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 line [O III]lambda 4363 in the stacked spectra of a sample of local analogs of high-redshift galaxies. These local analogs share the same location as z similar to 2 star-forming galaxies on the [O III]lambda 5007/H beta versus [N II]lambda 6584/H alpha 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(O/H)< 8.4) and the N2 (log([N II]lambda 6584/H alpha))/O3N2 (log(([O III]lambda 5007/H beta)/([N II]lambda 6584/H alpha))) 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 H II 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 (log(([O III]lambda lambda 4959,5007+[O II]lambda lambda 3726,3729)/H beta)), O32(log([O III]lambda lambda 4959,5007/[O II]lambda lambda 3726,3729)), log([O III]lambda 5007/H beta), and log([Ne III]lambda 3869/[O II]lambda 3727) 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. Assuming that temperature structure variations are minimal and ISM conditions do not change dramatically from z similar to 2 to z similar to 5, these empirical calibrations can be used to measure relative metallicities in galaxies with redshifts up to z similar to 5.0 in ground-based observations.