Thomson scattering optical depth of the microwave background versus limiting UV magnitude. The colours represent our three different galaxy UV LF parametrizations: FIT (blue), MIN (cyan) and MAX (magenta). The solid line corresponds to the FID (ζ_ion= 1) L_ν model and the shaded regions are bounded by the SOFT (ζ_ion= 0.5) and HARD (ζ_ion= 2) models. The WMAP-7 τ_e= 0.088 ± 0.015 (Komatsu et al. 2011) is indicated with a grey band. The top panel is for f_esc= 20 per cent, the bottom left for f_esc= 5 per cent and the bottom right for f_esc= 50 per cent. M_lim, ζ_ion and f_esc are assumed constant in these calculations, and we used a clumping factor of ⁠.