We present the first large-scale radiative transfer simulations of cosmic reionization, in a simulation volume of (100 h −1 Mpc) 3 . This is more than a two orders of magnitude improvement over previous simulations. We achieve this by combining the results from extremely large, cosmological, N-body simulations with a new, fast and efficient code for 3D radiative transfer, C 2 -RAY, which we have recently developed. These simulations allow us to do the first numerical studies of the large-scale structure of reionization which at the same time, and crucially, properly take account of the dwarf galaxy ionizing sources which are primarily responsible for reionization. In our realization, reionization starts around z ∼ 21, and final overlap occurs by z ∼ 11. The resulting electron-scattering optical depth is in good agreement with the first-year Wilkinson Microwave Anisotropy Probe (WMAP) polarization data. We show that reionization clearly proceeded in an inside-out fashion, with the high-density regions being ionized earlier, on average, than the voids. Ionization histories of smaller-size (5-10 comoving Mpc) subregions exabit a large scatter about the mean and do not describe the global reionization history well. This is true even when these subregions are at the mean density of the universe, which shows that small-box simulations of reionization have little predictive power for the evolution of the mean ionized fraction. The minimum reliable volume size for such predictions is ∼30 Mpc. We derive the power spectra of the neutral, ionized and total gas density fields and show that there is a significant boost of the density fluctuations in both the neutral and the ionized components relative to the total at arcmin and larger scales. We find two populations of H II regions according to their size, numerous, mid-sized (∼10-Mpc) regions and a few, rare, very large regions tens of Mpc in size. Thus, local overlap on fairly large scales of tens of Mpc is reached by z ∼ 13, when our volume is only about 50 per cent ionized, and well before the global overlap. We derive the statistical distributions of the ionized fraction and ionized gas density at various scales and for the first time show that both distributions are clearly non-Gaussian. All these quantities are critical for predicting and interpreting the observational signals from reionization from a variety of observations like 21-cm emission, Lyα emitter statistics, Gunn-Peterson optical depth and small-scale cosmic microwave background secondary anisotropies due to patchy reionization.

Radiative transfer (RT) simulations are now at the forefront of numerical astrophysics. They are becoming crucial for an increasing number of astrophysical and cosmological problems; at the same time their computational cost has come within reach of currently available computational power. Further progress is retarded by the considerable number of different algorithms (including various flavours of ray tracing and moment schemes) developed, which makes the selection of the most suitable technique for a given problem a non‐trivial task. Assessing the validity ranges, accuracy and performances of these schemes is the main aim of this paper, for which we have compared 11 independent RT codes on five test problems: (0) basic physics; (1) isothermal H ii region expansion; (2) H ii region expansion with evolving temperature; (3) I‐front trapping and shadowing by a dense clump and (4) multiple sources in a cosmological density field. The outputs of these tests have been compared and differences analysed. The agreement between the various codes is satisfactory although not perfect. The main source of discrepancy appears to reside in the multifrequency treatment approach, resulting in different thicknesses of the ionized‐neutral transition regions and the temperature structure. The present results and tests represent the most complete benchmark available for the development of new codes and improvement of existing ones. To further this aim all test inputs and outputs are made publicly available in digital form.

In this paper we investigate how the dark matter 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. For an SO halo defined via an overdensity of 178 versus the background matter density and an FOF halo defined via a linking length of 0.2 times the mean inter-particle separation 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 the FOF algorithm.

We present the first limits on the Epoch of Reionization 21 cm H I power spectra, in the redshift range z=7.9-10.6, using the Low-Frequency Array (LOFAR) High-Band Antenna (HBA). In total, 13.0 hr of data were used from observations centered on the North Celestial Pole. After subtraction of the sky model and the noise bias, we detect a non-zero 56 13 mK D < ( ) at k=0.053 h cMpc −1 in the range z=9.6-10.6. The excess variance decreases when optimizing the smoothness of the direction-and frequency-dependent gain calibration, and with increasing the completeness of the sky model. It is likely caused by (i) residual side-lobe noise on calibration baselines, (ii) leverage due to nonlinear effects, (iii) noise and ionosphere-induced gain errors, or a combination thereof. Further analyses of the excess variance will be discussed in forthcoming publications.