# Homework Help: Intergallactic photons free mean path

1. Mar 29, 2010

### Luther_Harkon

1. The problem statement, all variables and given/known data

Intergallactic ionized gas produces X ray photons via the bremsstrahlung process
$$e^-\ p\rightarrow e^-\ p\ \gamma$$
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 ∼ $$10^{14} M_\odot$$ and a radius of several Mpc.

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

2. Relevant equations

Show that the mean free path of a photon is $$\lambda_\gamma=1/(n\sigma)\gg1Mpc$$, where $$\sigma$$ 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