Reionization temperature/pressure modelling

[cmbant]

Following https://github.com/cmbant/CAMB/issues/171, currently the baryon temperature and pressure ignore reionization completely. Some simple model to fit expected changes over reionization to get leading-order correction approximately correct?

[cmbant]

[cmbant]

Augment Code: I implemented a simple reionization heating model in PR #183 that addresses this issue.

Model Description

The implementation adds a smooth heating model that:

1. Temperature evolution: Smoothly heats the baryon temperature T_b from the recombination value to ~10^4 K following the shape of the reionization ionization fraction x_e

2. Sound speed transition: Maps the baryon sound speed cs^2 smoothly from the original pre-reionization formula to an ideal gas form cs^2 = γ k_B T / (μ m_p) with γ=5/3

3. Preserves original behavior: Before reionization, the code uses the exact original cs^2 calculation. The transition is controlled by a weight yheat that follows the reionization progression:

   yheat = (x_e - x_e_recomb) / (x_e_final - x_e_recomb)
   

4. Smooth interpolation: The final quantities are:

   T_gas = T_recomb + yheat * (T_reion - T_recomb)
   cs^2 = (1 - yheat) * cs^2_orig + yheat * cs^2_ideal
   

Control Parameter

The model is controlled by a new boolean parameter include_heating in the reionization model (default True). Setting it to False recovers the original behavior.

Effects on Matter Power Spectrum

The plots above show the fractional effect on the matter power spectrum. The heating model produces the expected suppression on small scales (k > 1 h/Mpc) due to increased baryon pressure during reionization, with effects reaching ~few percent level at k ~ 100-1000 h/Mpc.

The model provides a leading-order correction that captures the main physical effect while maintaining computational efficiency and backward compatibility.