(Proposal ID) S15A-120 (PI) Onodera, Masato (Proposal Title) Fundamental metallicity relation at z>3: Are galaxies gas-regulated systems? (Abstract) Star-forming galaxies in the local Universe are known to lie on a tight s urface in the stellar mass (M_*)-star formation rate (SFR)-metallicity (Z) space, with a strikingly small scatter of 0.05 dex. Studies of the Z(M_*,SFR) have suggested it may be constant to z~2.5 even as the SFR at given mass increases by a factor of twenty --- leading to the idea of a "fundamental metallicity relation'' (FMR). There is some observational evidence for a change in behavior at z>3. Theoretically, a simple model of star-formation in galaxies naturally reproduces the form and constancy of the FMR. However, this gas-regulated system may break down at very high redshifts because of the convergence of a number of timescales. Here by adding 3 night to 1 already allocated night, we propose to complete a Keck/MOSFIRE spectroscopic campaign for ~50 galaxies at 33 across a wide range of M_* and SFR yet being explored. Using metallicities and SFRs from the emission lines, and M_* from SED fitting, we will investigate the existence and form of Z(M_*,SFR) at z>3 in detail and thereby gain new insights into the flow of gas into and out of galaxies at high redshifts.