We combine high resolution hydrodynamical simulations with an intermediate resolution, dark matter only simulation and an analytical model for the growth of ionized regions to estimate the large scale distribution and redshift evolution of the visibility of Lyman-alpha emission in 6<=z<=8 galaxies. The inhomogeneous distribution of neutral hydrogen during the reionization process results in significant fluctuations in the Lyman-alpha transmissivity on large scales. The transmissivity depends not only on the ionized fraction of the intergalactic medium by volume and the amplitude of the local ionizing background, but is also rather sensitive to the evolution of the relative velocity shift of the Lyman-alpha emission line due to resonant scattering. We reproduce a decline in the space density of Lyman-alpha emitting galaxies as rapid as observed with a rather rapidly evolving neutral fraction between z=6-8, and a typical Lyman-alpha line velocity offset of 100 km/s redward of systemic at z=6 which decreases toward higher redshift. The new (02/2015) Planck results indicate such a recent end to reionization is no longer disfavoured by constraints from the cosmic microwave background.
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