Spectral energy distribution of the ionizing radiation in comparison to the ionization potential of several species. The thick line represents the UV background at z ~ 2.0 according to the model of (Haardt & Madau 2001, HM01), which is adopted as ionizing radiation for test case A (see Sect. 4). The thin line indicates an example of a modified spectrum, where the main characteristics varied in this work are marked with arrows. They are measured in deviation from the HM01 spectrum in dex as indicated in the inset. These are (1) the height of the He ii Lyα re-emission peak at 3 Ryd Δ₁; (2) the flux level in the energy range 3 < E < 4   Ryd Δ₂; and (3) the depth of the He ii break at 4 Ryd Δ₃. The presented modified SED can parameterized with Δ₁ =  + 0.5, Δ₂ =  −0.7, and Δ₃ =  −0.5, and is adopted for test case B in Sect. 4.