PROPERTIES OF HIGH-REDSHIFT LYMAN-ALPHA CLOUDS .2. STATISTICAL PROPERTIES OF THE CLOUDS

Curve-of-growth analysis, applied to the Lyman series absorption ratios deduced in our previous paper, yields a measurement of the logarithmic slope of distribution of Lyman-alpha clouds in column density N. The observed exponential distribution of the clouds' equivalent widths W is then shown to require a broad distribution of velocity parameters b, extending up to 80 km s-1. We show how the exponential itself emerges in a natural way. An absolute normalization for the differential distribution of cloud numbers in z, N, and b is obtained. By detailed analysis of absorption fluctuations along the line of sight (including correlations among neighboring spectral frequency bins) we are able to put upper limits on the cloud-cloud correlation function xi on several megaparsec length scales. We show that observed b values, if thermal, are incompatible, in several different ways, with the hypothesis of equilibrium heating and ionization by a background UV flux. Either a significant component of b is due to bulk motion (which we argue against on several grounds), or else the clouds are out of equilibrium, and hotter than is implied by their ionization state, a situation which could be indicative of recent adiabatic collapse.