Using Strong Lines to Estimate Abundances in Extragalactic H <scp>ii</scp> Regions and Starburst Galaxies

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 H II 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 [N II]/[O II] provides a very reliable diagnostic since it is ionization parameter independent and does not have a local maximum. This ratio has not previously been used historically because of worries about reliable calibration over such a long baseline, and reddening correction concerns. However, we show that the use of classical reddening curves and standard calibration are quite sufficient to allow this [N II]/[O II] diagnostic to be used with confidence as a reliable abundance indicator. As we had shown, the commonly used abundance diagnostic R 23 depends strongly on the ionization parameter, while the commonly used ionization parameter diagnostic [O III]/[O II] depends strongly on abundance. The iterative method of solution presented here allows both of these parameters to be obtained without recourse to the use of temperature-sensitive line ratios involving faint emission lines. We compare three commonly used abundance diagnostic techniques and show that individually, they contain systematic and random errors. This is a problem affecting many abundance diagnostics, and the errors generally have not been properly studied or understood due to the lack of a reliable comparison abundance, except for very low metallicities, where the [O III] λ4363 auroral line is used. Here we show that the average of these techniques provides a fairly reliable comparison abundance indicator against which to test new diagnostic methods. The cause of the systematic effects are discussed, and we present a new " optimal " abundance diagnostic method based on the use of line ratios involving [N II], [O II], [O III], [S II], 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.