Our model doesn’t match the \(z > 5\) HI Effective Optical Depth, to fix it I will try to modify the HI photoionization rates to change the amount of neutral Hydrogen.

Fraction of neutral Hydrogen from the Modified P19 model and fraction rescaled to match the Effective Optical Depth from Bosman 2021 (SAZERAC).

The goal now is to modify the HI photoionization rate to match the rescaled HI fraction.

Rescale the rates separately:

First I try separating Gamma for \(z < 5.8\) and \(z > 5.8\) then I allow to rescale by different amounts and I can shift the \(z > 5.8\) part in Redshift.

The results:

Analytical Fit to Gamma:

Reconstruct \(\Gamma\) from the HI fraction

Take the evolution of HI fraction and use that to compute \(\Gamma\)

The solution is off by \(\sim 10^4\) !!!!

I’m not taking into account recombination, recombination is almost as efficient as photoionization:

Actually the gas is probably in ionization Equilibrium. By equating:

Collisional + Photo Ionization = Recombinatio I can compute the photionization rate required to have the rescaled HI fractions.

Now I run a \(1024^3\) simulation with the new photoionization rate:

Photoionization Rate:

Temperature Evolution

How to construct modified Photoheating Rates