3.5. Spatial temperature variations
3.5.1. Temperature gradients
At high metallicities, as explained above, large temperature gradients are expected in ionized nebulae. Therefore, empirical methods based on [O III] 4363/5007 will underestimate the abundances of heavy elements, since the [O III] 4363 line will be essentially emitted in the high temperature zones, inducing a strong overestimate of the average Te. Therefore, although with very large telescopes it will now be possible to measure [O III] 4363 even in high metallicity giant H II regions, one should refrain from exploiting this line in the usual way. Doing this, one would necessarily find sub-solar oxygen abundances, even for giant H II regions with metallicities well above solar (Fig. 3 of Stasinska 2002). High metallicity luminous PNe offer a much safer way to probe the metallicity in central parts of galaxies (see Sect. 5.3 for the relevance of PNe as metallicity indicators of their environment). Indeed the higher effective temperatures and the higher densities in luminous PNe induce higher values of Te in the O++ zone and a shallower temperature gradient, leading to a negligible bias in the derived abundances (see Fig. 4 of Stasinska 2002).
While Te-based empirical methods are biased for metal rich giant H II regions, tailored photoionization modeling to reproduce the distribution of the emission in the H, H, He I 5876, [O II] 3727 and [O III] 5007 lines are worth trying. As suggested by Stasinska (1980a), at high metallicity, regions emitting strongly [O III] 5007 will be decoupled from the regions emitting strongly in the recombination lines, and would be almost cospatial with regions emitting most of [O II] 3727. While the models of Stasinska (1980a) were made under spherical symmetry, the statement is more general, because it relies of the principles of ionization and thermal balance outlined in Sects. 1.1 and 1.2.