Thomson Scattering Hot Ionised Hydrogen Region

[leonmate]

Homework Statement

Consider photons crossing a large hot ionised hydrogen region with constant electron density n_e = 5*10⁵ m^-3. Assuming that the photons and the electrons interact via Thomson scattering (with Thomson scattering cross section, σ_T = 6.65*10^-29 m², what is the thickness Δx that this region should have in order to be 'optically thick'?

Homework Equations

Sifting through my textbooks I've found a few useful equations:

Optical depth for the medium for Thomson scattering:
τ = ∫ σ_T * n_e dx

Mean free path:

l = (σ_T * n_e)^-1

The Attempt at a Solution

So, I've thought about this problem a couple of ways. The main issue is I can't find a definition for 'optically thick'. At what point does the gas region become optically thick. Is it when it is larger than the mean free path? I've also got a few notes about self-absorption processes in optically thick mediums, I don't know how to make that relevant either.

Another note, I've also read:

'For a completely ionized hydrogen gas, ne is equal to the number density of protons that carry most of the mass'
from my textbook: The Physics of Astrophysical Processes, Bradt.

So, if this is the case then I need to swap out my Thomson cross section as this is related to the mass of the particles and it would now be ~10^-35 m².

This increases the mean free path significantly also, from 3*10²² up by a factor of 10⁶

Any hints would be greatly appreciated!

 

[Bystander]

'optically thick'?

An unusual term. Could it be in reference to "extinction coefficient?" Not a hint --- more a wild guess at the meaning of "optically thick."

 

[leonmate]

Thanks for the reply, I've found what my lecturer was after.

He's defined optically thick as the gas thickness being greater than the mean free length path. It was hidden away in some exercises and solutions, not in the notes for some reason though.

Also, any thoughts on the fact I should be considering the protons over electrons because of their much larger mass? I don't think it's what he's looking for in the question but I'm curious if it's a valid point.

 

[Bystander]

thoughts on ... protons over electrons

The "stellar" gang should be in fairly frequently since it's Sunday --- better source than I --- stick around and they'll get to you.

Edit: @mfb