Metallicity of the intergalactic medium using pixel statistics. III. Silicon

We study the abundance of silicon in the intergalactic medium by analyzing the statistics of Si IV, C IV, and H I pixel optical depths in a sample of 19 high-quality quasar absorption spectra, which we compare with realistic spectra drawn from a hydrodynamical simulation. Simulations with a constant and uniform Si/C ratio, a C distribution as derived in Paper II of this series, and a UV background (UVB) model from Haardt & Madau reproduce the observed trends in the ratio of Si IV and C IV optical depths, tau(Si IV)/tau(C IV). The ratio tau(Si Iv)/tau(C IV) depends strongly on tau(C IV), but it is nearly independent of redshift for fixed tau(C IV) and is inconsistent with a sharp change in the hardness of the UVB at zapproximate to3. Scaling the simulated optical depth ratios gives a measurement of the global Si/C ratio (using our fiducial UVB, which includes both galaxy and quasar contributions) of [Si/C]=0.77+/-0.05, with a possible systematic error of similar to0.1 dex. The inferred [Si/C] depends on the shape of the UVB (harder backgrounds leading to higher [Si/C]), ranging from [Si/C]similar or equal to1.5 for a quasar-only UVB to [Si/C]similar to0.25 for a UVB including both galaxies and artificial softening; this provides the dominant uncertainty in the overall [Si/C]. Examination of the full tau(Si IV)/tau(C IV) distribution yields no evidence for inhomogeneity in [Si/C] and constrains the width of a lognormal probability distribution in [Si/C] to be much smaller than that of [C/H]; this implies a common origin for Si and C. Since the inferred [Si/C] depends on the UVB shape, this also suggests that inhomogeneities in the hardness of the UVB are small. There is no evidence for evolution in [Si/C]. Variation in the inferred [Si/C] with density depends on the UVB and rules out the quasar-only model unless [Si/C] increases sharply at low density. Comparisons with low-metallicity halo stars and nucleosynthetic yields suggest either that our fiducial UVB is too hard or that supermassive Population Ill stars might have to be included. The inferred [Si/C], if extrapolated to low density, corresponds to a contribution to the cosmic Si abundance of [Si/H]=-2.0, or Omega(Si)similar or equal to3.2x10(-7), a significant fraction of all Si production expected by zapproximate to3.