Electron temperature relations and the direct N, O, Ne, S, and Ar abundances of 49 959 star-forming galaxies in DESI data release 2

We present the largest direct-method abundance catalogue of galaxies to date, containing measurements of 49 959 starforming galaxies at z < 0.96 from DESI (Dark Energy Spectroscopic Instrument) data release 2. By directly measuring electron temperatures across multiple ionization zones, we provide constraints on a number of electron temperature relations. Using the temperature measurements, we derive reliable abundances for N, O, Ne, S, and Ar, and measure the evolution of abundances and abundance ratios of as a function of metallicity and other galaxy properties. Our measurements include direct oxygen abundances for 49 507 galaxies, leading to the discovery of the two most metalpoor galaxies in the nearby Universe, with oxygen abundances of 12 + log(O/H) = 6.77(+0.03) (-0.03) dex (1.2 per cent Z(circle dot)) and 12 + log(O/H) = 6.81(+0.04) (-0.04 )dex (1.3 per cent Z(circle dot)). We identify a rare outlier population of 24 galaxies with high-N/O ratios at low metallicity, reminiscent of galaxy abundances observed in the early Universe. We find the Ne/O ratio is constant at low metallicity but increases gradually at 12 + log(O/H) > 8.105 +/- 0.004 dex. We show that the S/O and Ar/O abundance ratios are strongly correlated, consistent with the expected additional Type Ia enrichment channel for S and Ar. In this work, we present an initialsurvey of the key properties of the sample, with this data setserving as a foundation for extensive future work on galaxy abundances at low redshift.