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We study a population of significantly sub-solar enrichment galaxies atz=1.99, to investigate how molecular gas, dust and star-formation relate inlow-metallicity galaxies at the peak epoch of star-formation. We target oursample with several deep ALMA and VLA datasets, and find no individualdetections of CO[4-3], CO[1-0] or dust, in stark contrast to the $>$60%detection rate expected for solar-enrichment galaxies with these MS HalphaSFRs. We find that both low and high density molecular gas (traced by CO[1-0]and CO[4-3] respectively) are affected by the low enrichment, showing sampleaverage (stacked) luminosity deficits $>$0.5-0.7 dex below expectations. Thisis particularly pertinent for the use of high-J CO emission as a proxy ofinstantaneous star-formation rate. Our individual galaxy data and stackedconstraints point to a strong inverse dependence $\propto Z^{\gamma}$ ofgas-to-dust ratios (G/D) and CO-to-H$_{2}$ conversion factors (aco) onmetallicity at z$\sim$2, with $\gamma_{\rm G/D}<$-2.2 and $\gamma_{\alpha_{\rmCO}}<$-0.8, respectively. We quantify the importance of comparing G/D and acovs. metallicity trends from the literature on a common, suitably normalisedmetallicity scale. When accounting for systematic offsets between differentmetallicity scales, our z$\sim$2 constraints on these scaling relations areconsistent with the corresponding relations for local galaxies. However, amongthose local relations, we favour those with a steep/double power-law dependenceof G/D on metallicity. Finally, we discuss the implications of these findingsfor (a) gas mass measurements for sub-M$^{*}$ galaxies, and (b) efforts toidentify the characteristic galaxy mass scale contributing most to the comovingmolecular gas density at z=2.

Suppressed CO emission and high G/D ratios in z=2 galaxies with sub-solar gas-phase metallicity