Derive the Gunn-Peterson optical depth expression....

  • #1

Homework Statement

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?

Homework Equations

(1). Tau=nσ

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!

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