CO Emission, Molecular Gas, and Metallicity in Main-sequence Star-forming Galaxies at z ∼ 2.3

We present observations of CO(3-2) in 13 main-sequence z = 2.0-2.5 star-forming galaxies at $\mathrm{log}({M}_{* }/{M}_{\odot })=10.2\mbox{--}10.6$ that span a wide range in metallicity (O/H) based on rest-optical spectroscopy. We find that ${L}_{\mathrm{CO}(3-2)}^{{\prime} }$ /SFR decreases with decreasing metallicity, implying that the CO luminosity per unit gas mass is lower in low-metallicity galaxies at z ~ 2. We constrain the CO-to-H₂ conversion factor (α _CO) and find that α _CO inversely correlates with metallicity at z ~ 2. We derive molecular gas masses (M _mol) and characterize the relations among M _*, SFR, M _mol, and metallicity. At z ~ 2, M _mol increases and the molecular gas fraction (M _mol/M _*) decreases with increasing M _*, with a significant secondary dependence on SFR. Galaxies at z ~ 2 lie on a near-linear molecular KS law that is well-described by a constant depletion time of 700 Myr. We find that the scatter about the mean SFR-M _*, O/H-M _*, and M _mol-M _* relations is correlated such that, at fixed M _*, z ~ 2 galaxies with larger M _mol have higher SFR and lower O/H. We thus confirm the existence of a fundamental metallicity relation at z ~ 2, where O/H is inversely correlated with both SFR and M _mol at fixed M _*. These results suggest that the scatter of the z ~ 2 star-forming main sequence, mass-metallicity relation, and M _mol-M _* relation are primarily driven by stochastic variations in gas inflow rates. We place constraints on the mass loading of galactic outflows and perform a metal budget analysis, finding that massive z ~ 2 star-forming galaxies retain only 30% of metals produced, implying that a large mass of metals resides in the circumgalactic medium. *The data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation.