  We determine the gas-phase oxygen abundance for a sample of 695 galaxies and
H II regions with reliable detections of [O III]4363, using the
temperature-sensitive Te method. Our aims are to estimate the validity of
empirical methods such as R23, R23-P, log([N II]/Halpha) (N2), log[([O
III]/Hbeta)/([N II]/Halpha)] (O3N2), and log([S II]/Halpha) (S2), and
especially to re-derive (or add) the calibrations of R23, N2, O3N2 and S2
indices for oxygen abundances on the basis of this large sample of galaxies
with Te-based abundances. We select 531 star-forming galaxies from the
SDSS-DR4, and 164 galaxies and H II regions from literature for such study.
Their (O/H) abundances obtained from Te are within 7.1<12+log(O/H)<8.5 mostly.
For roughly half of the SDSS samples, the Bayesian abundances obtained by the
MPA/JHU group are overestimated by ~0.34 dex compared with the Te-based (O/H)
measurements, possibly due to the treatment of nitrogen enrichment in the
models they used. R23 and R23-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 relatively consistent O/H abundances with
the Te-method, but with some scatter. The relations of N2, O3N2, S2 with
log(O/H) are consistent with the photoionization model calculations of Kewley &
Doptita (2002), but R23 does not match well. Then we derive analytical
calibrations for O/H from R23, N2, O3N2 and S2 indices on the basis of this
large sample of galaxies, especially including the excitation parameter P as an
additional parameter in the N2 calibration. These can be used as calibration
references in the future studies about metallicities of galaxies.
