Absorption spectrum of the Z = 3.78 QSO 2000-330. II - The redshift and equivalent width distributions of primordial hydrogen clouds

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Abstract

We present an analysis of the distribution in redshift z and equivalent width W of the number density of Lyman-α lines detected in the spectra of high-redshift QSOs. We use a sample which is reasonably homogeneous as regards spectral resolution and signal-to-noise ratio and covers a wider range of z (1.50-3.78) than previous studies. This is achieved principally by including results from the z = 3.78 QSO 2000-330. We extend the lower end of the range by including data down to 3040 Å from the bright z = 1.7 BL Lac object 0215 + 015. Unlike previous studies, we exclude from our Lyα sample those Lyα lines which occur in known heavy-element (metal-line) systems. However, we also present results with these lines included and thereby demonstrate that this has a marked effect on the distribution of the number density of lines with redshift. Our analysis, which uses the method of maximum likelihood, has led to a reappraisal of much of the previous work. Our conclusions are: (1) There is incontrovertible evidence for evolution in the number density of Lyα lines of the form dN/dz ∝ (1 + z)γ, with γ = 2.17 ± 0.36. (2) However, within individual QSOs we find a countervailing trend in dN/dz which previous studies have failed to recognize. (3) We attribute this trend to the influence of luminous QSOs on their environment over distances of order 4 Mpc. (4) We confirm previous results that the distribution in equivalent width W is well represented by an exponential increase in the number density of lines with decreasing W for W > 0.2 Å. However, we show that the line density rises even more steeply for W <0.2 Å. (5) From our results for the distributions in number density and equivalent width we deduce strong evolution with epoch in the H I column density of individual clouds, as indeed suggested by current theoretical models.

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