, selected to be representative of the full KBSS-MOSFIRE spectroscopic survey. Since the same massive stars are responsible for the observed FUV continuum and the excitation of the observed nebular emission, a self-consistent stellar population synthesis model must simultaneously match the details of the far-UV stellar+nebular continuum and-- when inserted as the excitation source in photoionization models-- account for all observed nebular emission line ratios. We find that only models including massive star binaries, having low stellar metallicity (Z_*/Z_{sun} ~ 0.1) but relatively high ionized gas-phase oxygen abundances (Z_{neb}/Z_{sun} ~ 0.5), can successfully match all of the observational constraints. We argue that this apparent discrepancy is naturally explained by highly super-solar O/Fe [4-5 times (O/Fe)_{sun}], expected for gas whose enrichment is dominated by the products of core-collapse supernovae. Once the correct ionizing spectrum is identified, photoionization models reproduce all of the observed strong emission line ratios, the direct T_e measurement of O/H, and allow accurate measurement of the gas-phase abundance ratios of N/O and C/O -- both of which are significantly sub-solar but, as for O/Fe, are in remarkable agreement with abundance patterns observed in Galactic thick disk, bulge, and halo stars with similar O/H. High nebular excitation is the rule at high-z (and rare at low-z) because of systematically shorter enrichment timescales (<<1 Gyr): low Fe/O environments produce harder (and longer-lived) stellar EUV spectra at a given O/H, enhanced by dramatic effects on the evolution of massive star binaries.
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