Properties of high-redshift Lyman-alpha clouds. I - Statistical analysis of the Schneider-Schmidt-Gunn quasars
Techniques for statistical analysis of the Lyman-alpha forest in high-redshift quasars are developed, and applied to the low-resolution (25 A) spectra of 29 of the 33 quasars in the Schneider-Schmidt-Gunn sample. We extrapolate each quasar's continuum shortward of Lyman-alpha emission, then consider each spectral bin of each quasar to be an (approximately) independent measurement of the absorption due to the Lyman-alpha clouds. With several thousand such measurements thus available, we can obtain good determinations of some interesting properties of clouds in the redshift range 2.5-4.3 without actually resolving any single cloud. We find that the mean absorption increases with z approximately as a power law (1 + z) exp (gamma + 1) with gamma = 2.46 +/- 0.37. The mean ratio of Lyman-alpha to Lyman-beta absorption in the clouds is 0.476 +/- 0.054. We also detect, and obtain ratios, for Lyma-gamma, delta, and possibly epsilon.