Nicole Drakos
Research Blog
Welcome to my Research Blog.
This is mostly meant to document what I am working on for myself, and to communicate with my colleagues. It is likely filled with errors!
This project is maintained by ndrakos
IGM Neutral Fraction
In this post, I calculate the IGM neutral fraction.
The Ionized Fraction
As outlined in the previous post the volume-filling fraction of ionized gas is:
\[\frac{ dQ_{\rm HII} }{ dt} = \frac{ \dot{n}_{\rm ion} } {\langle n_H \rangle} - \frac{Q}{\bar{t}_{\rm rec}}\]where:
- \(\dot{n}_{\rm ion}\) can be calculated directly from the catalog.
- \(\langle n_H \rangle =1.9\times 10^{-7} cm^{-3}\).
- \(t_{\rm rec} = [ C_{\rm HII} \alpha_B (1 + (1-X)/4X) \langle n_H \rangle (1+z)^3 ]^{-1}\).
- \(X=0.75\).
- \(C_{\rm HII} = 3\) (but I will later replace this with a time dependent value).
- \(\alpha_B = 2.6 \times 10^{-13} (T/10^4 {\rm K})^{0.76} {\rm cm^3 s^{-1}}\).
- \(T=10^4\) K (I will vary this later to see the effects).
For \(\dot{n}_{\rm ion}\) I will use all the galaxies in the DREaM catalog. Later on, I can decide if I should make a cut in luminosity. I will interpolate this to get \(\dot{n}_{\rm ion}\) as a function of \(z\)
Calculation
First, I reframed this in terms of redshift:
\[\frac{ dQ_{\rm HII} }{ dt} = \frac{ dQ_{\rm HII} }{ dz}\frac{ dz}{ dt} = -(1+z)H(z) \frac{ dQ_{\rm HII} }{ dz}\]where I can just calculate \(H(z)\) from some package; I used colossus.
I need a boundary condition. In this case, I will use \(Q_{\rm HII}=0\) at \(z=12\)
I integrating the equation to \(z=4\) using odeint and set a maximum \(dQ_{\rm HII}\) value of 1.
The neutral fraction is simply \(1-Q_{\rm HII}\).
Results
Here are my results, compared to the data compiled by Naidu2020. It looks great! There are a few modelling choices I want to explore later, but this is enough to get started.
