Correlation between the Mean Matter Density and the Width of the Saturated Lyα Absorption

We report a scaling of the mean matter density with the width of the saturated Lyα absorptions. This property is established using the “pseudo-hydro” technique (Croft et al. 1998). It provides a constraint for the inversion of the Lyα forest, which encounters difficulty in the saturated region. With a Gaussian density profile and the scaling relation, a simple inversion of the simulated Lyα forests shows that the onedimensional mass power spectrum is well recovered on scales above 2 hMpc, or roughly k . 0.03 kms, at z = 3. The recovery underestimates the power on small scales, but improvement is possible with a more sophisticated algorithm.