The MOSDEF Survey: Direct Observational Constraints on the Ionizing Photon Production Efficiency, xi_(rm ion), at z~2

We combine spectroscopic measurements of H$\alpha$ and H$\beta$ and UV continuum photometry for a sample of 673 galaxies from the MOSFIRE Deep Evolution Field survey to constrain hydrogen ionizing photon production efficiencies ($\xi_{\rm ion}$, xi_ion) at z=1.4-2.6. We find average log(xi_ion/[Hz erg$^{-1}$])=25.06 (25.34), assuming the Calzetti (SMC) curve for the UV dust correction and a scatter of 0.28 dex in xi_ion distribution. After accounting for observational uncertainties and variations in dust attenuation, we conclude that the remaining scatter in xi_ion is likely dominated by galaxy-to-galaxy variations in stellar populations, including the slope and upper-mass cutoff of the initial mass function, stellar metallicity, star-formation burstiness, and stellar evolution (e.g., single/binary star evolution). Moreover, xi_ion is elevated in galaxies with high ionization states (high [OIII]/[OII]) and low oxygen abundances (low [NII]/H$\alpha$ and high [OIII]/H$\beta$) in the ionized ISM. However, xi_ion does not correlate with the offset from the z~0 star-forming locus in the BPT diagram, suggesting no change in the hardness of ionizing radiation accompanying the offset from the z~0 sequence. We also find that galaxies with blue UV spectral slopes ($\langle\beta\rangle$=-2.1) have elevated xi_ion by a factor of ~2 relative to the average xi_ion of the sample ($\langle\beta\rangle$=-1.4). If these blue galaxies are similar to those at z > 6, our results suggest that a lower Lyman continuum escape fraction is required for galaxies to maintain reionization, compared to the canonical xi_ion predictions from stellar population models. Furthermore, we demonstrate that even with robustly dust-corrected H$\alpha$, the UV dust attenuation can cause on average a ~0.3dex systematic uncertainty in xi_ion calculations.