The direct oxygen abundances of metal-rich galaxies derived from electron temperature

Context. Direct measurement of oxygen abundance for metal-rich galaxies from electron temperature is difficult or impossible since temperature-sensitive auroral lines generally become too weak to be measured. Aims. We aim to derive the electron temperature (T-e) in the gas of metal-rich star-forming galaxies, which can be obtained from their ratios of auroral lines [O II]lambda lambda 7320, 7330 to nebular lines [OII]lambda 3727, in order to establish a more robust mass-metallicity relationship, and compare the Te-based (O/H) abundances with those from empirical strong-line calibrations, such as R-23 (=([OII]lambda 3727+[OIII]lambda lambda 4959, 5007)/H beta). Methods. We obtained 27 spectra by stacking the spectra of several hundred (even several thousand) star-forming galaxies selected from the SDSS-DR4 in each of the 27 stellar mass bins from log(M-*) similar to 8.0 to 10.6 ( in units of log( M-circle dot)). This stack method sufficiently improves the signal-to-noise ratio of the auroral lines [OII]lambda lambda 7320, 7330. Using a two-zone model for the temperature structure, we derive the electron temperature t(2) in the low ionization region from the [OII]lambda lambda 7320, 7330/[OII]lambda 3727 ratio, and then use a relation derived by fitting H II region models to estimate the electron temperature t(3) in the high ionization region from t(2). Then, the direct (O/H) abundances are obtained from t(2), t(3) and the related line-ratios. The emission lines have been carefully corrected for dust extinction using the Balmer line ratio after correcting for the underlying stellar absorption. Results. Combining our results with those from the literature with lower metallicities, we are able to provide a new relationship between the direct measurements of (O/H) and R23, which still shows an upper and a lower branch with the transition around 12 + log(O/H) similar to 8.0-8.2. It also shows that the empirical R-23 method will overestimate log(O/H) by 0.2 to 0.6 dex. The new metal-mass relationship of the galaxies with moderate metallicities is fitted by a linear fit (12 + log(O/H) = 6.223 + 0.231 x log( M*)) confirming that empirical methods significantly overestimate (O/H). We also derived their (N/O) abundance ratios on the basis of the Te method, which are consistent with the combination of the primary and secondary components of nitrogen. Conclusions. This study provides for the first time a method to calibrate direct O/H abundances (from T-e) for a large range of galaxies within a stellar mass range of similar to 5 x 10(8) M-circle dot to 4 x 10(10) M-circle dot.