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We have used a combination of stellar population synthesis and photoionization models to develop a set of ionization parameter and abundance diagnostics based only on the use of the strong optical emission lines. These models are applicable to both extragalactic HII regions and star-forming galaxies. We show that, because our techniques solve explicitly for both the ionization parameter and the chemical abundance, the diagnostics presented here are an improvement on earlier techniques based on strong emission-line ratios. Our techniques are applicable at all metallicities. In particular, for metallicities above half solar, the ratio NII/OII provides a very reliable diagnostic since it is ionization parameter independant and does not have a local maximum. This ratio has not been used historically because of worries about reddening corrections. However, we show that the use of classical reddening curves is quite sufficient to allow this NII/OII diagnostic to be used with confidence as a reliable abundance indicator. The cause of systematic and random errors inherent in previous techniques are discussed, and we present a new `optimal' abundance diagnostic method based on the use of line ratios involving NII, OII, OIII, SII and the Balmer lines. This combined diagnostic appears to suffer no apparent systematic errors, can be used over the entire abundance range and significantly reduces the random error inherent in previous techniques. Finally, we give a recommended procedure for the derivation of abundances in the case that only spectra of limited wavelength coverage are available so that the optimal method can no longer be used.
Kewley et al. (Sun,) studied this question.