Reionization simulations powered by GPUs I: the structure of the Ultraviolet radiation field

We present a set of cosmological simulations with radiative transfer in order to model the reionization history of the Universe. Galaxy formation and the associated star formation are followed self-consistently with gas and dark matter dynamics using the RAMSES code, while radiative transfer is performed as a post-processing step using a moment-based method with M1 closure relation in the ATON code. The latter has been ported to a multiple Graphics Processing Units (GPU) architecture using CUDA + MPI, resulting in an overall acceleration (x80) that allows us to tackle radiative transfer problems at resolution of 1024^3 + 2 levels of refinement for the hydro adaptive grid and 1024^3 for the RT cartesian grid. We observe a good convergence between our different resolution runs as long as the effects of finite resolution on the star formation history are properly taken into account. We also show that the neutral fraction depends on the total mass density, in a way close to the predictions of photoionization equilibrium, as long as the effect of self-shielding is included in the background radiation model. However we still fail at reproducing the z=6 constraints on the H neutral fraction and the intensity of the UV background. In order to account for unresolved density fluctuations, we added a simple clumping factor model. Using our most spatially resolved simulation (12.5 Mpc/h-1024^3) to calibrate our subgrid model, we have resimulated our largest box (100 Mpc/h 1024^3), successfully reproducing the observed level of H neutral fraction at z=6. We don't reproduce the photoionization rate inferred from the same observations. We argue that this discrepancy could be explained by the fact that the average radiation intensity and the average neutral fraction depends on different regions of the gas density distribution, so that one quantity cannot be simply deduced from the other.