We present a set of cosmological simulations with radiative transfer in order to model the reionization history of the universe from z = 18 down to z = 6. 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 the M1 closure relation in the ATON code. The latter has been ported to a multiple Graphics Processing Unit (GPU) architecture using the CUDA language together with the MPI library, resulting in an overall acceleration that allows us to tackle radiative transfer problems at a significantly higher resolution than previously reported: 10243 + 2 levels of refinement for the hydrodynamic adaptive grid and 10243 for the radiative transfer Cartesian grid. We reach a typical acceleration factor close to 100x when compared to the CPU version, allowing us to perform 1/4 million time steps in less than 3000 GPU hr. We observe good convergence properties between our different resolution runs for various volume-and mass-averaged quantities such as neutral fraction, UV background, and Thomson optical depth, 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 are included in the background radiation model. Although our simulation suite has reached unprecedented mass and spatial resolution, we still fail in reproducing the z ∼ 6 constraints on the neutral fraction of hydrogen and the intensity of the UV background. In order to account for unresolved density fluctuations, we have modified our chemistry solver with a simple clumping factor model. Using our most spatially resolved simulation (12.5 Mpch-1 with 10243 particles) to calibrate our subgrid model, we have resimulated our largest box (100 Mpch-1 with 10243 particles) with the modified chemistry, successfully reproducing the observed level of neutral hydrogen in the spectra of high-redshift quasars. We however did not reproduce the average photoionization rate inferred from the same observations. We argue that this discrepancy could be partly explained by the fact that the average radiation intensity and the average neutral fraction depend on different regions of the gas density distribution, so that one quantity cannot be simply deduced from the other.
All Science Journal Classification (ASJC) codes
- Astronomy and Astrophysics
- Space and Planetary Science
- Dark ages, reionization, first stars
- Methods: numerical
- Radiative transfer online-only material: color figures