  We aim to derive the electron temperature Te in the gas of metal-rich
star-forming galaxies, which can be obtained from their ratios of auroral lines
[O II]7320,7330 to nebular lines [O II]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 R23. 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*) ~8.0 to 10.6 (logMsun). This "stack" method sufficiently
improves the signal-to-noise ratio of the auroral lines [O II]7320,7330, which
allow us to reliably obtain the electron temperature t2 in the low ionization
region from the ratio of [O II]7320,7330 to [O II]3727, then t3 in the high
ionization region from t2 by using a relation, and then the direct (O/H)
abundances from Te. The results show that the empirical R23 method will
overestimate the log(O/H) by 0.2 to 0.6 dex for these moderate metal-rich
galaxies. 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*logM*)
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. For actual use, we re-derive the relations of 12+log(O/H)(Bay) vs.
logM* and 12+log(O/H)(Bay) vs. logR23 from the SDSS-DR4 data, which are a bit
different from those derived from DR2.

Astrophysics