I would now like to give a personal synopsis of what I see as some of the main results and outstanding problems in the area of chemical abundances in extragalactic H II regions. The first theme that stands out is the mass-metallicity relation, which seems to hold all the way from the largest spirals, such as M 81 (Figure 2), down to the smallest Local Group irregulars, such as Gr 8 (see Skillman et al. 1988b). This ubiquitous empirical relationship must be accounted for by any convincing model of galactic chemical evolution. It may simply reflect the ease with which hot, metal-rich supernova ejecta can escape from low-mass galaxies, but also implies that there are major similarities in the evolution of all galaxies. A second important issue is that of the relative evolution of different elements as compared to oxygen. Probably the clearest case is that of nitrogen, for which there seem to multiple nucleosynthetic sites. Some nitrogen must be made by an effectively "primary" mechanism, either in massive stars via supernovae or Wolf-Rayet star winds, or in intermediate-mass stars by triple-alpha followed by CN-cycle burning and mixing. As the overall metallicity increases and the stellar population evolves, some nitrogen begins to be produced according to the "secondary" formula. The other elements studied so far, chiefly S, Ar, Ne, and C, mostly seem to follow O/H (but note that abundances for the iron-peak elements are not accessible for extragalactic H II regions).
Next, there remain a number of what I will call "zero-point" questions. There remains a factor of two or three systematic difference between the nebular and stellar abundance scales, (O/H)Orion (O/H). This may either be a true abundance difference, or it may arise from different systematic errors between the two types of analysis. For example, the nominal nebular abundances are always too low if allowance is not made for the presence of temperature inhomogeneities (see 2.1.2.). This issue can be investigated by obtaining multiple diagnostics for the physical parameters, from weak optical lines or infrared measurements, or by spatially resolving the spatial structure. A second problem is the discrepancy between the N/O ratio as determined from optical and infrared techniques, (N++/O++) (N+/O+). Possible factors which may contribute to the resolution of this problem include ionization-structure effects, non-collisional excitation of the optical lines (Rubin 1986), or the presence of significant density inhomogeneities (Rubin 1989).
Finally, there is the question of the origin of the "excitation"-metallicity relation, the empirical observation that regions with low O/H abundances tend to be more highly ionized. As mentioned above, there are number of different ways in which such a relationship could arise. The first possible cause is a systematic change in the geometry or dumpiness of nebulae as a function of metallicity, producing an effective decrease in the ionization parameter U (see Section 2.2.) as the O/H abundance increases. This possibility has been emphasized by Mathis (1985) and by Dopita and Evans (1986). The second mechanism for lowering the nebular ionization level is by softening the radiation field, which can be accomplished in various ways. Balick and Sneden (1976) pointed out that more metal-rich stars will have deeper ionization edges in their atmospheres. However, calculations using recent model atmospheres stars show that the metal-edge effect in the photospheres is diminished for surface temperatures as high as those in the metal-poor H II regions (Skillman 1989). Dust internal to the nebula might also soften the radiation field, but only for certain assumed optical dust properties, as discussed above. A number of workers have advocated the idea that there is actually a systematic change of some sort in the initial mass function (IMF) with metallicity. Shields and Tinsley (1976) suggested a smaller upper limit to the stellar masses, while Terlevich (1986) and others prefer to invoke a change in the IMF slope. (See Scab 1986, however, for a critical discussion regarding the lack of direct evidence for a varying IMF.)
As hinted above, there is another way to soften the radiation field, without invoking a varying IMF. Stars with different metallicities are predicted to follow different evolutionary tracks. In particular, metal-rich stars tend to have stronger winds, and therefore will spend more time in the Wolf-Rayet (W-R) stage, or else the W-R stage may set in at lower stellar masses. Recent evolutionary models therefore predict that there should be a higher incidence of W-R stars in more metal-rich populations, the trend that is seen in these extragalactic H II regions (Arnault, Kunth, and Schild 1989. Now, since most W-R stars are cooler than main sequence stars of the same mass, the integrated UV radiation field will be effectively "softened" in such regions (e.g. Kunth and Joubert 1985). The presence of W-R stars provides a double "whammy" to the H II region; not only do these stars soften the overall radiation field, but they also provide a natural way to sweep out the local volume and drive down the filling factor, f, and ionization parameter, U (e.g. Dopita and Evans 1986). In lower-metallicity regions, with fewer or no W-R stars, the gas will be less compressed and the ionization parameter larger. It thus seems possible that metallicity-dependent evolution, rather than a metallicity-dependent IMF, can fully account for the empirical ionization-abundance correlation in extragalactic H II regions; this hypothesis ought to be examined further and tested against new observations in the coming years.