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 present the largest-volume (425 Mpc/h=607 Mpc on a side) full radiative transfer simulation of cosmic reionization to date. We show that there is significant additional power in density fluctuations at very large scales. We systematically investig
ate the effects this additional power has on the progress, duration and features of reionization, as well as on selected reionization observables. We find that comoving simulation volume of ~100 Mpc/h per side is sufficient for deriving a convergent mean reionization history, but that the reionization patchiness is significantly underestimated. We use jackknife splitting to quantify the convergence of reionization properties with simulation volume for both mean-density and variable-density sub-regions. We find that sub-volumes of ~100 Mpc/h per side or larger yield convergent reionization histories, except for the earliest times, but smaller volumes of ~50 Mpc/h or less are not well converged at any redshift. Reionization history milestones show significant scatter between the sub-volumes, of Delta z=0.6-1 for ~50 Mpc/h volumes, decreasing to Delta z=0.3-0.5 for ~100 Mpc/h volumes, and $Delta z$~0.1 for ~200 Mpc/h volumes. If we only consider mean-density sub-regions the scatter decreases, but remains at Delta z~0.1-0.2 for the different size sub-volumes. Consequently, many potential reionization observables like 21-cm rms, 21-cm PDF skewness and kurtosis all show good convergence for volumes of ~200 Mpc/h, but retain considerable scatter for smaller volumes. In contrast, the three-dimensional 21-cm power spectra at large scales (k<0.25 h/Mpc) do not fully converge for any sub-volume size. These additional large-scale fluctuations significantly enhance the 21-cm fluctuations, which should improve the prospects of detection considerably, given the lower foregrounds and greater interferometer sensitivity at higher frequencies. (abridged)
In this paper we investigate how the halo mass function evolves with redshift, based on a suite of very large (with N_p = 3072^3 - 6000^3 particles) cosmological N-body simulations. Our halo catalogue data spans a redshift range of z = 0-30, allowing
us to probe the mass function from the dark ages to the present. We utilise both the Friends-of-Friends (FOF) and Spherical Overdensity (SO) halofinding methods to directly compare the mass function derived using these commonly used halo definitions. The mass function from SO haloes exhibits a clear evolution with redshift, especially during the recent era of dark energy dominance (z < 1). We provide a redshift-parameterised fit for the SO mass function valid for the entire redshift range to within ~20% as well as a scheme to calculate the mass function for haloes with arbitrary overdensities. The FOF mass function displays a weaker evolution with redshift. We provide a `universal fit for the FOF mass function, fitted to data across the entire redshift range simultaneously, and observe redshift evolution in our data versus this fit. The relative evolution of the mass functions derived via the two methods is compared and we find that the mass functions most closely match at z=0. The disparity at z=0 between the FOF and SO mass functions resides in their high mass tails where the collapsed fraction of mass in SO haloes is ~80% of that in FOF haloes. This difference grows with redshift so that, by z>20, the SO algorithm finds a ~50-80% lower collapsed fraction in high mass haloes than does the FOF algorithm, due in part to the significant over-linking effects known to affect the FOF method.
The prospect of detecting the first galaxies by observing their impact on the intergalactic medium as they reionized it during the first billion years leads us to ask whether such indirect observations are capable of diagnosing which types of galaxie
s were most responsible for reionization. We attempt to answer this by considering a set of large-scale radiative transfer simulations of reionization in sufficiently large volumes to make statistically meaningful predictions of observable signatures, while also directly resolving all atomically-cooling halos down to 10^8 M_solar. We focus here on predictions of the 21-cm background, to see if upcoming observations are capable of distinguishing a universe ionized primarily by high-mass halos from one in which both high-mass and low-mass halos are responsible, and to see how these results depend upon the uncertain source efficiencies. We find that 21-cm fluctuation power spectra observed by the first generation EoR/21-cm radio interferometer arrays should be able to distinguish the case of reionization by high-mass halos alone from that by both high- and low-mass halos, together. Some reionization scenarios yield very similar power spectra and rms evolution and thus can only be discriminated by their different mean reionization history and 21-cm PDF distributions. We find that the skewness of the 21-cm PDF distribution smoothed over LOFAR-like window shows a clear feature correlated with the rise of the rms due to patchiness. Measurements of the mean photoionization rates are sensitive to the average density of the regions being studied and therefore could be strongly skewed in certain cases. (abridged)
We present the first detailed structure formation and radiative transfer simulations of the reionization history of our cosmic neighbourhood. To this end, we follow the formation of the Local Group of galaxies and nearby clusters by means of constrai
ned simulations, which use the available observational constraints to construct a representation of those structures which reproduces their actual positions and properties at the present time. We find that the reionization history of the Local Group is strongly dependent on the assumed photon production efficiencies of the ionizing sources, which are still poorly constrained. If sources are relatively efficient, i.e. the process is photon-rich, the Local Group is primarily ionized externally by the nearby clusters. Alternatively, if the sources are inefficient, i.e. reionization is photon-poor the Local Group evolves largely isolated and reionizes itself. The mode of reionization, external vs. internal, has important implications for the evolution of our neighbourhood, in terms of e.g. its satellite galaxy populations and primordial stellar populations. This therefore provides an important avenue for understanding the young universe by detailed studies of our nearby structures.
We present some preliminary results from a series of extremely large, high-resolution N-body simulations of the formation of early nonlinear structures. We find that the high-z halo mass function is inconsistent with the Sheth-Tormen mass function, w
hich tends to over-estimate the abundance of rare halos. This discrepancy is in rough agreement with previous results based on smaller simulations. We also show that the number density of minihaloes is correlated with local matter density, albeit with a significant scatter that increases with redshift, as minihaloes become increasingly rare. The average correlation is in rough agreement with a simple analytical extended Press-Schechter model, but can differ by up to factor of 2 in some regimes.
The development of radiation hydrodynamical methods that are able to follow gas dynamics and radiative transfer self-consistently is key to the solution of many problems in numerical astrophysics. Such fluid flows are highly complex, rarely allowing
even for approximate analytical solutions against which numerical codes can be tested. An alternative validation procedure is to compare different methods against each other on common problems, in order to assess the robustness of the results and establish a range of validity for the methods. Previously, we presented such a comparison for a set of pure radiative transfer tests (i.e. for fixed, non-evolving density fields). This is the second paper of the Cosmological Radiative Transfer (RT) Comparison Project, in which we compare 9 independent RT codes directly coupled to gasdynamics on 3 relatively simple astrophysical hydrodynamics problems: (5) the expansion of an H II region in a uniform medium; (6) an ionization front (I-front) in a 1/r^2 density profile with a flat core, and (7), the photoevaporation of a uniform dense clump. Results show a broad agreement between the different methods and no big failures, indicating that the participating codes have reached a certain level of maturity and reliability. However, many details still do differ, and virtually every code has showed some shortcomings and has disagreed, in one respect or another, with the majority of the results. This underscores the fact that no method is universal and all require careful testing of the particular features which are most relevant to the specific problem at hand.
Observations of high-redshift Ly-alpha sources are a major tool for studying the high-redshift Universe. We discuss the effect of the reionizing intergalactic medium on the observability of Ly-alpha sources based on large simulations of early structu
re formation with radiative transfer. This takes into account self-consistently the reionization history, density, velocity and ionization structures and nonlinear source clustering. We find that all fields are highly anisotropic and as a consequence there are very large variations in opacity among the different lines-of-sight. The velocity effects, from both infall and source peculiar velocity are most important for the luminous sources, affecting the line profile and depressing the bright end of the luminosity function. The line profiles are generally asymmetric and the line centers of the luminous sources are always absorbed due to the high density of the local IGM. For both luminous and average sources the damping wing effects are of similar magnitude and remain significant until fairly late. The ionizing flux in the ionized patch surrounding a high density peak is generally strongly dominated, particularly at late times, by the cluster of faint sources, rather than the central massive galaxy. The IGM absorption does not change appreciably the correlation function of sources at high redshift. Our derived luminosity function assuming constant mass-to-light ratio provides an excellent match to the shape of the observed luminosity function at z=6.6 with faint-end slope of alpha=-1.5. The resulting mass-to-light ratio implies that the majority of sources responsible for reionization are too faint to be observed by the current surveys. (abridged)
The redshifted 21-cm line of distant neutral H atoms provides a probe of the cosmic ``dark ages and the epoch of reionization (``EOR) which ended them. The radio continuum produced by this redshifted line can be seen in absorption or emission against
the CMB at meterwaves, yielding information about the thermal and ionization history of the universe and the primordial density perturbation spectrum that led to galaxy and large-scale structure formation. Observing this 21-cm background is a great challenge. A new generation of low-frequency radio arrays is currently under development to search for this background. Accurate theoretical predictions of the spectrum and anisotropy of this background, necessary to guide and interpret future observations, are also quite challenging. It is necessary to model the inhomogeneous reionization of the intergalactic medium and determine the spin temperature of the 21-cm transition and its variations in time and space as it decouples from the temperature of the CMB. Here, we focus on just a few of the predictions for the 21-cm background from the EOR, based on our newest, large-scale simulations of patchy reionization. These simulations are the first with enough N-body particles (from 5 to 29 billion) and radiative transfer rays to resolve the formation of and trace the ionizing radiation from each of the millions of dwarf galaxies believed responsible for reionization, down to 10^8 M_solar, in a cubic volume large enough (90 and 163 comoving Mpc on a side) to make meaningful statistical predictions of the fluctuating 21-cm background. (abridged)
The Cosmic Dark Ages and the Epoch of Reionization constitute a crucial missing link in our understanding of the evolution of the intergalactic medium and the formation and evolution of galaxies. Due to the complex nature of this global process it is
best studied through large-scale numerical simulations. This presents considerable computational challenges. The dominant contributors of ionizing radiation were dwarf galaxies. These tiny galaxies must be resolved in very large cosmological volumes in order to derive their clustering properties and the corresponding observational signatures correctly, which makes this one of the most challenging problems of numerical cosmology. We have recently performed the largest and most detailed simulations of the formation of early cosmological large-scale structures and their radiative feedback leading to cosmic reionization. This was achieved by running extremely large (up to 29 billion-particle) N-body simulations of the formation of the Cosmic Web, with enough particles and sufficient force resolution to resolve all the galactic halos with total masses larger than 10^8 Solar masses in computational volumes of up to (163 Mpc)^3. These results were then post-processed by propagating the ionizing radiation from all sources by using fast and accurate ray-tracing radiative transfer method. Both of our codes are parallelized using a combination of MPI and OpenMP and to this date have been run efficiently on up to 2048 cores (N-body) and up to 10000 cores (radiative transfer) on the newly-deployed Sun Constellation Linux Cluster at the Texas Advanced Computing Center. In this paper we describe our codes, parallelization strategies, scaling and some preliminary scientific results. (abridged)
