2.2.2. The Bright Line (or ``Empirical'') Method
What if it is not possible to measure the faint emission lines from the upper levels that are necessary for measuring temperatures in the direct method? It turns out that one can still do pretty well at determining an oxygen abundance with just the brightest lines. Pagel et al. (1979) developed a method to do just this. The method is based on the simple observation that at high metallicities (low HII region temperatures) the bulk of the cooling is done by the IR fine structure lines, while at low metallicities (high HII region temperatures), the bulk of the cooling is done by the high excitation optical lines. Thus, the combined strengths of the optical oxygen lines (3727 + 4959 + 5007) relative to H (the "R23" parameter) increases with decreasing abundance. This relationship was recalibrated by Edmunds & Pagel (1984) and others, but has changed little since then. While relatively uncertain at trans-solar abundances (where there is little change in R23 with abundance), it was thought that this method could provide abundances with uncertainties of roughly 0.2 dex.
Of course, the oxygen line strengths can't increase forever with decreasing oxygen abundance, and this relationship turns around at roughly 10% of the solar oxygen abundance. Thus, there is a region of increased uncertainty and the overall relationship is bi-valued. The ambiguity of high versus low-metallicity regimes can be overcome through the observation of additional emission lines (e.g., the [S II] and [N II] lines are relatively strong at high abundances and drop dramatically in strength at low abundances). It turns out that at low abundances (less than 10% of the solar abundance) R23 is a fairly accurate measure of the oxygen abundance (Skillman 1989).
McGaugh (1991) constructed a grid of photoionization models, in part, to recalibrate the R23 vs. O/H relationship (his Figure 11 gives a comparison of a number of previous calibrations). This work was very important in that it showed that a metallicity dependent initial mass function was not necessary to explain the observed trend of softer ionizing radiation fields with increased metallicity. More work has been done on this since, but McGaugh's conclusion remains true. Despite the importance of this paper, I have reservations about a second conclusion from the work. McGaugh claimed that R23 could be calibrated so that it would be comparable in accuracy to the results obtainable by the direct methods not only in the low abundance regime, but also at higher abundances.
I disagree with this second conclusion for three reasons. The first is that the proposed improvement in the calibration, the addition of the [O III]/[O II] ratio as a second parameter in the calibration, does not add sensitivity at higher metallicities (it is no longer sensitive to the ionization parameter). The second reason is that at higher metallicities, R23 has a stronger density dependence (since the IR lines are carrying the bulk of the cooling and since increased density leads to more collisional de-excitations, and thus a lower cooling efficiency) which is not true at lower metallicities (Stasinska 1990; Oey & Kennicutt (1993). The third reason is that the role of dust (both through depletion of refractory elements onto grains and through its effects on the heating/cooling balance) is also more important at higher abundances (see Shields & Kennicutt 1995 and the next section). Thus, when using the McGaugh calibration, I would recommend a minimum uncertainty of at least 0.2 dex (and probably larger for trans-solar metallicity objects).