In this chapter we provide an overview of the current status of the simulations and modelling of the Cosmic Dawn and Epoch of Reionization. We discuss the modelling requirements as dictated by the characteristic scales of the problem and the SKA inst
rumental properties and the planned survey parameters. Current simulations include most of the relevant physical processes. They can follow the full nonlinear dynamics and are now reaching the required scale and dynamic range, although small-scale physics still needs to be included at sub-grid level. However, despite a significant progress in developing novel numerical methods for efficient utilization of current hardware they remain quite computationally expensive. In response, a number of alternative approaches, particularly semi-analytical/semi-numerical methods, have been developed. While necessarily more approximate, if appropriately constructed and calibrated on simulations they could be used to quickly explore the vast parameter space available. Further work is still required on including some physical processes in both simulations and semi-analytical modelling. This hybrid approach of fast, approximate modelling calibrated on numerical simulations can then be used to construct large libraries of reionization models for reliable interpretation of the observational data.
We measure several properties of the reionization process and the corresponding low-frequency 21-cm signal associated with the neutral hydrogen distribution, using a large volume, high resolution simulation of cosmic reionization. The brightness temp
erature of the 21-cm signal is derived by post-processing this numerical simulation with a semi-analytical prescription. Our study extends to high redshifts (z ~ 25) where, in addition to collisional coupling, our post-processed simulations take into account the inhomogeneities in the heating of the neutral gas by X-rays and the effect of an inhomogeneous Lya radiation field. Unlike the well-studied case where spin temperature is assumed to be significantly greater than the temperature of the cosmic microwave background due to uniform heating of the gas by X-rays, spatial fluctuations in both the Lya radiation field and X-ray intensity impact predictions related to the brightness temperature at z > 10, during the early stages of reionization and gas heating. The statistics of the 21-cm signal from our simulation are then compared to existing analytical models in the literature and we find that these analytical models provide a reasonably accurate description of the 21-cm power spectrum at z < 10. Such an agreement is useful since analytical models are better suited to quickly explore the full astrophysical and cosmological parameter space relevant for future 21-cm surveys. We find, nevertheless, non-negligible differences that can be attributed to differences in the inhomogeneous X-ray heating and Lya coupling at z > 10 and, with upcoming interferometric data, these differences in return can provide a way to better understand the astrophysical processes during reionization.
