Predominantly Low Metallicities Measured in a Stratified Sample of Lyman
  Limit Systems at z=3.7
  We measured metallicities for 33 z=3.4-4.2 absorption line systems drawn from
a sample of H I-selected-Lyman limit systems (LLSs) identified in Sloan Digital
Sky Survey (SDSS) quasar spectra and stratified based on metal line features.
We obtained higher-resolution spectra with the Keck Echellette Spectrograph and
Imager, selecting targets according to our stratification scheme in an effort
to fully sample the LLS population metallicity distribution. We established a
plausible range of H I column densities and measured column densities (or
limits) for ions of carbon, silicon, and aluminum, finding ionization-corrected
metallicities or upper limits. Interestingly, our ionization models were better
constrained with enhanced $\alpha$-to-aluminum abundances, with a median
abundance ratio of [$\alpha$/Al]=0.3. Measured metallicities were generally
low, ranging from [M/H]=-3 to -1.68, with even lower metallicities likely for
some systems with upper limits. Using survival statistics to incorporate
limits, we constructed the cumulative distribution function (CDF) for LLS
metallicities. Recent models of galaxy evolution propose that galaxies
replenish their gas from the low-metallicity intergalactic medium (IGM) via
high-density H I "flows" and eject enriched interstellar gas via outflows.
Thus, there has been some expectation that LLSs at the peak of cosmic star
formation ($z\approx3$) might have a bimodal metallicity distribution. We
modeled our CDF as a mix of two Gaussian distributions, one reflecting the
metallicity of the IGM and the other representative of the interstellar medium
of star-forming galaxies. This bimodal distribution yielded a poor fit. A
single Gaussian distribution better represented the sample with a low mean
metallicity of [M/H] $\approx -2.5$.
