The DESIRED strong-line calibrations: I. New empirical metallicity relations for the local and high-redshift universe

We present the most comprehensive set of empirical optical strong-line metallicity calibrations to date, based on the DEep Spectra of Ionised REgions Database (DESIRED), the largest compilation of H ii regions and galaxies with direct electron-temperature determinations. We construct a high-quality calibration sample of 2392 spectra: 1029 extragalactic H ii regions, 1296 local star-forming galaxies, and 67 high-redshift (z > 2) galaxies, drawn from 201 independent literature references, spanning 12 + log (O/H) ∈ [6.79, 9.07]. Physical conditions and chemical abundances are derived homogeneously using up-to-date atomic data. We derive 27 strong-line calibrations covering oxygen-, nitrogen-, sulphur-, argon-, and neon-based line ratios, including 4 previously uncalibrated diagnostics, with reported validity ranges and intrinsic dispersions (typically ∼0.15 − 0.35 dex). For the first time in a systematic calibration framework, all relations are presented for both the homogeneous temperature case (t2 = 0) and a scenario including temperature inhomogeneities (t2 > 0), thereby reconciling abundances from recombination lines (RLs) and collisionally excited lines (CELs) and directly tackling the abundance discrepancy problem. A comparison with previous calibrations shows that the DESIRED relations span the broadest validity intervals while remaining anchored to the empirical data. Comparisons with z > 2 galaxies show that several DESIRED calibrations remain consistent with independent high-redshift relations within their intrinsic scatter, whereas others display systematic offsets associated with elevated N/O or harder ionising conditions. Thus, DESIRED calibrations can provide reliable metallicity estimates at high redshift for a subset of diagnostics, while highlighting the need to account for diagnostic-specific redshift evolution.