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(Modified) We measure the distribution of carbon in the intergalactic medium as a function of redshift z and overdensity delta. 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. A careful analysis of 19 high-quality quasar absorption spectra reveals that the carbon abundance is spatially highly inhomogeneous and is well-described by a lognormal distribution for fixed delta and z. Using data in the range log (delta) = -0. 5 - 1. 8 and z = 1. 8 - 4. 1, and a renormalized version of the Haardt & Madau (2001) model for the UV background radiation from galaxies and quasars, we measure a median metallicity of C/H = -3. 47 + 0. 08 (z-3) + 0. 65log (delta) -0. 5 and a lognormal scatter of sigma (C/H) = 0. 76 + 0. 02 (z-3) - 0. 23log (delta) -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 (OmegaC = 2e-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 delta < 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 collisional ionization) and of the evolution of the effective Lyman-alpha optical depth.
Schaye et al. (Mon,) studied this question.