Abstract:

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 darkmatter 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 Graphical Processing Units (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 hydrodynamics adaptive grid and 10243 for the radiative transfer
Cartesian grid. We reach typical acceleration factor close to 100× when compared to the CPU version,
allowing us to perform 1/4 million time steps in less than 3000 GPU hours.

We observe good convergence properties between our different resolution runs for various volumeand
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 at 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 Mpc/h with
10243 particles) to calibrate our subgrid model, we have resimulated our largest box (100 Mpc/h with
10243 particles) with the modified chemistry, successfully reproducing the observed level of neutral
Hydrogen in the spectra of high redshift quasars. We however didn’t reproduce (by a factor of 2)
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 depends on different regions of the gas density distribution, so that one quantity cannot be
simply deduced from the other.