How Do You Calculate Hydrogen Ionization Using a Metagalactic Radiation Field?

[astrofunk21]

Hey guys, so I'm working on a project and was given some slightly vague instructions. I am supposed to be using a metagalactic ionizing radiation field value (Gamma) to find the ionization of Hydrogen as a function of density.

I'm coming to you guys with a vague description because I'm hoping someone will have a sense of what is being looked for. I'm confused if I'm trying to find a rate of ionization, or a shear number of ionized particles?

What I have that may be of use is the following density formula:

n=Γ_HI/α (1 - n_HI/n)^-2 n_HI/n

Once again, sorry if this is all vague. Feel free to ask questions and I'll try to answer!

 

[astrofunk21]

To add onto this, the metagalactic ionizing radiation field should be taken as sort of an O-type star in the case of a Stromgren Sphere.

Also I'm pretty sure the ionization of H means the mass fraction of ionized gas...right?

 

[Ken G]

It looks like you are supposed to assume there is a fixed radiative ionization rate, per neutral H, which will be proportional to the radiation field, which is proportional to Gamma. You assume the rate of radiative recombination equals the rate of radiative ionization, and use that to get the ionized fraction. If you do all this per volume, it means you consider a cubic meter or some such thing, and equate the neutral hydrogens times Gamma to the ionized hydrogens times the electron density (since the radiative recombination rate is proportional to electron density). When you realize that the electrons come from the ionized hydrogens, you realize that both of those last two things are proportional to 1-nHI/n, so that's where those terms come from in that equation. Solve for nHI, the neutral fraction, as a function of n, the density of hydrogen nuclei.