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-H _2 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.