The high redshift Lyman-alpha forest, in particular the Gunn-Peterson trough, is the most unambiguous signature of the neutral to ionized transition of the intergalactic medium (IGM) taking place during the Epoch of Reionization (EoR). Recent studies, e.g. Kulkarni et al. (2019a) and Keating et al. (2019), showed that reproducing the observed Lyman-alpha opacities after overlap required a non-monotonous evolution of cosmic emissivity: rising, peaking at z=6, and then decreasing onwards to z=4. Such an evolution is puzzling considering galaxy build-up and the cosmic star formation rate are still continously on the rise at these epochs. Here, we use new RAMSES-CUDATON simulations to show that such a peaked evolution may occur naturally in a fully coupled radiation-hydrodynamical framework. In our fiducial run, cosmic emissivity at z>6 is dominated by a low mass (M$_{rm DM}<2.10^9$ M$_{odot}$), high escape fraction halo population, driving reionization, up to overlap. Approaching z=6, this population is radiatively suppressed due to the rising ionizing UV background, and its emissivity drops. In the meantime, the high mass halo population builds up and its emissivity rises, but not fast enough to compensate the dimming of the low mass haloes, because of low escape fractions. The combined ionizing emissivity of these two populations therefore naturally results in a rise and fall of the cosmic emissivity, from z=12 to z=4, with a peak at z=6. An alternative run, which features higher escape fractions for the high mass haloes and later suppression at low mass, leads to overshooting the ionizing rate, over-ionizing the IGM and therefore too low Lyman-alpha opacities.
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