Volume filling fraction of neutral hydrogen as a function of redshift. In the left panel, we carry out calculations assuming a constant global escape fraction (f_esc), as marked, given by the best fit to a selection of observational data (Jung et al. 2020; Gaikwad et al. 2023; Nakane et al. 2024; Umeda et al. 2024). Shaded areas represents the range of values obtained with the five runs using different random seeds. In the right panel, we show results using the escape fractions as in Chisholm et al. (2022), using our beta slopes as presented in Sect. 3.6. Solid, dashed, and dotted lines show results for the different halo masses (10⁹, 10^9.5 and 10^8.5 M_⊙) below which the baryonic content is completely suppressed due to the UVB. For clarity, shaded area are omitted in this panel, but would be similar as in the left one.