The upcoming SKA1-Low radio interferometer will be sensitive enough to produce tomographic imaging data of the redshifted 21-cm signal from the Epoch of Reionization. Due to the non-Gaussian distribution of the signal, a power spectrum analysis alone will not provide a complete description of its properties. Here, we consider an additional metric which could be derived from tomographic imaging data, namely the bubble size distribution of ionized regions. We study three methods that have previously been used to characterize bubble size distributions in simulation data for the hydrogen ionization fraction -the spherical-average, mean-free-path and friends-offriends methods -and apply them to simulated 21-cm data cubes. Our simulated data cubes have the (sensitivity-dictated) resolution expected for the SKA1-Low reionization experiment and we study the impact of both the light-cone and redshift space distortion effects. To identify ionized regions in the 21-cm data we introduce a new, self-adjusting thresholding approach based on the K-Means algorithm. We find that the fraction of ionized cells identified in this way consistently falls below the mean volume-averaged ionized fraction. From a comparison of the three bubble size methods, we conclude that all three methods are useful, but that the mean-free-path method performs best in terms of tracking the progress of reionization and separating different reionization scenarios. The light-cone effect is found to affect data spanning more than about 10 MHz in frequency (∆z ∼ 0.5). We find that redshift space distortions only marginally affect the bubble size distributions.

We present analysis of the normalised 21-cm bispectrum from fully-numerical simulations of intergalactic-medium heating by stellar sources and high-mass X-ray binaries (HMXB) during the cosmic dawn. Lyman-α coupling is assumed to be saturated, we therefore probe the nature of non-Gaussianities produced by X-ray heating processes. We find the evolution of the normalised bispectrum to be very different from that of the power spectrum. It exhibits a turnover whose peak moves from large to small scales with decreasing redshift, and corresponds to the typical separation of emission regions. This characteristic scale reduces as more and more regions move into emission with time. Ultimately, small-scale fluctuations within heated regions come to dominate the normalised bispectrum, which at the end of the simulation is almost entirely driven by fluctuations in the density field. To establish how generic the qualitative evolution of the normalised bispectrum we see in the stellar + HMXB simulation is, we examine several other simulations -two fully-numerical simulations that include QSO sources, and two with contrasting source properties produced with the semi-numerical simulation 21CMFAST . We find the qualitative evolution of the normalised bispectrum during X-ray heating to be generic, unless the sources of X-rays are, as with QSOs, less numerous and so exhibit more distinct isolated heated profiles. Assuming mitigation of foreground and instrumental effects are ultimately effective, we find that we should be sensitive to the normalised bispectrum during the epoch of heating, so long as the spin temperature has not saturated by z ≈ 19.

Observations of the epoch of reionization give us clues about the nature and evolution of the sources of ionizing photons, or early stars and galaxies. We present a new suite of structure formation and radiative transfer simulations from the PRACE4LOFAR project designed to investigate whether the mechanism of radiative feedback, or the suppression of star formation in ionized regions from UV radiation, can be inferred from these observations. Our source halo mass extends down to 10 8 M ⊙ , with sources in the mass range 10 8 to 10 9 M ⊙ expected to be particularly susceptible to feedback from ionizing radiation, and we vary the aggressiveness and nature of this suppression. Not only do we have four distinct source models, we also include two box sizes (67 Mpc and 349 Mpc), each with two grid resolutions. This suite of simulations allows us to investigate the robustness of our results. All of our simulations are broadly consistent with the observed electron-scattering optical depth of the cosmic microwave background and the neutral fraction and photoionization rate of hydrogen at z ∼ 6. In particular, we investigate the redshifted 21-cm emission in anticipation of upcoming radio interferometer observations. We find that the overall shape of the 21-cm signal and various statistics are robust to the exact nature of source suppression, the box size, and the resolution. There are some promising model discriminators in the non-Gaussianity and small-scale power spectrum of the 21-cm signal.

Recent observations suggest that helium became fully ionized around redshift z ∼ 3. The He II optical depth derived from the Lyman-α forest decreases substantially from this period to z ∼ 2; moreover, it fluctuates strongly near z ∼ 3 and then evolves smoothly at lower redshifts. From these opacities, we compute, using a semi-analytic model, the evolution of the mean photoionization rate and the attenuation length for helium over the redshift range 2.0 z 3.2. This model includes an inhomogeneous metagalactic radiation background, which is expected during and after helium reionization. We find that assuming a uniform background underestimates the required photoionization rate by up to a factor ∼ 2. When averaged over the (few) available lines of sight, the effective optical depth exhibits a discontinuity near z ≈ 2.8, but the measurement uncertainties are sizable. This feature translates into a jump in the photoionization rate and, provided the quasar emissivity evolves smoothly, in the effective attenuation length, perhaps signaling the helium reionization era. We then compute the evolution of the effective optical depth for a variety of simple helium reionization models, in which the measured quasar luminosity function and the attenuation length, as well as the evolving He III fraction, are inputs. A model with reionization ending around redshift z ≈ 2.7 is most consistent with the data, although the constraints are not strong thanks to the sparseness of the data.

We introduce a novel technique, called "granulometry", to characterize and recover the mean size and the size distribution of H II regions from 21-cm tomography. The technique is easy to implement, but places the previously not very well defined concept of morphology on a firm mathematical foundation. The size distribution of the cold spots in 21-cm tomography can be used as a direct tracer of the underlying probability distribution of H II region sizes. We explore the capability of the method using large-scale reionization simulations and mock observational data cubes while considering capabilities of SKA1-low and a future extension to SKA2. We show that the technique allows the recovery of the H II region size distribution with a moderate signal-to-noise ratio from wide-field imaging (SNR 3), for which the statistical uncertainty is sample variance dominated. We address the observational requirements on the angular resolution, the field-of-view, and the thermal noise limit for a successful measurement. To achieve a full scientific return from 21-cm tomography and to exploit a synergy with 21cm power spectra, we suggest an observing strategy using wide-field imaging (several tens of square degrees) by an interferometric mosaicking/multi-beam observation with additional intermediate baselines (∼ 2 − 4 km) in a SKA phase 2.