Density biases and temperature relations for DESIRED H ii regions

We present a first study based on the analysis of the DEep Spectra of Ionized REgions Data base (DESIRED). This is a compilation of 190 high signal-to-noise ratio optical spectra of H II regions and other photoionized nebulae, mostly observed with 8-10 m telescopes and containing similar to 29 380 emission lines. We find that the electron density -n(e) - of the objects is underestimated when [S II] lambda 6731/lambda 6716 and/or [O II]lambda 3726/lambda 3729 are the only density indicators available. This is produced by the non-linear density dependence of the indicators in the presence of density inhomogeneities. The average underestimate is similar to 300 cm(-3) in extragalactic H II regions, introducing systematic overestimates of T-e ([O II]) and T e([S II]) compared to T e ([N II]). The highsensitivity of [O II]lambda lambda 7319 + 20 + 30 + 31/lambda lambda 3726 + 29 and [S II]lambda lambda 4069 + 76/lambda lambda 6716 + 31 to density makes them more suitable for the diagnosis of the presence of high-density clumps. If T-e ([N II]) is adopted, the density underestimate has a small impact in the ionic abundances derived from optical spectra, being limited to up to similar to 0.1 dex when auroral [S II] and/or [O II] lines are used. However, these density effects are critical for the analysis of infrared fine structure lines, such as those observed by the JWST in local star forming regions, implying strong underestimates of the ionic abundances. We present temperature relations between T (e)([O III]), T (e) ([Ar III]), T (e) ([S III]), and T (e) ([N II]) for the extragalactic H II regions. We confirm a non-linear dependence between T (e) ([O III]) and T (e)([N II]) due to a more rapid increase of T (e) ([O III]) at lower metallicities.