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 HII regions and galaxies with direct electron-temperature determinations. We construct a high-quality calibration sample of 2392 spectra: 1029 extragalactic HII regions, 1296 local star-forming galaxies, and 67 high-redshift ($z > 2$) galaxies, drawn from 201 independent literature references, spanning $12+\log({\rm O/H}) \in [6.79, 9.07]$. 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 $\sim0.15-0.35$~dex). For the first time in a systematic calibration framework, all relations are presented for both the homogeneous temperature case ($t^2 = 0$) and a scenario including temperature inhomogeneities ($t^2 > 0$), 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.