Density biases and temperature relations for DESIRED HII regions

We present a first study based on the analysis of the DEep Spectra of Ionized REgions Database (DESIRED). This is a compilation of 190 high signal-to-noise ratio optical spectra of HII regions and other photoionized nebulae, mostly observed with 8-10m telescopes and containing $\sim$29380 emission lines. We find that the electron density --$n_{\rm e}$-- of the objects is underestimated when [SII] $\lambda6731/\lambda6716$ and/or [OII] $\lambda3726/\lambda3729$ 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 $\sim 300$ cm$^{-3}$ in extragalactic HII regions, introducing systematic overestimates of $T_{\rm e}$([OII]) and $T_{\rm e}$([SII]) compared to $T_{\rm e}$([NII]). The high-sensitivity of [OII] $λ\lambda7319+20+30+31/λ\lambda3726+29$ and [SII] $λ\lambda4069+76/λ\lambda6716+31$ to density makes them more suitable for the diagnosis of the presence of high-density clumps. If $T_{\rm e}$([NII]) is adopted, the density underestimate has a small impact in the ionic abundances derived from optical spectra, being limited to up to $\sim$0.1 dex when auroral [SII] and/or [OII] 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 $T_{\rm e}$([OIII]), $T_{\rm e}$([ArIII]), $T_{\rm e}$([SIII]) and $T_{\rm e}$([NII]) for the extragalactic HII regions. We confirm a non-linear dependence between $T_{\rm e}$([OIII])-$T_{\rm e}$([NII]) due to a more rapid increase of $T_{\rm e}$([OIII]) at lower metallicities.