Intergallactic photons free mean path

[Luther_Harkon]

Homework Statement

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

Homework 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?

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!

 

[mark726]

The reason why the mean free path cannot be computed using the Thomson cross section on protons is because the bremsstrahlung process involves the interaction between electrons and protons, not photons and protons. The Thomson cross section is a measure of the probability of interaction between photons and charged particles, but in this case, the charged particles are both electrons and protons. Therefore, the Thomson cross section cannot be used to accurately calculate the mean free path of photons in this scenario.

In addition, the Thomson cross section is only valid for low energy photons, while the photons produced in the bremsstrahlung process are high energy X-rays. This means that the Thomson cross section would not accurately represent the interactions between the photons and the charged particles in this process.

In summary, the Thomson cross section cannot be used to accurately calculate the mean free path of photons in this scenario because it does not take into account the interactions between electrons and protons, and it is only valid for low energy photons.