The Lyα Forest atz∼ 4: Keck HIRES Observations of Q0000−26

We derive H I column density and Doppler width distributions for a sample of Lyα clouds with 3.4 14.5 may be present. The Doppler width distribution of the clouds is consistent with a Gaussian function with a mean of 23 km s–1 and a dispersion of 8 km s–1 but with a cutoff at 15 km s–1, i.e., no clouds with b < 15 km s–1 are required to describe the data. While the H I column density distribution found here is consistent with that derived from similar quality data at lower redshifts, both the mean Doppler width and the cutoff value are smaller than those found at lower redshift. There is a hint for clustering in the clouds line-of-sight distribution in the velocity interval 100 < Δv < 160 km s–1, but the evidence is only marginal. Analyses of the proximity effect indicate a value of JLLν ~ 2 × 10–22 ergs s–1 cm–2 Hz–1 sr–1 for the mean intensity of the megagalactic UV ionizing background at z ~ 4.1, which is consistent with that expected from high-redshift quasars.