Properties of high-redshift Lyman-alpha clouds. I. Statistical analysis of the Schneider-Schmidt-Gunn quasars

Techniques for statistical analysis of the Lyman-α forest in high-redshift quasars are developed, and applied to the low-resolution (25 Å) spectra of 29 of the 33 quasars in the Schneider-Schmidt-Gunn (SSG) sample. We extrapolate each quasar's continuum shortward of Lyman-α emission, then consider each spectral bin of each quasar to be an (approximately) independent measurement of the absorption due to the Lyman-α clouds. With several thousand such measurements thus available, we can obtain good determinations of some interesting properties of clouds in the redshift range 2.5 < z < 4.3 without actually resolving any single cloud. We find that the mean absorption increases with z approximately as a power law (1 + z)^γ+1 with γ = 2.46 ± 0.37. The mean ratio of Lyman-α to Lyman-β absorption in the clouds is 0.476 ± 0.054. We also detect, and obtain ratios, for Lyman-γ, δ, and possibly ∈. We are also able to quantify the fluctuations of the absorption around its mean, and find that these are comparable to, or perhaps slightly larger than, that expected from an uncorrelated distribution of clouds. The techniques in this paper, which include the use of bootstrap resampling of the quasar sample to obtain estimated errors and error covariances, and a mathematical treatment of absorption from a (possibly nonuniform) stochastic distribution of lines, should be applicable to future, more extensive, data sets.