Evolution of the volume-averaged ionization parameter log ⟨U⟩ as a function log U_in and log U_out in the model grid. We show only a subsample corresponding to models with no X-ray source and stopping at the ionization front (cut = 1). This figure complements the discussion on the possible caveats induced by the use of U_in as a primary parameter in our grid (see Sect. 3.2.3). We note that U_in only sets an upper limit on the actual volume averaged log ⟨U⟩. Variations in terms of metallicity and initial density n₀ yield different geometries, which cover a large range of volume averaged log ⟨U⟩ for the same U_in.