Using a large sample of 38,478 star-forming galaxies selected from the Second Data Release of the Sloan Digital Sky Survey database (SDSS-DR2), we derive analytical calibrations for oxygen abundances from several metallicity-sensitive emission-line ratios:Hβ. This consistent set of strong-line oxygen abundance calibrations will be useful for future abundance studies. Among these calibrations, [N ii]/[O ii] is the best for metal-rich galaxies due to its independence on ionization parameter and low scatter. Dust extinction must be considered properly at first. These calibrations are more suitable for metal-rich galaxies (8.4<12+log(O/H)<9.3), and for the nuclear regions of galaxies. The observed relations are consistent with those expected from the photoionization models of Kewley & Dopita (2002). However, most of the observational data spread in a range of ionization parameter q from 1 × 10 7 to 8 × 10 7 cm s −1 , corresponding to logU =−3.5 to −2.5, narrower than that suggested by the models. We also estimate the (N/O) abundance ratios of this large sample of galaxies, and these are consistent with the combination of a "primary" and a dominant "secondary" components of nitrogen.

Aims. Our aims are to estimate the validity of empirical methods, such as R 23 , R 23 − P, log([N ii]/Hα) (N2), log[([O iii]/Hβ)/ ([N ii]/Hα)] (O3N2), and log([S ii]/Hα) (S2), and to re-derive (or add) the calibrations of R 23 , N2, O3N2, and S2 indices for oxygen abundances on the basis of a large sample of galaxies with T e -based abundances.Methods. We determined the gas-phase oxygen abundance for a sample of 695 galaxies and H ii regions with reliable detections of [O iii]4363, using the reliable and direct temperature-sensitive (T e ) method of measuring metallicity. We selected 531 star-forming galaxies from the SDSS-DR4 database with strong emission lines, including [O iii]4363 detected at a signal-to-noise ratio higher than 5σ, as well as 164 galaxies and H ii regions from the literature with T e measurements. The O/H abundances were derived from a two-zone model for the temperature structure, assuming a relationship between high ionization and low ionization species. Results. We compare our (O/H) Te measurements of the SDSS sample with the abundances obtained by the MPA/JHU group who used multiple strong emission lines and Bayesian techniques (Tremonti et al. 2004). For roughly half of the sample the Bayesian abundances are overestimated ∼0.34 dex, possibly due to the treatment of nitrogen enrichment in the models they used. The R 23 and R 23 − P methods systematically overestimate the O/H abundance by a factor of ∼0.20 dex and ∼0.06 dex, respectively. The N2 index, rather than the O3N2 index, provides more consistent O/H abundances with the T e -method, but with some scatter. The relations of N2, O3N2, and S2 with log(O/H) are consistent with the photoionization model calculations of Kewley & Doptita (2002), but R 23 does not match well. We derive analytical calibrations for O/H from R 23 , N2, O3N2, and S2 indices on the basis of this large sample, including the excitation parameter P as an additional parameter in the N2 calibration. These empirical calibrations are free of the systematic problems inherent in abundance calibrations based on photoionization models. Conclusions. We conclude that the N2, O3N2, and S2 indices are useful indicators for calibrating metallicities of galaxies with 12 + log(O/H) < 8.5 and that the R 23 index works well for the metal-poor galaxies with 12+log(O/H) < 7.9. For the intermediate metallicity range (7.9 < 12 + log(O/H) < 8.4), the R 23 and R 23 − P methods are unreliable for characterizing the O/H abundances,