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Observations of the redshifted 21-cm hyperfine line of neutral hydrogen from early phases of the Universe such as Cosmic Dawn and the Epoch of Reionization promise to open a new window onto the early formation of stars and galaxies. We present the first upper limits on the power spectrum of redshifted 21-cm brightness temperature fluctuations in the redshift range z  = 19.8–25.2 (54–68 MHz frequency range) using 14 h of data obtained with the LOFAR-Low Band Antenna (LBA) array. We also demonstrate the application of a multiple pointing calibration technique to calibrate the LOFAR-LBA dual-pointing observations centred on the North Celestial Pole and the radio galaxy 3C220.3. We observe an unexplained excess of |$\sim 30\!-\!50{{\ \rm per\ cent}}$| in Stokes / noise compared to Stokes V for the two observed fields, which decorrelates on ≳12 s and might have a physical origin. We show that enforcing smoothness of gain errors along frequency direction during calibration reduces the additional variance in Stokes I compared Stokes V introduced by the calibration on sub-band level. After subtraction of smooth foregrounds, we achieve a 2σ upper limit on the 21-cm power spectrum of |$\Delta _{21}^2 \lt (14561\, \text{mK})^2$| at |$k\sim 0.038\, h\, \text{cMpc}^{-1}$| and |$\Delta _{21}^2 \lt (14886\, \text{mK})^2$| at |$k\sim 0.038 \, h\, \text{cMpc}^{-1}$| for the 3C220 and NCP fields respectively and both upper limits are consistent with each other. The upper limits for the two fields are still dominated by systematics on most k modes. [ABSTRACT FROM AUTHOR]

One approach to extracting the global 21-cm signal from total-power measurements at low radio frequencies is to parametrize the different contributions to the data and then fit for these parameters. We examine parametrizations of the 21-cm signal itself, and propose one based on modelling the Ly α background, intergalactic medium temperature and hydrogen ionized fraction using tanh functions. This captures the shape of the signal from a physical modelling code better than an earlier parametrization based on interpolating between maxima and minima of the signal, and imposes a greater level of physical plausibility. This allows less biased constraints on the turning points of the signal, even though these are not explicitly fit for. Biases can also be alleviated by discarding information which is less robustly described by the parametrization, for example by ignoring detailed shape information coming from the covariances between turning points or from the high-frequency parts of the signal, or by marginalizing over the high-frequency parts of the signal by fitting a more complex foreground model. The fits are sufficiently accurate to be usable for experiments gathering 1000 h of data, though in this case it may be important to choose observing windows which do not include the brightest areas of the foregrounds. Our assumption of pointed, single-antenna observations and very broad-band fitting makes these results particularly applicable to experiments such as the Dark Ages Radio Explorer, which would study the global 21-cm signal from the clean environment of a low lunar orbit, taking data from the far side. [ABSTRACT FROM AUTHOR]

The precise form of the foregrounds for sky-averaged measurements of the 21-cm line during and before the epoch of reionization is unknown. We suggest that the level of complexity in the foreground models used to fit global 21-cm data should be driven by the data, under a Bayesian model selection methodology. A first test of this approach is carried out by applying nested sampling to simplified models of global 21-cm data to compute the Bayesian evidence for the models. If the foregrounds are assumed to be polynomials of order n in log-log space, we can infer the necessity to use n = 4 rather than n = 3 with <2 h of integration with limited frequency coverage, for reasonable values of the n = 4 coefficient. Using a higher order polynomial does not necessarily prevent a significant detection of the 21-cm signal. Even for n = 8, we can obtain very strong evidence distinguishing a reasonable model for the signal from a null model with 128 h of integration. More subtle features of the signal may, however, be lost if the foregrounds are this complex. This is demonstrated using a simpler model for the signal that only includes absorption. The results highlight some pitfalls in trying to quantify the significance of a detection from errors on the parameters of the signal alone. [ABSTRACT FROM AUTHOR]

The Square Kilometre Array (SKA) will have a low frequency component (SKA-low) which has as one of its main science goals the study of the redshifted 21 cm line from the earliest phases of star and galaxy formation in the Universe. This 21 cm signal provides a new and unique window both on the time of the formation of the first stars and accreting black holes and the subsequent period of substantial ionization of the intergalactic medium. The signal will teach us fundamental new things about the earliest phases of structure formation, cosmology and even has the potential to lead to the discovery of new physical phenomena. Here we present a white paper with an overview of the science questions that SKA-low can address, how we plan to tackle these questions and what this implies for the basic design of the telescope. [ABSTRACT FROM AUTHOR]

ABSTRACT We present a new probe of primordial non-Gaussianity via the 21-cm radiation from minihaloes at high redshifts. We calculate the fluctuations in the brightness temperature (measured against the cosmic microwave background) of the 21-cm background from minihaloes containing H i at redshift ∼6-20, and find a significant enhancement due to small non-Gaussianity with amplitude fNL ≲ 1. This enhancement can be attributed to the non-linear bias which is strongly increased in the presence of non-Gaussianity. We show that our results are robust against changes in the assumed mass function and some physical aspects of minihalo formation, but are nevertheless sensitive to the presence of strong radiation sources within or around the minihaloes. Our findings are relevant for constraining and searching for small primordial non-Gaussianity with upcoming radio telescopes such as Low-Frequency Array (LOFAR) and Square Kilometre Array (SKA). [ABSTRACT FROM AUTHOR]

The ability to subtract foreground contamination from low-frequency observations is crucial to reveal the underlying 21 cm signal. The traditional line-of-sight methods can deal with the removal of diffuse emission and unresolved point sources, but not bright point sources. In this paper, we introduce a foreground cleaning technique in Fourier space, which allows us to handle all such foregrounds simultaneously and thus sidestep any special treatments to bright point sources. Its feasibility is tested with a simulated data cube for the 21 CentiMeter Array experiment. This data cube includes more realistic models for the 21 cm signal, continuum foregrounds, detector noise, and frequency-dependent instrumental response. We find that a combination of two weighting schemes can be used to protect the frequency coherence of foregrounds: the uniform weighting in the uv plane and the inverse-variance weighting in the spectral fitting. The visibility spectrum is therefore well approximated by a quartic polynomial along the line of sight. With this method, we demonstrate that the huge foreground contamination can be cleaned out effectively with residuals on the order of ~ 10 mK, while the spectrally smooth component of the cosmological signal is also removed, bringing about a systematic underestimate in the extracted power spectrum primarily on large scales. [ABSTRACT FROM AUTHOR]

One of the aims of the Low Frequency Array (LOFAR) Epoch of Reionization (EoR) project is to measure the power spectrum of variations in the intensity of redshifted 21-cm radiation from the EoR. The sensitivity with which this power spectrum can be estimated depends on the level of thermal noise and sample variance, and also on the systematic errors arising from the extraction process, in particular from the subtraction of foreground contamination. We model the extraction process using realistic simulations of the cosmological signal, the foregrounds and noise, and so estimate the sensitivity of the LOFAR EoR experiment to the redshifted 21-cm power spectrum. Detection of emission from the EoR should be possible within 360 h of observation with a single station beam. Integrating for longer, and synthesizing multiple station beams within the primary (tile) beam, then enables us to extract progressively more accurate estimates of the power at a greater range of scales and redshifts. We discuss different observational strategies which compromise between depth of observation, sky coverage and frequency coverage. A plan in which lower frequencies receive a larger fraction of the time appears to be promising. We also study the nature of the bias which foreground fitting errors induce on the inferred power spectrum and discuss how to reduce and correct for this bias. The angular and line-of-sight power spectra have different merits in this respect, and we suggest considering them separately in the analysis of LOFAR data. [ABSTRACT FROM AUTHOR]

The Universe's Epoch of Reionization can be studied using a number of observational probes that provide complementary or corroborating information. Each of these probes suffers from its own systematic and statistical uncertainties. It is therefore useful to consider the mutual information that these data sets contain. In this paper, we present a cross-correlation study between the kinetic Sunyaev–Zel'dovich effect – produced by the scattering of cosmic microwave background (CMB) photons off free electrons produced during the reionization process – and the cosmological 21 cm signal – which reflects the neutral hydrogen content of the Universe, as a function of redshift. The study is carried out using a simulated reionization history in scale N-body simulations with radiative transfer. In essence, we find that the two probes anticorrelate. The significance of the anticorrelation signal depends on the extent of the reionization process, wherein extended histories result in a much stronger signal compared to instantaneous cases. Unfortunately, however, once the primary CMB fluctuations are included into our simulation they serve as a source of large correlated noise that renders the cross-correlation signal insignificant, regardless of the reionization scenario. [ABSTRACT FROM AUTHOR]

One of the problems facing experiments designed to detect redshifted 21-cm emission from the epoch of reionization (EoR) is the presence of foregrounds which exceed the cosmological signal in intensity by orders of magnitude. While fitting them so that they can be removed, we must be careful to minimize ‘overfitting’, in which we fit away some of the cosmological signal, and ‘underfitting’, in which real features of the foregrounds cannot be captured by the fit, polluting the signal reconstruction. We argue that in principle it would be better to fit the foregrounds non-parametrically – allowing the data to determine their shape – rather than selecting some functional form in advance and then fitting its parameters. Non-parametric fits often suffer from other problems, however. We discuss these before suggesting a non-parametric method, Wp smoothing, which seems to avoid some of them. After outlining the principles of Wp smoothing, we describe an algorithm used to implement it. Some useful results for implementing an alternative algorithm are given in an appendix. We apply Wp smoothing to a synthetic data cube for the Low Frequency Array (LOFAR) EoR experiment. This cube includes realistic models for the signal, foregrounds, instrumental response and noise. The performance of Wp smoothing, measured by the extent to which it is able to recover the variance of the cosmological signal and to which it avoids the fitting residuals being polluted by leakage of power from the foregrounds, is compared to that of a parametric fit, and to another non-parametric method (smoothing splines). We find that Wp smoothing is superior to smoothing splines for our application, and is competitive with parametric methods even though in the latter case we may choose the functional form of the fit with advance knowledge of the simulated foregrounds. Finally, we discuss how the quality of the fit is affected by the frequency resolution and range, by the characteristics of the cosmological signal and by edge effects. [ABSTRACT FROM AUTHOR]

Detecting redshifted 21-cm emission from neutral hydrogen in the early Universe promises to give direct constraints on the epoch of reionization (EoR). It will, though, be very challenging to extract the cosmological signal (CS) from foregrounds and noise which are orders of magnitude larger. Fortunately, the signal has some characteristics which differentiate it from the foregrounds and noise, and we suggest that using the correct statistics may tease out signatures of reionization. We generate mock data cubes simulating the output of the Low Frequency Array (LOFAR) EoR experiment. These cubes combine realistic models for Galactic and extragalactic foregrounds and the noise with three different simulations of the CS. We fit out the foregrounds, which are smooth in the frequency direction, to produce residual images in each frequency band. We denoise these images and study the skewness of the one-point distribution in the images as a function of frequency. We find that, under sufficiently optimistic assumptions, we can recover the main features of the redshift evolution of the skewness in the 21-cm signal. We argue that some of these features – such as a dip at the onset of reionization, followed by a rise towards its later stages – may be generic, and give us a promising route to a statistical detection of reionization. [ABSTRACT FROM AUTHOR]

We present an efficient method to generate large simulations of the epoch of reionization without the need for a full three-dimensional radiative transfer code. Large dark-matter-only simulations are post-processed to produce maps of the redshifted 21-cm emission from neutral hydrogen. Dark matter haloes are embedded with sources of radiation whose properties are either based on semi-analytical prescriptions or derived from hydrodynamical simulations. These sources could either be stars or power-law sources with varying spectral indices. Assuming spherical symmetry, ionized bubbles are created around these sources, whose radial ionized fraction and temperature profiles are derived from a catalogue of one-dimensional radiative transfer experiments. In case of overlap of these spheres, photons are conserved by redistributing them around the connected ionized regions corresponding to the spheres. The efficiency with which these maps are created allows us to span the large parameter space typically encountered in reionization simulations. We compare our results with other, more accurate, three-dimensional radiative transfer simulations and find excellent agreement for the redshifts and the spatial scales of interest to upcoming 21-cm experiments. We generate a contiguous observational cube spanning redshift 6 to 12 and use these simulations to study the differences in the reionization histories between stars and quasars. Finally, the signal is convolved with the Low Frequency Array (LOFAR) beam response and its effects are analysed and quantified. Statistics performed on this mock data set shed light on possible observational strategies for LOFAR. [ABSTRACT FROM AUTHOR]

We present a method for extracting the expected cosmological 21-cm signal from the epoch of re-ionization, taking into account contaminating radiations and random instrumental noise. The method is based on the maximum a posteriori probability (MAP) formalism and employs the coherence of the contaminating radiation along the line-of-sight and the three-dimensional correlations of the cosmological signal. We test the method using a detailed and comprehensive modelling of the cosmological 21-cm signal and the contaminating radiation. The signal is obtained using a high-resolution N-body simulation where the gas is assumed to trace the dark matter and is re-ionized by stellar radiation computed from semi-analytic galaxy formation recipes. We model contaminations to the cosmological signal from synchrotron and free–free galactic foregrounds and extragalactic sources including active galactic nuclei, radio haloes and relics, synchrotron and free–free emission from star-forming galaxies and free–free emission from dark matter haloes and the intergalactic medium. We provide tests of the reconstruction method for several rms values of instrumental noise from to 250 mK. For low instrumental noise, the recovered signal, along individual lines-of-sight, fits the true cosmological signal with a mean rms difference of for , and for . The one-dimensional power spectrum is nicely reconstructed for all values of considered here, while the reconstruction of the two-dimensional power spectrum and the Minkowski functionals is good only for noise levels of the order of few mK. [ABSTRACT FROM AUTHOR]

A soft ultraviolet radiation field, eV, that permeates neutral intergalactic gas during the epoch of reionization (EoR) excites the 2p (directly) and 2s (indirectly) states of atomic hydrogen. Because the 2s state is metastable, the lifetime of atoms in this level is relatively long, which may cause the 2s state to be overpopulated relative to the 2p state. It has recently been proposed that for this reason, neutral intergalactic atomic hydrogen gas may be detected in absorption in its 3-cm fine-structure line against the cosmic microwave background out to very high redshifts. In particular, the optical depth in the fine-structure line through neutral intergalactic gas surrounding bright quasars during the EoR may reach . The resulting surface brightness temperature of tens of μK (in absorption) may be detectable with existing radio telescopes. Motivated by this exciting proposal, we perform a detailed analysis of the transfer of radiation, and reanalyse the detectability of the fine-structure line in neutral intergalactic gas surrounding high-redshift quasars. We find that proper radiative transfer modelling causes the fine-structure absorption signature to be reduced tremendously to . We therefore conclude that neutral intergalactic gas during the EoR cannot reveal its presence in the 3-cm fine-structure line to existing radio telescopes. [ABSTRACT FROM AUTHOR]

Future high-redshift 21-cm experiments will suffer from a high degree of contamination, due both to astrophysical foregrounds and to non-astrophysical and instrumental effects. In order to reliably extract the cosmological signal from the observed data, it is essential to understand very well all data components and their influence on the extracted signal. Here we present simulated astrophysical foregrounds data cubes and discuss their possible statistical effects on the data. The foreground maps are produced assuming 5°× 5° windows that match those expected to be observed by the LOFAR epoch of reionization (EoR) key science project. We show that with the expected LOFAR–EoR sky and receiver noise levels, which amount to ≈52 mK at 150 MHz after 400 h of total observing time, a simple polynomial fit allows a statistical reconstruction of the signal. We also show that the polynomial fitting will work for maps with realistic yet idealized instrument response, i.e. a response that includes only a uniform uv coverage as a function of frequency and ignores many other uncertainties. Polarized Galactic synchrotron maps that include internal polarization and a number of Faraday screens along the line of sight are also simulated. The importance of these stems from the fact that the LOFAR instrument, in common with all current interferometric EoR experiments, has an instrumentally polarized response. [ABSTRACT FROM AUTHOR]

A one-dimensional radiative transfer code is developed to track the ionization and heating pattern around the first miniquasars and Population III stars. The code follows the evolution of the ionization of the species of hydrogen and helium and the intergalactic medium temperature profiles as a function of redshift. The radiative transfer calculations show that the ionization signature of the first miniquasars and stars is very similar yet the heating pattern around the two is very different. Furthermore, the first massive miniquasars do produce large ionized bubbles around them, which can potentially be imaged directly using future radio telescopes. It is also shown that the ionized bubbles not only stay ionized for considerable time after the switching off of the source, but also continue to expand for a short while due to secondary collisions prompted by the X-ray part of their spectra. Varying spectral shapes also produced sizable variations in ionized fraction and temperature profile. We also compare the radiative transfer results with the analytical approximation usually adopted for heating by miniquasars and find that, because of the inadequate treatment of the He species, the analytical approach leads to an underestimation of the temperature in the outer radii by a factor of ≈5. Population III stars – with masses in the range of and modelled as blackbodies at a temperature of 50 000 K – are found to be efficient in ionizing their surroundings. The lack of very high energy photons limits the extent of heating of these first stars and has a distinctly different signature from that of the miniqsos. Observational effects on the 21-cm brightness temperature, the thermal and kinetic Sunyaev–Ze'ldovich effects, are also studied in the context of the upcoming radio and microwave telescopes like LOFAR and SPT. [ABSTRACT FROM AUTHOR]

A simple analytical model is used to calculate the X-ray heating of the intergalactic medium (IGM) for a range of black hole masses. This process is efficient enough to decouple the spin temperature of the IGM from the cosmic microwave background (CMB) temperature and produce a differential brightness temperature of the order of ∼ 5–20 mK out to distances as large as a few comoving Mpc, depending on the redshift, black hole mass and lifetime. We explore the influence of two types of black holes, those with and without ionizing ultraviolet radiation. The results of the simple analytical model are compared to those of a full spherically symmetric radiative transfer code. Two simple scenarios are proposed for the formation and evolution of black hole mass density in the Universe. The first considers an intermediate mass black hole that form as an end-product of pop III stars, whereas the second considers supermassive black holes that form directly through the collapse of massive haloes with low spin parameter. These scenarios are shown not to violate any of the observational constraints, yet produce enough X-ray photons to decouple the spin temperature from that of the CMB. This is an important issue for future high-redshift 21-cm observations. [ABSTRACT FROM AUTHOR]

We propose use of the thickness of the ionization front as a discriminant between alternative modes of reionization in the early Universe, by stars or by miniquasars. Assuming a photoionization–recombination balance, we find that for miniquasar sources the transition from neutral to ionized intergalactic medium is extended and has two features. The first is a sudden steep increase in the neutral fraction with a typical width of 5–10 comoving megaparsecs, depending on the miniquasar power. The second feature is a long wing that represents a much slower transition from a neutral fraction of to 1. The angular resolution of LOFAR is expected to resolve these scales and will, therefore, play an important role in discriminating the hard sources of ionizing photons from the stellar ones. [ABSTRACT FROM AUTHOR]