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We calibrate here cosmological radiative transfer simulation with ATON/RAMSESwith a range of measurements of the Lyman alpha opacity from QSO absorptionspectra. We find the Lyman alpha opacity to be very sensitive to the exacttiming of hydrogen reionisation. Models reproducing the measured evolution ofthe mean photoionisation rate and average mean free path reach overlap at z ~ 7and predict an accelerated evolution of the Lyman alpha opacity at z > 6consistent with the rapidly evolving luminosity function of Lyman alphaemitters in this redshift range. Similar to "optically thin" simulations ourfull radiative transfer simulations fail, however, to reproduce thehigh-opacity tail of the Lyman alpha opacity PDF at z > 5. We argue that thisis due to spatial UV fluctuations in the post-overlap phase of reionisation onsubstantially larger scales than predicted by our source model, where theionising emissivity is dominated by large numbers of sub-L* galaxies. Wefurther argue that this suggests a significant contribution to the ionising UVbackground by much rarer bright sources at high redshift.

Calibrating cosmological radiative transfer simulations with Lyman alpha  forest data: Evidence for large spatial UV background fluctuations at z ~ 5.6  - 5.8 due to rare bright sources