"Direct" Gas-Phase Metallicity in Local Analogs of High-Redshift Galaxies: Empirical Metallicity Calibrations for High-Redshift Star-Forming Galaxies

We study the direct gas-phase oxygen abundance using the well-detected auroral [OIII]4363 line in the stacked spectra of a sample of local analogs of high-redshift galaxies. These local analogs share the same location as $z\sim2$ star-forming galaxies on the Baldwin-Phillips-Terlevich diagram. This type of analog has the same ionized interstellar medium (ISM) properties as high-redshift galaxies. We establish empirical metallicity calibrations between the direct gas-phase oxygen abundances ($7.8<12+\log(\rm{O/H})<8.4$) and the N2/O3N2 indices in our local analogs. We find significant systematic offsets between the metallicity calibrations for our local analogs of high-redshift galaxies and those derived from the local HII regions and a sample of local reference galaxies selected from the Sloan Digital Sky Survey (SDSS). The N2 and O3N2 metallicities will be underestimated by 0.05-0.1~dex relative to our calibration if one simply applies the local metallicity calibration in previous studies to high-redshift galaxies. Local metallicity calibrations also cause discrepancies of metallicity measurements in high-redshift galaxies using the N2 and O3N2 indicators. In contrast, our new calibrations produce consistent metallicities between these two indicators. We also derive metallicity calibrations for R23, O32, log([OIII]/H\beta), and log([NeIII]/[OII]) indices in our local analogs, which show significant offset compared to those in the SDSS reference galaxies. By comparing with MAPPINGS photoionization models, the different empirical metallicity calibration relations in the local analogs and the SDSS reference galaxies can be shown to be primarily due to the change of ionized ISM conditions.