Investigating the electron temperature of [Ar IV] in planetary nebulae using the DESIRED database
(Abridged) We investigate the behaviour of the electron temperature derived from [Ar IV] lines, Te([Ar IV]), in a sample of PNe to characterize the thermal structure of high-excitation gas and compare it with the predictions of standard photoionisation models. Using the DEep Spectra of ionised REgions Data Base Extended (DESIRED-E), we selected a sample of 57 PNe for which Te([Ar IV]), Te([O III]), and ne([Ar IV]) could be determined simultaneously and homogeneously. We performed a detailed comparison between these observational diagnostics and a suite of over 160000 photoionisation models from the Mexican Million Models Database (3MdB). We find that the observed Te([Ar IV]) values are systematically higher than those predicted by pure photoionisation models for a given Te([O III]), i.e. approximately 31 percent of the PNe sample exhibits a Te([Ar IV]) more than 2sigma higher than photoionization model predictions. This discrepancy persists regardless of the specific set of auroral lines used for the diagnostic or the choice of atomic data (transition probabilities and collision strengths) adopted in the calculations. Other high-ionisation Te diagnostics, compiled from the DESIRED database or from the literature, however, do not show such behaviour, though the statistics for these are much more limited. The fact that models succeed for the highest-ionisation species but fail specifically for [Ar IV] suggests that the discrepancy is not due to a global inner-nebula heating mechanism. Instead, it points toward a localized physical effect or a limitation in the current understanding of the ionisation stratification and atomic physics specific to the Argon ion stages. This "[Ar IV] anomaly" must be resolved to ensure the reliability of abundance determinations in high-excitation nebulae.