Beyond the [OIII]4363 auroral line: [NeIII]3868 as a direct tracer of the electron temperature

Context. Auroral lines enable accurate measurements of chemical abundances in ionized gaseous nebulae because they are sensitive to the electron temperature. However, metal-enriched systems remain a challenge because even deep observations cannot retrieve auroral lines: they are intrinsically faint. Aims. To overcome this limitation, we present a novel approach to estimating electron temperatures in conditions where the [O III]{\ensuremath{\lambda}}4363 auroral line is barely detectable (T$_{e}$ < 11 000 K). This approach relies on the detection of [Ne III]{\ensuremath{\lambda}}3868 and [O III]{\ensuremath{\lambda}}4959,5007, which are among the brightest rest-frame optical emission lines. Methods. By means of detailed photoionization models, we derived a tight relation between the O3Ne3 {\ensuremath{\equiv}}[O III]{\ensuremath{\lambda}}4959,5007/[Ne III]{\ensuremath{\lambda}}3868 ratio and the electron temperature weighted in the O$^{++}$ dominated region. We tested the validity of this relation in a large sample of galaxies that cover a wide range of redshifts z {\ensuremath{\sim}} 0─9 and extragalactic HII regions. Results. Our results show that the O3Ne3 ratio, in combination with the O3O2 ratio (tracer of ionization), yields electron temperature estimates that are consistent within the uncertainties with those based on [O III]{\ensuremath{\lambda}}4363. The proposed relation can be used to estimate the electron temperature in the cool (equivalently, high-metal) regime [6000, 13 500 K] where the emissivity of [O III]{\ensuremath{\lambda}}4363 drops drastically.