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Homework Help: Intergallactic photons free mean path

  1. Mar 29, 2010 #1
    1. The problem statement, all variables and given/known data

    Intergallactic ionized gas produces X ray photons via the bremsstrahlung process
    [tex]
    e^-\ p\rightarrow e^-\ p\ \gamma
    [/tex]
    In contrast to photons produced in a star (see previous exercises) these X ray photons escape from the galaxy cluster. Indeed, the largest galaxy clusters contain a few thousand galaxies with a total mass ∼ [tex]10^{14} M_\odot[/tex] and a radius of several Mpc.

    Note. take [tex]n_{e^-}=n_p\sim\Omega_B\rho_c/m_p[/tex]

    2. Relevant equations

    Show that the mean free path of a photon is [tex]\lambda_\gamma=1/(n\sigma)\gg1Mpc[/tex], where [tex]\sigma[/tex] can be approximated by the Thomson cross-section of photons on electrons. Why not on photons?


    3. The attempt at a solution

    I had no problem in showing that the free mean path of photons , when given the conditions shown here, is much greater than 1 Mpc. But I am quite confused on why can't be the free mean path computed by the Thomson cross section on protons. Any clue on that?

    Thanks!
     
    Last edited: Mar 29, 2010
  2. jcsd
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