Epoch Of Reionization Experiments Research Articles

A comparison of numerical methods for computing the reionization of intergalactic hydrogen and helium by a central radiating source

ABSTRACT We compare numerical methods for solving the radiative transfer equation in the context of the photoionization of intergalactic gaseous hydrogen and helium by a central radiating source. Direct integration of the radiative transfer equation and solutions using photon packets are examined, both for solutions to the time-dependent radiative transfer equation and in the infinite-speed-of-light approximation. The photon packet schemes are found to be more generally computationally efficient than a direct integration scheme. While all codes accurately describe the growth rate of hydrogen and helium ionization zones, it is shown that a fully time-dependent method is required to capture the gas temperature and ionization structure in the near zone of a source when an ionization front expands at a speed close to the speed of light. Applied to quasi-stellar objects in the Epoch of Reionization (EoR), temperature differences as high as 5 × 104 K result in the near zone for solutions of the time-dependent radiative transfer equation compared with solutions in the infinite-speed-of-light approximation. Smaller temperature differences are found following the nearly full photoionization of helium in gas in which the hydrogen was already ionized and the helium was singly ionized. Variations found in the temperature and ionization structure far from the source, where the gas is predominantly neutral, may affect some predictions for 21-cm EoR experiments.

North Celestial Region Observed with 21 CentiMeter Array

The 21 CentiMeter Array (21CMA) is a radio interferometer in western China. The key science objective of 21CMA is statistically measuring the redshifted H i 21 cm signal of the Epoch of Reionization (EoR). In order to achieve this, a catalog of radio sources is necessary for both calibration and foreground removal. In this work, we present a catalog of 832 radio sources within a radius of 5° around the North Celestial Pole region observed with 21CMA. Three days of data taken in 2013 are used in the analysis, with a frequency coverage from 75 to 200 MHz and an angular resolution of about two arcminutes at 200 MHz. Flux densities and estimated spectral indices of the radio sources are provided in the source catalog. For simplicity, only the east–west baseline is used for the observations to avoid the so-called w − term in the data analysis. The longest baseline along the east–west direction is 2780 m. Comparing our source counts with other radio observations, we find a good agreement with the observations made with the Giant Metrewave Radio Telescope and Murchison Widefield Array. Our data reduction is still limited by grating lobes of very bright sources in the field due to the redundant configuration of 21CMA. We note that understanding the properties of radio sources, and modeling and removing the radio sources are challenges for the EoR experiments.

External calibrator in global signal experiment for detection of the epoch of reionization

We present a conceptual design study of external calibrators in the 21 cm experiment towards detecting the globally averaged radiation of the epoch of reionization (EoR). Employment of external calibrator instead of internal calibrator commonly used in current EoR experiments allows removing instrumental effects such as beam pattern, receiver gain and instability of the system if the conventional three-position switch measurements are implemented in a short time interval. Furthermore, in the new design the antenna system is placed in an underground anechoic chamber with an open/closing ceiling to maximally reduce the environmental effect such as RFI and ground radiation/reflection. It appears that three of the four external calibrators proposed in this paper, including two indoor artificial transmitters and one outdoor celestial radiation (the Galactic polarization), fail to meet our purpose. Diurnal motion of the Galactic diffuse emission turns out to be the most probable source as an external calibrator, for which we have discussed the observational strategy and the algorithm of extracting the EoR signal.

Predictions for measuring the 21-cm multifrequency angular power spectrum using SKA-Low

ABSTRACT The light-cone effect causes the mean as well as the statistical properties of the redshifted 21-cm signal ${T_{\rm b}}(\hat{\boldsymbol {n}}, \nu)$ to change with frequency ν (or cosmic time). Consequently, the statistical homogeneity (ergodicity) of the signal along the line-of-sight (LoS) direction is broken. This is a severe problem particularly during the Epoch of Reionization (EoR) when the mean neutral hydrogen fraction ($\bar{x}_{\rm {H\,{\small I}}}$) changes rapidly as the Universe evolves. This will also pose complications for large bandwidth observations. These effects imply that the 3D power spectrum P(k) fails to quantify the entire second-order statistics of the signal as it assumes the signal to be ergodic and periodic along the LoS. As a proper alternative to P(k), we use the multifrequency angular power spectrum (MAPS) ${\mathcal {C}}_{\ell }(\nu _1,\nu _2)$, which does not assume the signal to be ergodic and periodic along the LoS. Here, we study the prospects for measuring the EoR 21-cm MAPS using future observations with the upcoming SKA-Low. Ignoring any contribution from the foregrounds, we find that the EoR 21-cm MAPS can be measured at a confidence level ≥5σ at angular scales ℓ ∼ 1300 for total observation time tobs ≥ 128 h across ∼44 MHz observational bandwidth. We also quantitatively address the effects of foregrounds on MAPS detectability forecast by avoiding signal contained within the foreground wedge in $({\boldsymbol {k}}_\perp , k_\parallel)$ plane. These results are very relevant for the upcoming large bandwidth EoR experiments as previous predictions were all restricted to individually analysing the signal over small frequency (or equivalent redshift) intervals.

The Lyman Alpha Reference Sample. X. Predicting Lyα Output from Star-forming Galaxies Using Multivariate Regression*

Abstract Understanding the production and escape of Lyα radiation from star-forming galaxies is a long-standing problem in astrophysics. The ability to predict the Lyα luminosity of galaxies would open up new ways of exploring the epoch of reionization (EOR) and estimating Lyα emission from galaxies in cosmological simulations where radiative transfer calculations cannot be done. We apply multivariate regression methods to the Lyman Alpha Reference Sample data set to obtain a relation between the galaxy properties and the emitted Lyα. The derived relation predicts the Lyα luminosity of our galaxy sample to good accuracy, regardless of whether we consider only direct observables (rms dispersion around the relation of ∼0.19 dex) or derived physical quantities (rms ∼ 0.27 dex). We confirm the predictive ability on a separate sample of compact star-forming galaxies and find that the prediction works well, but that aperture effects on measured Lyα luminosity may be important, depending on the redshift of the galaxy. We apply statistical feature selection techniques to determine an order of importance of the variables in our data set, enabling future observations to be optimized for predictive ability. When using physical variables, we are able to determine that the most important predictive parameters are, in order, star formation rate, dust extinction, compactness, and the gas covering fraction. We discuss the application of our results in terms of studying the EOR and intensity mapping experiments.

Contribution of Radio Halos to the Foreground for SKA EoR Experiments

The overwhelming foreground contamination is one of the primary impediments to probing the Epoch of Reionization (EoR) through measuring the redshifted 21 cm signal. Among various foreground components, radio halos are less studied and their impacts on the EoR observations are still poorly understood. In this work, we employ the Press-Schechter formalism, merger-induced turbulent re-acceleration model, and the latest SKA1-Low layout configuration to simulate the SKA "observed" images of radio halos. We calculate the one-dimensional power spectra from simulated images and find that radio halos can be about $10^4$, $10^3$ and $10^{2.5}$ times more luminous than the EoR signal on scales of $0.1\,\text{Mpc}^{-1} < k < 2\,\text{Mpc}^{-1}$ in the 120-128, 154-162, and 192-200 MHz bands, respectively. By examining the two-dimensional power spectra inside properly defined EoR windows, we find that the power leaked by radio halos can still be significant, as the power ratios of radio halos to the EoR signal on scales of $0.5\,\text{Mpc}^{-1} \lesssim k \lesssim 1\,\text{Mpc}^{-1}$ can be up to about 230-800%, 18-95%, and 7-40% in the three bands, when the 68% uncertainties caused by the variation of the number density of bright radio halos are considered. Furthermore, we find that radio halos located inside the far side-lobes of the station beam can also impose strong contamination within the EoR window. In conclusion, we argue that radio halos are severe foreground sources and need serious treatments in future EoR experiments.

Separating the EoR signal with a convolutional denoising autoencoder: a deep-learning-based method

When applying the foreground removal methods to uncover the faint cosmological signal from the epoch of reionization (EoR), the foreground spectra are assumed to be smooth. However, this assumption can be seriously violated in practice since the unresolved or mis-subtracted foreground sources, which are further complicated by the frequency-dependent beam effects of interferometers, will generate significant fluctuations along the frequency dimension. To address this issue, we propose a novel deep-learning-based method that uses a 9-layer convolutional denoising autoencoder (CDAE) to separate the EoR signal. After being trained on the SKA images simulated with realistic beam effects, the CDAE achieves excellent performance as the mean correlation coefficient ($\bar{\rho}$) between the reconstructed and input EoR signals reaches $0.929 \pm 0.045$. In comparison, the two representative traditional methods, namely the polynomial fitting method and the continuous wavelet transform method, both have difficulties in modelling and removing the foreground emission complicated with the beam effects, yielding only $\bar{\rho}_{\text{poly}} = 0.296 \pm 0.121$ and $\bar{\rho}_{\text{cwt}} = 0.198 \pm 0.160$, respectively. We conclude that, by hierarchically learning sophisticated features through multiple convolutional layers, the CDAE is a powerful tool that can be used to overcome the complicated beam effects and accurately separate the EoR signal. Our results also exhibit the great potential of deep-learning-based methods in future EoR experiments.

The hydrogen epoch of reionization array dish III: measuring chromaticity of prototype element with reflectometry

The experimental efforts to detect the redshifted 21 cm signal from the Epoch of Reionization (EoR) are limited predominantly by the chromatic instrumental systematic effect. The delay spectrum methodology for 21 cm power spectrum measurements brought new attention to the critical impact of an antenna's chromaticity on the viability of making this measurement. This methodology established a straightforward relationship between time-domain response of an instrument and the power spectrum modes accessible to a 21 cm EoR experiment. We examine the performance of a prototype of the Hydrogen Epoch of Reionization Array (HERA) array element that is currently observing in Karoo desert, South Africa. We present a mathematical framework to derive the beam integrated frequency response of a HERA prototype element in reception from the return loss measurements between 100-200 MHz and determined the extent of additional foreground contamination in the delay space. The measurement reveals excess spectral structures in comparison to the simulation studies of the HERA element. Combined with the HERA data analysis pipeline that incorporates inverse covariance weighting in optimal quadratic estimation of power spectrum, we find that in spite of its departure from the simulated response, HERA prototype element satisfies the necessary criteria posed by the foreground attenuation limits and potentially can measure the power spectrum at spatial modes as low as $k_{\parallel} > 0.1h$~Mpc$^{-1}$. The work highlights a straightforward method for directly measuring an instrument response and assessing its impact on 21 cm EoR power spectrum measurements for future experiments that will use reflector-type antenna.

Status of Foreground and Instrument Challenges for 21cm EoR experiments – Design Strategies for SKA and HERA

AbstractDirect detection of the Epoch of Reionization (EoR) via redshifted 21 cm line of H i will reveal the nature of the first stars and galaxies as well as revolutionize our understanding of a poorly explored evolutionary phase of the Universe. Projects such as the MWA, LOFAR, and PAPER commenced in the last decade with the promise of high significance statistical detection of the EoR, but have so far only weakly constrained models owing to unforeseen challenges from bright foreground sources and instrument systematics. It is essential for next generation instruments like the HERA and SKA to have these challenges addressed. I present an analysis of these challenges – wide-field measurements, antenna beam chromaticity, reflections in the instrument, and antenna position errors – along with performance specifications and design solutions that will be critical to designing successful next-generation instruments in enabling the first detection and also in placing meaningful constraints on reionization models.

An Improved Statistical Point-source Foreground Model for the Epoch of Reionization

Abstract We present a sophisticated statistical point-source foreground model for low-frequency radio Epoch of Reionization (EoR) experiments using the 21 cm neutral hydrogen emission line. Motivated by our understanding of the low-frequency radio sky, we enhance the realism of two model components compared with existing models: the source count distributions as a function of flux density and spatial position (source clustering), extending current formalisms for the foreground covariance of 2D power-spectral modes in 21 cm EoR experiments. The former we generalize to an arbitrarily broken power law, and the latter to an arbitrary isotropically correlated field. This paper presents expressions for the modified covariance under these extensions, and shows that for a more realistic source spatial distribution, extra covariance arises in the EoR window that was previously unaccounted for. Failure to include this contribution can yield bias in the final power-spectrum and under-estimate uncertainties, potentially leading to a false detection of signal. The extent of this effect is uncertain, owing to ignorance of physical model parameters, but we show that it is dependent on the relative abundance of faint sources, to the effect that our extension will become more important for future deep surveys. Finally, we show that under some parameter choices, ignoring source clustering can lead to false detections on large scales, due to both the induced bias and an artificial reduction in the estimated measurement uncertainty.

RADIO SOURCES IN THE NCP REGION OBSERVED WITH THE 21 CENTIMETER ARRAY

ABSTRACT We present a catalog of 624 radio sources detected around the North Celestial Pole (NCP) with the 21 Centimeter Array (21CMA), a radio interferometer dedicated to the statistical measurement of the epoch of reionization (EoR). The data are taken from a 12 hr observation made on 2013 April 13, with a frequency coverage from 75 to 175 MHz and an angular resolution of ∼4′. The catalog includes flux densities at eight sub-bands across the 21CMA bandwidth and provides the in-band spectral indices for the detected sources. To reduce the complexity of interferometric imaging from the so-called “w” term and ionospheric effects, the present analysis is restricted to the east–west baselines within 1500 m only. The 624 radio sources are found within 5° around the NCP down to ∼0.1 Jy. Our source counts are compared, and also exhibit a good agreement, with deep low-frequency observations made recently with the GMRT and MWA. In particular, for fainter radio sources below ∼1 Jy, we find a flattening trend of source counts toward lower frequencies. While the thermal noise (∼0.4 mJy) is well controlled to below the confusion limit, the dynamical range (∼104) and sensitivity of current 21CMA imaging are largely limited by calibration and deconvolution errors, especially the grating lobes of very bright sources, such as 3C061.1, in the NCP field, which result from the regular spacings of the 21CMA. We note that particular attention should be paid to the extended sources, and their modeling and removal may constitute a large technical challenge for current EoR experiments. Our analysis may serve as a useful guide to the design of next generation low-frequency interferometers like the Square Kilometre Array.

EFFECTS OF ANTENNA BEAM CHROMATICITY ON REDSHIFTED 21 cm POWER SPECTRUM AND IMPLICATIONS FOR HYDROGEN EPOCH OF REIONIZATION ARRAY

ABSTRACT Unaccounted for systematics from foregrounds and instruments can severely limit the sensitivity of current experiments from detecting redshifted 21 cm signals from the Epoch of Reionization (EoR). Upcoming experiments are faced with a challenge to deliver more collecting area per antenna element without degrading the data with systematics. This paper and its companions show that dishes are viable for achieving this balance using the Hydrogen Epoch of Reionization Array (HERA) as an example. Here, we specifically identify spectral systematics associated with the antenna power pattern as a significant detriment to all EoR experiments which causes the already bright foreground power to leak well beyond ideal limits and contaminate the otherwise clean EoR signal modes. A primary source of this chromaticity is reflections in the antenna-feed assembly and between structures in neighboring antennas. Using precise foreground simulations taking wide-field effects into account, we provide a generic framework to set cosmologically motivated design specifications on these reflections to prevent further EoR signal degradation. We show that HERA will not be impeded by such spectral systematics and demonstrate that even in a conservative scenario that does not perform removal of foregrounds, HERA will detect the EoR signal in line-of-sight k-modes, Mpc−1, with high significance. Under these conditions, all baselines in a 19-element HERA layout are capable of detecting EoR over a substantial observing window on the sky.

Parametrizing Epoch of Reionization foregrounds: a deep survey of low-frequency point-source spectra with the Murchison Widefield Array

Experiments that pursue detection of signals from the Epoch of Reionization (EoR) are relying on spectral smoothness of source spectra at low frequencies. This article empirically explores the effect of foreground spectra on EoR experiments by measuring high-resolution full-polarization spectra for the 586 brightest unresolved sources in one of the MWA EoR fields using 45 h of observation. A novel peeling scheme is used to subtract 2500 sources from the visibilities with ionospheric and beam corrections, resulting in the deepest, confusion-limited MWA image so far. The resulting spectra are found to be affected by instrumental effects, which limit the constraints that can be set on source-intrinsic spectral structure. The sensitivity and power-spectrum of the spectra are analysed, and it is found that the spectra of residuals are dominated by PSF sidelobes from nearby undeconvolved sources. We release a catalogue describing the spectral parameters for each measured source.

THE IMPACT OF THE IONOSPHERE ON GROUND-BASED DETECTION OF THE GLOBAL EPOCH OF REIONIZATION SIGNAL

The redshifted 21 cm line of neutral hydrogen (H i), potentially observable at low radio frequencies (∼50–200 MHz), is a promising probe of the physical conditions of the intergalactic medium during Cosmic Dawn and the Epoch of Reionization (EoR). The sky-averaged H i signal is expected to be extremely weak (∼100 mK) in comparison to the Galactic foreground emission (∼104 K). Moreover, the sky-averaged spectra measured by ground-based instruments are affected by chromatic propagation effects (∼tens of kelvin) originating in the ionosphere. We analyze data collected with the upgraded Broadband Instrument for Global Hydrogen Reionization Signal system deployed at the Murchison Radio-astronomy Observatory to assess the significance of ionospheric effects on the detection of the global EoR signal. The ionospheric effects identified in these data are, particularly during nighttime, dominated by absorption and emission. We measure some properties of the ionosphere, such as the electron temperature (Te ≈ 470 K at nighttime), magnitude, and variability of optical depth (τ100 MHz ≈ 0.01 and δτ ≈ 0.005 at nighttime). According to the results of a statistical test applied on a large data sample, very long integrations (∼100 hr collected over approximately 2 months) lead to increased signal-to-noise ratio even in the presence of ionospheric variability. This is further supported by the structure of the power spectrum of the sky temperature fluctuations, which has flicker noise characteristics at frequencies ≳10−5 Hz, but becomes flat below ≈10−5 Hz. Hence, we conclude that the stochastic error introduced by the chromatic ionospheric effects tends to zero in an average. Therefore, the ionospheric effects and fluctuations are not fundamental impediments preventing ground-based instruments from integrating down to the precision required by global EoR experiments, provided that the ionospheric contribution is properly accounted for in the data analysis.

21CMMC: an MCMC analysis tool enabling astrophysical parameter studies of the cosmic 21 cm signal

We introduce 21CMMC: a parallelized, Monte Carlo Markov Chain analysis tool, incorporating the epoch of reionization (EoR) seminumerical simulation 21CMFAST. 21CMMC estimates astrophysical parameter constraints from 21 cm EoR experiments, accommodating a variety of EoR models, as well as priors on model parameters and the reionization history. To illustrate its utility, we consider two different EoR scenarios, one with a single population of galaxies (with a mass-independent ionizing efficiency) and a second, more general model with two different, feedback-regulated populations (each with mass-dependent ionizing efficiencies). As an example, combining three observations (z=8, 9 and 10) of the 21 cm power spectrum with a conservative noise estimate and uniform model priors, we find that interferometers with specifications like the Low Frequency Array/Hydrogen Epoch of Reionization Array (HERA)/Square Kilometre Array 1 (SKA1) can constrain common reionization parameters: the ionizing efficiency (or similarly the escape fraction), the mean free path of ionizing photons and the log of the minimum virial temperature of star-forming haloes to within 45.3/22.0/16.7, 33.5/18.4/17.8 and 6.3/3.3/2.4 per cent, ~$1\sigma$ fractional uncertainty, respectively. Instead, if we optimistically assume that we can perfectly characterize the EoR modelling uncertainties, we can improve on these constraints by up to a factor of ~few. Similarly, the fractional uncertainty on the average neutral fraction can be constrained to within $\lesssim10$ per cent for HERA and SKA1. By studying the resulting impact on astrophysical constraints, 21CMMC can be used to optimize (i) interferometer designs; (ii) foreground cleaning algorithms; (iii) observing strategies; (iv) alternative statistics characterizing the 21 cm signal; and (v) synergies with other observational programs.

The impact of foregrounds on redshift space distortion measurements with the highly redshifted 21-cm line

The highly redshifted 21-cm line of neutral hydrogen has become recognized as a unique probe of cosmology from relatively low redshifts (z ∼ 1) up through the Epoch of Reionization (EoR) (z ∼ 8) and even beyond. To date, most work has focused on recovering the spherically averaged power spectrum of the 21-cm signal, since this approach maximizes the signal to noise in the initial measurement. However, like galaxy surveys, the 21-cm signal is affected by redshift space distortions, and is inherently anisotropic between the line of sight and transverse directions. A measurement of this anisotropy can yield unique cosmological information, potentially even isolating the matter power spectrum from astrophysical effects. However, in interferometric measurements, foregrounds also have an anisotropic footprint between the line of sight and transverse directions: the so-called foreground ‘wedge’. Although foreground subtraction techniques are actively being developed, a ‘foreground avoidance’ approach of simply ignoring contaminated modes has arguably proven most successful to date. In this work, we analyse the effect of this foreground anisotropy in recovering the redshift space distortion signature in 21-cm measurements at both high and intermediate redshifts. We find the foreground wedge corrupts nearly all of the redshift space signal for even the largest proposed EoR experiments (Hydrogen Epoch of Reionization Array and the Square Kilometre Array), making cosmological information unrecoverable without foreground subtraction. The situation is somewhat improved at lower redshifts, where the redshift-dependent mapping from observed coordinates to cosmological coordinates significantly reduces the size of the wedge. Using only foreground avoidance, we find that a large experiment like Canadian Hydrogen Intensity Mapping Experiment can place non-trivial constraints on cosmological parameters.

Constraining the epoch of reionization with the variance statistic: simulations of the LOFAR case

Several experiments are underway to detect the cosmic redshifted 21-cm signal from neutral hydrogen from the Epoch of Reionization (EoR). Due to their very low signal-to-noise ratio, these observations aim for a statistical detection of the signal by measuring its power spectrum. We investigate the extraction of the variance of the signal as a first step towards detecting and constraining the global history of the EoR. Signal variance is the integral of the signal's power spectrum, and it is expected to be measured with a high significance. We demonstrate this through results from a simulation and parameter estimation pipeline developed for the Low Frequency Array (LOFAR)-EoR experiment. We show that LOFAR should be able to detect the EoR in 600 hours of integration using the variance statistic. Additionally, the redshift ($z_r$) and duration ($\Delta z$) of reionization can be constrained assuming a parametrization. We use an EoR simulation of $z_r = 7.68$ and $\Delta z = 0.43$ to test the pipeline. We are able to detect the simulated signal with a significance of 4 standard deviations and extract the EoR parameters as $z_r = 7.72^{+0.37}_{-0.18}$ and $\Delta z = 0.53^{+0.12}_{-0.23}$ in 600 hours, assuming that systematic errors can be adequately controlled. We further show that the significance of detection and constraints on EoR parameters can be improved by measuring the cross-variance of the signal by cross-correlating consecutive redshift bins.

OPENING THE 21 cm EPOCH OF REIONIZATION WINDOW: MEASUREMENTS OF FOREGROUND ISOLATION WITH PAPER

We present new observations with the Precision Array for Probing the Epoch of Reionization (PAPER) with the aim of measuring the properties of foreground emission for 21cm Epoch of Reionization experiments at 150 MHz. We focus on the footprint of the foregrounds in cosmological Fourier space to understand which modes of the 21cm power spectrum will most likely be compromised by foreground emission. These observations confirm predictions that foregrounds can be isolated to a "wedge"-like region of 2D (k-perpendicular, k-parallel)-space, creating a window for cosmological studies at higher k-parallel values. We also find that the emission extends past the nominal edge of this wedge due to spectral structure in the foregrounds, with this feature most prominent on the shortest baselines. Finally, we filter the data to retain only this "unsmooth" emission and image specific k-parallel modes of it. The resultant images show an excess of power at the lowest modes, but no emission can be clearly localized to any one region of the sky. This image is highly suggestive that the most problematic foregrounds for 21cm EoR studies will not be easily identifiable bright sources, but rather an aggregate of fainter emission.

THE IMPACT OF POINT-SOURCE SUBTRACTION RESIDUALS ON 21 cm EPOCH OF REIONIZATION ESTIMATION

Precise subtraction of foreground sources is crucial for detecting and estimating 21cm HI signals from the Epoch of Reionization (EoR). We quantify how imperfect point source subtraction due to limitations of the measurement dataset yields structured residual signal in the dataset. We use the Cramer-Rao lower bound, as a metric for quantifying the precision with which a parameter may be measured, to estimate the residual signal in a visibility dataset due to imperfect point source subtraction. We then propagate these residuals into two metrics of interest for 21cm EoR experiments - the angular and two-dimensional power spectrum - using a combination of full analytic covariant derivation, analytic variant derivation, and covariant Monte Carlo simulations. This methodology differs from previous work in two ways: (1) it uses information theory to set the point source position error, rather than assuming a global root-mean-square error, and (2) it describes a method for propagating the errors analytically, thereby obtaining the full correlation structure of the power spectra. The methods are applied to two upcoming low-frequency instruments: the Murchison Widefield Array and the Precision Array for Probing the Epoch of Reionization. In addition to the actual antenna configurations, we apply the methods to minimally-redundant and maximally-redundant configurations. We find that for peeling sources above 1 Jy, the amplitude of the residual signal, and its variance, will be smaller than the contribution from thermal noise for the observing parameters proposed for upcoming EoR experiments, and that optimal subtraction of bright point sources will not be a limiting factor for EoR parameter estimation. We then use the formalism to provide an ab initio analytic derivation motivating the 'wedge' feature in the two-dimensional power spectrum, complementing previous discussion in the literature.

Power spectrum extraction for redshifted 21-cm Epoch of Reionization experiments: the LOFAR case

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 hours 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.