(Proposal ID) S13B-088 (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 surface in the stellar mass-star formation rate (SFR)-metallicity 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 evidence for a change in behaviour at z > 3, based however on a small sample. A simple model of star-formation in galaxies, in which the SFR is regulated by the gas mass present naturally reproduces the form and constancy of the FMR. However, the gas-regulator system may break down at very high redshifts because of the convergence of a number of timescales in galaxies. Here we propose a Keck/MOSFIRE spectroscopy for about 60 galaxies at 3 < z_spec < 3.8 to measure metallicities in order to study the Z(m, SFR) relation at z > 3 with a statistically significant sample. Using metallicities and SFRs from the emission lines, and stellar masses from SED fitting (properly assessing the contribution from the emission lines to the broad-band flux) 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.