The DESIRED electron temperature relations in star-forming regions of the local Universe

Abstract

(Abridged) Aims. We present a homogeneous observational study of electron temperature ($T_{\mathrm{e}}$) relations between ionic species: $T_{\mathrm{e}}$([N II]), $T_{\mathrm{e}}$([O II]), $T_{\mathrm{e}}$([O III]), $T_{\mathrm{e}}$([S II]), $T_{\mathrm{e}}$([S III]) and $T_{\mathrm{e}}$([Ar III]), using 699 spectra of Galactic and extragalactic H II regions and local star-forming galaxies (SFGs). Methods. We use the DEep Spectra of Ionised REgions Database Extended (DESIRED-E), comprising more than 3000 spectra with direct $T_{\mathrm{e}}$ determinations, selecting those with at least two $T_{\mathrm{e}}$ diagnostics. We recompute electron density ($n_{\mathrm{e}}$) and $T_{\mathrm{e}}$ using updated atomic data and a consistent methodology. The resulting $T_{\mathrm{e}}$--$T_{\mathrm{e}}$ relations are analysed using orthogonal distance regression, quantifying total and intrinsic dispersions and comparing slopes with previous works and photoionisation models. Results. Relations involving low-ionisation $T_{\mathrm{e}}$ diagnostics show large intrinsic dispersions, especially for $T_{\mathrm{e}}$([O II]) and $T_{\mathrm{e}}$([S II]), likely due to sensitivity to $n_{\mathrm{e}}$ inhomogeneities, recombination contributions, and uncertainties. In contrast, relations using $T_{\mathrm{e}}$([N II]) show lower dispersions, indicating that this diagnostic provides a more reliable estimate of the low-ionisation zone temperature when only higher-ionisation $T_{\mathrm{e}}$ diagnostics are available, despite observational difficulties at low metallicity. Overall, slopes agree with model predictions, particularly for relations with low intrinsic dispersion, such as those involving $T_{\mathrm{e}}$([N II]) and $T_{\mathrm{e}}$([S III]). These results provide a robust empirical basis for estimating $T_{\mathrm{e}}$ when limited diagnostics are available.

16 pages, 8 figures, 3 tables (2 longtables online). Accepted for publication in Astronomy and Astrophysics