(Proposal ID) S17B-061 (PI) Onodera, Masato (Proposal Title) Direct metallicity measurement and ISM physical conditions at z>3 (Abstract) Physical conditions of ionized gas of star-forming regions in galaxies is known to evolve toward high redshift, showing more than an order of magnitude elevation in ionization parameters at z>3 than those in the local Universe. In order to unveil the origin of the elevated ionization parameter at high redshift, extensive photoionization modeling is essential, but currently the number of free parameters is large and an inevitable systematic uncertainty is observationally introduced by the metallicity measured with locally defined calibrations. Here, we propose a systematic near-IR spectroscopic observation of Ly alpha emitters at z=3.1 and 3.7 with Keck/MOSFIRE aiming at individually detecting [O III] lambda4363 for ~50 such objects, which enables us an unbiased estimate of gas-phase metallicity via the electron temperature method. By fixing metallicity as well as the electron temperature and density from the rest-frame emission line ratios, we will investigate which parameters, i.e., amount of ionizing flux, hardness of stellar spectra, or geometry of H II regions, are the dominant source(s) of the high ionization parameter. We will also provide a metallicty calibration tailored for z>3 star-forming galaxies and revisit the mass--metallicity relation and its dependence on star formation rate at high redshift.