Probing the low-redshift star formation rate as a function of
  metallicity through the local environments of type II supernovae
  Type II SNe can trace star formation to probe its global metallicity
distribution at low-redshift. We present oxygen and iron abundance
distributions of SN II progenitor regions that avoid many previous sources of
bias. Because Fe (rather than O) abundance drives the late stage evolution of
the massive stars that are the progenitors of CCSNe, and because Fe enrichment
lags O enrichment, we find a general conversion from O abundance to Fe
abundance. The distributions we present here are the best yet standard of
comparison for evaluating how rare classes of SNe depend on progenitor
metallicity. We measure the gas-phase O abundance of a representative subsample
of the hosts of SNe II from the first-year PTF SN search, using a combination
of SDSS spectra near the SN location (9) and new long slit spectroscopy (25).
The median metallicity of these 34 hosts is 12+log(O/H) = 8.65, with a median
error of 0.09. The median host galaxy stellar mass from fits to SDSS photometry
is 10^9.9 solar masses. They do not show a systematic offset in metallicity or
mass from a redshift-matched sample of the MPA/JHU value-added catalog. In
contrast to previous SN host metallicity studies, this sample is drawn from a
single, areal survey. SNe in the lowest-mass galaxies are not systematically
excluded. The metallicity distribution we find is statistically
indistinguishable from the metallicity distribution of SN II hosts found by
targeted surveys and by samples from multiple surveys with different selection
functions. Using the relationship between Fe and O abundances found for Milky
Way disk, bulge, and halo stars, we translate our O abundance distribution of
SN II environments into Fe abundance estimates. We find that though this sample
spans only 0.65 dex in O abundance, the gap between the Fe and O abundance is
50% wider at the low-metallicity end of our sample than at the high-metallicity
end. (abridged)
