2003ApJ...596..768S

We measure the distribution of carbon in the intergalactic medium as a function of redshift z and overdensity δ. Using a hydrodynamical simulation to link the H I absorption to the density and temperature of the absorbing gas, and a model for the UV background radiation, we convert ratios of C IV to H I pixel optical depths into carbon abundances. For the median metallicity this technique was described and tested in Paper I of this series. Here we generalize it to reconstruct the full probability distribution of the carbon abundance and apply it to 19 high-quality quasar absorption spectra. We find that the carbon abundance is spatially highly inhomogeneous and is well described by a lognormal distribution for fixed δ and z. Using data in the range logδ=-0.5-1.8 and z=1.8-4.1, and a renormalized version of the 2001 Haardt & Madau model for the UV background radiation from galaxies and quasars, we measure a median metallicity of [C/H]=-3.47^+0.07_–0.06+0.08^+0.09_–0.10(z-3)+0.65^+0.10_–0.14(logδ-0.5) and a lognormal scatter of σ([C/H])=0.76^+0.05_–0.08+0.02^+0.08_–0.12(z-3)-0.23^+0.09_–0.07(logδ-0.5). Thus, we find significant trends with overdensity but no evidence for evolution. These measurements imply that gas in this density range accounts for a cosmic carbon abundance of [C/H]=-2.80±0.13 (Ω_C~2x10^–7), with no evidence for evolution. The dominant source of systematic error is the spectral shape of the UV background, with harder spectra yielding higher carbon abundances. While the systematic errors due to uncertainties in the spectral hardness may exceed the quoted statistical errors for δ<10, we stress that UV backgrounds that differ significantly from our fiducial model give unphysical results. The measured lognormal scatter is strictly independent of the spectral shape, provided the background radiation is uniform. We also present measurements of the C III/C IV ratio (which rule out temperatures high enough for collisional ionization to be important for the observed C IV) and of the evolution of the effective Lyα optical depth.