Evolution of the integrated optical depth for the tanh functional form (with δz = 0.5, blue shaded area). The two envelopes mark the 68% and 95% confidence intervals. The red, black, and orange dashed lines are the models from Bouwens et al. (2015), Robertson et al. (2015), and Ishigaki et al. (2015), respectively, using high-redshift galaxy UV and IR fluxes and/or direct measurements.
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