Cosmic reionization is thought to be primarily fueled by the first generations of galaxies. We examine their stellar and gaseous properties, focusing on the star formation rates and the escape of ionizing photons, as a function of halo mass, redshift, and environment using the full suite of the Renaissance Simulations with an eye to provide better inputs to global reionization simulations. This suite, carried out with the adaptive mesh refinement code Enzo, is unprecedented in terms of their size and physical ingredients. The simulations probe overdense, average, and underdense regions of the universe of several hundred comoving Mpc 3 , each yielding a sample of over 3,000 halos in the mass range 10 7 − 10 9.5 M at their final redshifts of 15, 12.5, and 8, respectively. In the process, we simulate the effects of radiative and supernova feedback from 5,000 to 10,000 metal-free (Population III) stars in each simulation. We find that halos as small as 10 7 M are able to form stars due to metal-line cooling from earlier enrichment by massive Population III stars. However, we find such halos do not form stars continuously. Using our large sample, we find that the galaxy-halo occupation fraction drops from unity at virial masses above 10 8.5 M to ∼50% at 10 8 M and ∼10% at 10 7 M , quite independent of redshift and region. Their average ionizing escape fraction is ∼5% in the mass range 10 8 − 10 9 M and increases with decreasing halo mass below this range, reaching 40-60% at 10 7 M . Interestingly, we find that the escape fraction varies between 10-20% in halos with virial masses ∼ 3 × 10 9 M . Taken together, our results confirm the importance of the smallest galaxies as sources of ionizing radiation contributing to the reionization of the universe.

We present the largest-volume (425 h −1 Mpc = 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. Although the halo power spectra are unaffected by this, there is strong modulation of the halo abundance reaching very large scales. We systematically investigate 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 h −1 Mpc per side is sufficient for deriving a convergent mean reionization history, but that the reionization patchiness is significantly underestimated. In the large-scale volume the isolated ionized regions reach volumes up to 4-10 times larger (depending on the measure being used) than they do in a smaller, 114 h −1 = 163 Mpc volume with the same source properties and reionization history, though the abundance of smaller ionized patches agrees well in the two cases. We use jackknife splitting of the large simulation volume 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 h −1 Mpc per side or larger yield convergent reionization histories, except for the earliest times (corresponding to z ∼ > 20 − 25 for our parameters), but smaller volumes of ∼ 50 h −1 Mpc or less are not well converged at any redshift. Reionization history milestones, defined here as the redshifts at which the ionized fraction by mass reaches 10%, 50%, 90% and 99%, show significant scatter between the sub-volumes, of ∆z = 0.6 − 1 for ∼ 50 h −1 Mpc volumes, decreasing to ∆z = 0.3 − 0.5 for ∼ 100h −1 Mpc volumes, and ∆z ∼ 0.1 for ∼ 200 h −1 Mpc volumes. If we only consider mean-density sub-regions the scatter decreases, but remains at ∆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 h −1 Mpc, but retain considerable scatter for smaller volumes. In contrast, the three-dimensional 21-cm power spectra at large scales (k ∼ < 0.25 h Mpc −1 ) do not fully converge for any sub-volume size. These additional large-scale fluctuations significantly enhance the 21-cm fluctuations. At the rough beam-and bandwidth resolution expected for the LOFAR EoR experiment (3' and 440 kHz) and for our simulation parameters, the peak value of the rms 21-cm brightness temperature fluctuations as a function of frequency, derived from the large volume is ∼ 10% higher than for a ∼ 100 h −1 Mpc volume. At late times (high frequency), close to the overlap epoch, the signal derived from the large volume is up to 2.5 times larger, which should improve the prospects of detection considerably, given the lower foregrounds and greater interferometer sensitivity at higher frequencies.

The peculiar velocity of the intergalactic gas responsible for the cosmic 21‐cm background from the epoch of reionization and beyond introduces an anisotropy in the three‐dimensional power spectrum of brightness temperature fluctuations. Measurement of this anisotropy by future 21‐cm surveys is a promising tool for separating cosmology from 21‐cm astrophysics. However, previous attempts to model the signal have often neglected peculiar velocity or only approximated it crudely. This paper re‐examines the effects of peculiar velocity on the 21‐cm signal in detail, improving upon past treatment and addressing several issues for the first time. (1) We show that even the angle‐averaged power spectrum, P(k), is affected significantly by the peculiar velocity. (2) We re‐derive the brightness temperature dependence on atomic hydrogen density, spin temperature, peculiar velocity and its gradient and redshift to clarify the roles of thermal versus velocity broadening and finite optical depth. (3) We show that properly accounting for finite optical depth eliminates the unphysical divergence of the 21‐cm brightness temperature in overdense regions of the intergalactic medium found by previous work that employed the usual optically thin approximation. (4) We find that the approximation made previously to circumvent the diverging brightness temperature problem by capping the velocity gradient can misestimate the power spectrum on all scales. (5) We further show that the observed power spectrum in redshift space remains finite even in the optically thin approximation if one properly accounts for the redshift‐space distortion. However, results that take full account of finite optical depth show that this approximation is only accurate in the limit of high spin temperature. (6) We also show that the linear theory for redshift‐space distortion widely employed to predict the 21‐cm power spectrum results in a ∼30 per cent error in the observationally relevant wavenumber range k∼ 0.1–1 h Mpc−1, when strong ionization fluctuations exist (e.g. at the 50 per cent ionized epoch). We derive an alternative, quasi‐linear formulation which improves upon the accuracy of the linear theory. (7) We describe and test two numerical schemes to calculate the 21‐cm signal from reionization simulations to incorporate peculiar velocity effects in the optically thin approximation accurately, by real‐ to redshift‐space re‐mapping of the H i density. One is particle based, the other grid based, and while the former is most accurate, we demonstrate that the latter is computationally more efficient and can be optimized so as to achieve sufficient accuracy.

The intergalactic medium was reionized before redshift z ∼ 6, most likely by starlight which escaped from early galaxies. The very first stars formed when hydrogen molecules (H 2 ) cooled gas inside the smallest galaxies, minihalos of mass between 10 5 and 10 8 M ⊙ . Although the very first stars began forming inside these minihalos before redshift z ∼ 40, their contribution has, to date, been ignored in large-scale simulations of this cosmic reionization. Here we report results from the first reionization simulations to include these first stars and the radiative feedback that limited their formation, in a volume large enough to follow the crucial spatial variations that influenced the process and its observability. We show that, while minihalo stars stopped far short of fully ionizing the universe, reionization began much earlier with minihalo sources than without, and was greatly extended, which boosts the intergalactic electron-scattering optical depth and the largeangle polarization fluctuations of the cosmic microwave background significantly. Although within current WMAP uncertainties, this boost should be readily detectable by Planck. If reionization ended as late as z ov 7, as suggested by other observations, Planck will thereby see the signature of the first stars at high redshift, currently undetectable by other probes.

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