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Derive the Gunn-Peterson optical depth expression...

  1. May 18, 2015 #1
    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!
  2. jcsd
  3. May 24, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
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