Small-scale density fluctuations can significantly affect reionization, but are typically modelled quite crudely. Unresolved fluctuations in numerical simulations and analytical calculations are included using a gas clumping factor, typically assumed to be independent of the local environment. In Paper I, we presented an improved, local density-dependent model for the sub-grid gas clumping. Here, we extend this using an empirical stochastic model based on the results from high-resolution numerical simulations which fully resolve all relevant fluctuations. Our model reproduces well both the mean density-clumping relation and its scatter. We applied our stochastic model, along with the mean clumping one and the Paper I deterministic model, to create large-volume realizations of the clumping field, and used these in radiative transfer simulations of cosmic reionization. Our results show that the simplistic mean clumping model delays reionization compared to local density-dependent models, despite producing fewer recombinations overall. This is due to the very different spatial distribution of clumping, resulting in much higher photoionization rates in the latter cases. The mean clumping model produces smaller H II regions throughout most of reionization, but those percolate faster at late times. It also causes a significant delay in the 21-cm fluctuations peak and yields lower non-Gaussianity and many fewer bright pixels in the PDF distribution. The stochastic density-dependent model shows relatively minor differences from the deterministic one, mostly concentrated around overlap, where it significantly suppresses the 21-cm fluctuations, and at the bright tail of the 21-cm PDFs, where it produces noticeably more bright pixels.

We derive constraints on the thermal and ionization states of the intergalactic medium (IGM) at redshift approximate to 9.1 using new upper limits on the 21-cm power spectrum measured by the LOFAR radio telescope and a prior on the ionized fraction at that redshift estimated from recent cosmic microwave background (CMB) observations. We have used results from the reionization simulation code GRIZZLY and a Bayesian inference framework to constrain the parameters which describe the physical state of the IGM. We find that, if the gas heating remains negligible, an IGM with ionized fraction greater than or similar to 0.13 and a distribution of the ionized regions with a characteristic size greater than or similar to 8 h(-1) comoving megaparsec (Mpc) and a full width at half-maximum (FWHM) greater than or similar to 16 h(-1) Mpc is ruled out. For an IGM with a uniform spin temperature T-S greater than or similar to 3 K, no constraints on the ionized component can be computed. If the large-scale fluctuations of the signal are driven by spin temperature fluctuations, an IGM with a volume fraction less than or similar to 0.34 of heated regions with a temperature larger than CMB, average gas temperature 7-160 K, and a distribution of the heated regions with characteristic size 3.5-70 h(-1) Mpc and FWHM of less than or similar to 110 h(-1) Mpc is ruled out. These constraints are within the 95 per cent credible intervals. With more stringent future upper limits from LOFAR at multiple redshifts, the constraints will become tighter and will exclude an increasingly large region of the parameter space.

In this paper, we use radiative transfer+N-body simulations to explore the feasibility of measurements of cross-correlations between the 21-cm field observed by the Square Kilometre Array (SKA) and high-z Lyman alpha emitters (LAEs) detected in galaxy surveys with the Subaru Hyper Suprime-Cam (HSC), Subaru Prime Focus Spectrograph (PFS), and Wide Field Infrared Survey Telescope (WFIRST). 2 lcm-LAE cross-correlations are in fact a powerful probe of the epoch of reionization as they are expected to provide precious information on the progress of reionization and the typical scale of ionized regions at different redshifts. The next generation observations with SKA will have a noise level much lower than those with its precursor radio facilities, introducing a significant improvement in the measurement of the cross-correlations. We find that an SKA-HSC/PFS observation will allow to investigate scales below 10 and similar to 60 h(-1) Mpc at z = 7.3 and 6.6, respectively. WHR,ST will allow to access also higher redshifts, as it is expected to observe spectroscopically similar to 900 LAEs per deg(2) and unit redshi in the range 7.5 <= z <= 8.5. Because of the reduction of the shot noise compared to HSC and PFS, observations with WFIRST will result in more precise cross-correlations and increased observable scales.

The upcoming radio interferometer Square Kilometre Array (SKA) is expected to directly detect the redshifted 21-cm signal from the neutral hydrogen present during the Cosmic Dawn. Temperature fluctuations from X-ray heating of the neutral intergalactic medium can dominate the fluctuations in the 21-cm signal from this time. This heating depends on the abundance, clustering, and properties of the X-ray sources present, which remain highly uncertain. We present a suite of three new large-volume, 349 Mpc a side, fully numerical radiative transfer simulations including QSO-like sources, extending the work previously presented in Ross et al. (2017). The results show that our QSOs have a modest contribution to the heating budget, yet significantly impact the 21-cm signal. Initially, the power spectrum is boosted on large scales by heating from the biased QSO-like sources, before decreasing on all scales. Fluctuations from images of the 21-cm signal with resolutions corresponding to SKA1-Low at the appropriate redshifts are well above the expected noise for deep integrations, indicating that imaging could be feasible for all the X-ray source models considered. The most notable contribution of the QSOs is a dramatic increase in non-Gaussianity of the signal, as measured by the skewness and kurtosis of the 21-cm probability distribution functions. However, in the case of late Lyman-alpha saturation, this non-Gaussianity could be dramatically decreased particularly when heating occurs earlier. We conclude that increased non-Gaussianity is a promising signature of rare X-ray sources at this time, provided that Lyman-a saturation occurs before heating dominates the 21-cm signal.

We present the prospects of extracting information about the epoch of reionization by identifying the remaining neutral regions, referred to as islands, in tomographic observations of the redshifted 21-cm signal. Using simulated data sets we show that at late times the 21-cm power spectrum is fairly insensitive to the details of the reionization process but that the properties of the neutral islands can distinguish between different reionization scenarios. We compare the properties of these islands with those of ionized bubbles. At equivalent volume-filling fractions, neutral islands tend to be fewer in number but larger compared to the ionized bubbles. In addition, the evolution of the size distribution of neutral islands is found to be slower than that of the ionized bubbles and also their percolation behaviour differs substantially. Even though the neutral islands are relatively rare, they will be easier to identify in observations with the low frequency component of the Square Kilometre Array due to their larger size and the lower noise levels at lower redshifts. The size distribution of neutral islands at the late stages of reionization is found to depend on the source properties, such as the ionizing efficiency of the sources and their minimum mass. We find the longest line of sight through a neutral region to be more than 100 comoving Mpc until very late stages (90-95 per cent reionized), which may have relevance for the long absorption trough at z = 5.6-5.8 in the spectrum of quasar ULAS J0148+0600.

Observations of redshifted 21-cm radiation from neutral hydrogen during the epoch of reionization are considered to constitute the most promising tool to probe that epoch. One of the major goals of the first generation of low-frequency radio telescopes is to measure the 3D 21-cm power spectrum. However, the 21-cm signal could evolve substantially along the line-of-sight (LOS) direction of an observed 3D volume, since the received signal from different planes transverses to the LOS originated from different look-back times and could therefore be statistically different. Using numerical simulations we investigate this so-called light-cone effect on the spherically averaged 3D 21-cm power spectrum. For this version of the power spectrum, we find that the effect mostly averages out and observe a smaller change in the power spectrum compared to the amount of evolution in the mean 21-cm signal and its rms variations along the LOS direction. Nevertheless, changes up to similar to 50?per cent at large scales are possible. In general, the power is enhanced/suppressed at large/small scales when the effect is included. The cross-over mode below/above which the power is enhanced/suppressed moves towards larger scales as reionization proceeds. When considering the 3D power spectrum we find it to be anisotropic at the late stages of reionization and on large scales. The effect is dominated by the evolution of the ionized fraction of hydrogen during reionization and including peculiar velocities hardly changes these conclusions. We present simple analytical models which explain qualitatively all the features we see in the simulations.