The Low-Column Density Lyα Forest

We develop an analytical method based on the lognormal approximation tocompute the column density distribution of the Lyman-alpha forest in the lowcolumn density limit. We compute the column density distributions for sixdifferent cosmological models and found that the standard, COBE-normalized CDMmodel cannot fit the observations of the Lyman-alpha forest at z=3. Theamplitude of the fluctuations in that model has to be lowered by a factor ofalmost 3 to match observations. However, the currently viable cosmologicalmodels like the lightly tilted COBE-normalized CDM+Lambda model, the CHDM modelwith 20% neutrinos, and the low-amplitude Standard CDM model are all inagreement with observations, to within the accuracy of our approximation, forthe value of the cosmological baryon density at or higher than the old StandardBing Bang Nucleosynthesis value of 0.0125 for the currently favored value ofthe ionizing radiation intensity. With the low value for the baryon densityinferred by Hogan & Rugers (1996), the models can only marginally matchobservations.Comment: three postscript figures included, submitted to ApJ