Comparison of the H₂ fraction $\left(f_{{\text{H}}_2}=2\langle n_{{\text{H}}_2}\rangle /\langle n_{\text{H}}\rangle \right)$ as a function of 〈n_H〉 using different approaches. Left: the equilibrium $f_{{\text{H}}_2}$ from postprocessing the T15 galaxy with HYACINTH (black, green, and blue) compared with the $f_{{\text{H}}_2}$ from the simulation (red) and two analytical estimates − KMT-EQ (blue) and KMT-UV (turquoise). The lines show the median value in a given 〈n_H〉 bin while the shaded area encloses the 16th to 84th percentiles. The solid black line denotes the median $f_{{\text{H}}_2}$ when using a uniform CRIR of ζ_H = 3 × 10⁻¹⁷ s⁻¹ H⁻¹ for HYACINTH. We also show the median $f_{{\text{H}}_2}$ obtained from post-processing when using the CRIR from Sect. 2.2.5 (i.e. ζ_H ∝ χ²) with (dashed green line) and without (dotted green line) the upper limit on the CRIR as well as (solid blue line) the ζ_H − χ relation from Hu et al. (2021, i.e., ζ_H ∝ χ, normalised to ζ_H,MW = 10⁻¹⁶ s⁻¹ H⁻¹). Middle: the $f_{{\text{H}}_2}$ from the T15 simulation colour-coded by the strength of the UV field in the LW bands in Habing units, G₀ (from the simulation), in each grid cell. The red line is the same as in the left panel. Right: the post-processed $f_{{\text{H}}_2}$ (using a uniform ζ_H) for each grid cell within the simulated galaxy colour-coded by G₀. The black line is the same as in the left panel.