Aims. We aim to study the high-precision chemical abundances of metal-poor gas clouds at cosmic noon (2 < z < 4) and investigate the associated enrichment histories. Methods. We analyze the abundances of four newly discovered metal-poor gas clouds utilizing observations conducted with Keck/HIRES and VLT/UVES. These systems are classified as very metal-poor (VMP), with [Fe/H] < −2.57, and one system qualifies as an extremely metal-poor (EMP) Damped Lyman-α (DLA) system with [Fe/H] = −3.13 ± 0.06. In combination with new high-resolution data of two previously known EMP DLAs and 2 systems reported in the literature, we conduct a comprehensive analysis of eight of the most metal-poor gas clouds currently known. We focus on high-precision abundance measurements using the elements: C, N, O, Al, Si, and Fe. Results. Our findings indicate increasing evidence of elevated [O/Fe] abundances when [Fe/H] < −3. EMP DLAs are well-modeled with a mean value of [O/Fe]cen = +0.50 ± 0.04 and an intrinsic scatter of σint[O/Fe] = 0.13-0.04+0.06. While VMP DLAs are well-modeled with [O/Fe]cen = +0.40 ± 0.02 and σint, [O/Fe] = 0.06 ± 0.02. We further find tentative evidence of a redshift evolution of [C/O] across these most metal-poor DLAs with lower redshift systems showing elevated [C/O] ratios. Using the measured abundances, combined with a stochastic chemical enrichment model, we investigate the properties of the stellar population responsible for enriching EMP gas at cosmic noon. We find that the chemistry of these systems is best explained via the enrichment of just two massive progenitors, N⋆ = 2 ± 1, that ended their lives as core collapse SNe with a typical explosion energy Eexp = (1.6 ± 0.6)×1051 erg. These progenitors formed obeying a Salpeter-like power-law IMF, where all stars of mass greater than Mmax = 32-4+10M⊙ collapse directly to black holes and do not contribute to the metal enrichment.
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