2023ApJ...942...24S

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.