1. The problem statement, all variables and given/known data Derive an expression for the Gunn-Peterson optical depth Tau(λ) for Lyman limit absorption from smoothly distributed intergalactic neutral Hydrogen of comoving density n0 toward a QSO of emission redshift zem. Take the absorption cross section for Lyman-limit absorption to be: σ=5x10-18(λ/λLL)3 cm2 at wavelengths λ < λLL (and zero otherwise), where, λLL = 912 Angstroms, is the wavelength of the Lyman limit. Assume that the opitcal depth satisfies Tau<<1 so that e-Tau can be approximated as e-Tau=1-Tau, and assume an Einstein-de Sitter cosmological model. What limit on n0 could be set from the observation Tau<0.1 at redshift z = 3? 2. Relevant equations (1). Tau=nσ 3. The attempt at a solution What I am trying to do is to apply equation (1) and modifying the equation given in the problem to account for redshift. That is, σ=5x10-18(λ(z+1)/λLL)3 cm2. To end here seems a little too simple: Tau = n0 * 5x10-18(λ(z+1)/λLL)3 cm2 What else should I be looking for? Thanks in advance!