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.

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We present a new parallel PM N-body code named PMFAST that is freely available to the public. PMFAST is based on a two-level mesh gravity solver where the gravitational forces are separated into long and short range components. The decomposition scheme minimizes communication costs and allows tolerance for slow networks. The code approaches optimality in several dimensions. The force computations are local and exploit highly optimized vendor FFT libraries. It features minimal memory overhead, with the particle positions and velocities being the main cost. The code features support for distributed and shared memory parallelization through the use of MPI and OpenMP, respectively. The current release version uses two grid levels on a slab decomposition, with periodic boundary conditions for cosmological applications. Open boundary conditions could be added with little computational overhead. We present timing information and results from a recent cosmological production run of the code using a 3712^3 mesh with 6.4 x 10^9 particles. PMFAST is cost-effective, memory-efficient, and is publicly available.Comment: 18 pages, 11 figure

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, within the first billion years of cosmic time. The radio continuum produced by this redshifted line can be seen in absorption or emission against the cosmic microwave background ("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, as it is necessary to detect a diffuse signal at a brightness temperature that differs from that of the CMB at millikelvin levels and distinguish this from foreground continuum sources. 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. Toward this end, 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. In my talk, I summarized some of the theoretical progress in this area.Here, I will 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 ⊙ , 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.