The absorption length scale l_∗ regarding the stellar irradiation spectrum as a function of frequency ν or wavelength λ, respectively. From top to bottom, the different solid lines denote a density of , respectively. The two horizontal lines mark the highest and lowest resolution of the spherical grid. The right vertical axis shows the scale for the stellar spectra: from top to bottom, the dashed lines denote black body spectra of T_∗ = 100  000,30   000,10   000,and3000 K. The effect of potential dust evaporation is not included here, but would lead to a higher resolution of the numerical grid in terms of the irradiation spectrum.