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The detection of the Epoch of Reionization (EoR) delay power spectrum using a 'foreground avoidance method' highly depends on the instrument chromaticity. The systematic effects induced by the radio telescope spread the foreground signal in the delay domain, which contaminates the EoR window theoretically observable. Applied to the Hydrogen Epoch of Reionization Array (HERA), this paper combines detailed electromagnetic and electrical simulations in order to model the chromatic effects of the instrument, and quantify its frequency and time responses. In particular, the effects of the analogue receiver, transmission cables, and mutual coupling are included. These simulations are able to accurately predict the intensity of the reflections occurring in the 150-m cable which links the antenna to the backend. They also show that electromagnetic waves can propagate from one dish to another one through large sections of the array due to mutual coupling. The simulated system time response is attenuated by a factor 104 after a characteristic delay which depends on the size of the array and on the antenna position. Ultimately, the system response is attenuated by a factor 105 after 1400 ns because of the reflections in the cable, which corresponds to characterizable ka-modes above 0.7 $h\,\,\rm {Mpc}^{-1}$ at 150 MHz. Thus, this new study shows that the detection of the EoR signal with HERA Phase I will be more challenging than expected. On the other hand, it improves our understanding of the telescope, which is essential to mitigate the instrument chromaticity.

Characterizing the epoch of reionization (EoR) at z 6 via the redshifted 21 cm line of neutral Hydrogen (H i) is critical to modern astrophysics and cosmology, and thus a key science goal of many current and planned low-frequency radio telescopes. The primary challenge to detecting this signal is the overwhelmingly bright foreground emission at these frequencies, placing stringent requirements on the knowledge of the instruments and inaccuracies in analyses. Results from these experiments have largely been limited not by thermal sensitivity but by systematics, particularly caused by the inability to calibrate the instrument to high accuracy. The interferometric bispectrum phase is immune to antenna-based calibration and errors therein, and presents an independent alternative to detect the EoR H i fluctuations while largely avoiding calibration systematics. Here, we provide a demonstration of this technique on a subset of data from the Hydrogen Epoch of Reionization Array (HERA) to place approximate constraints on the brightness temperature of the intergalactic medium (IGM). From this limited data, at z=7.7 we infer "1σ"upper limits on the IGM brightness temperature to be ≤ 316 "pseudo"mK at κ =0.33 "pseudo"h Mpc-1 (data-limited) and ≤ 1000 "pseudo"mK at κ =0.875 "pseudo"h Mpc-1 (noise-limited). The "pseudo"units denote only an approximate and not an exact correspondence to the actual distance scales and brightness temperatures. By propagating models in parallel to the data analysis, we confirm that the dynamic range required to separate the cosmic H i signal from the foregrounds is similar to that in standard approaches, and the power spectrum of the bispectrum phase is still data-limited (at 106 dynamic range) indicating scope for further improvement in sensitivity as the array build-out continues.

The key challenge in the observation of the redshifted 21-cm signal from cosmic reionization is its separation from the much brighter foreground emission. Such separation relies on the different spectral properties of the two components, although, in real life, the foreground intrinsic spectrum is often corrupted by the instrumental response, inducing systematic effects that can further jeopardize the measurement of the 21-cm signal. In this paper, we use Gaussian Process Regression to model both foreground emission and instrumental systematics in ∼2 h of data from the Hydrogen Epoch of Reionization Array. We find that a simple co-variance model with three components matches the data well, giving a residual power spectrum with white noise properties. These consist of an 'intrinsic' and instrumentally corrupted component with a coherence scale of 20 and 2.4 MHz, respectively (dominating the line-of-sight power spectrum over scales kâ ≤ 0.2 h cMpc-1) and a baseline-dependent periodic signal with a period of ∼1 MHz (dominating over kâ ∼0.4-0.8 h cMpc-1), which should be distinguishable from the 21-cm Epoch of Reionization signal whose typical coherence scale is ∼0.8 MHz.

In 21-cm cosmology, precision calibration is key to the separation of the neutral hydrogen signal from very bright but spectrally smooth astrophysical foregrounds. The Hydrogen Epoch of Reionization Array (HERA), an interferometer specialized for 21-cm cosmology and now under construction in South Africa, was designed to be largely calibrated using the self-consistency of repeated measurements of the same interferometric modes. This technique, known as redundant-baseline calibration resolves most of the internal degrees of freedom in the calibration problem. It assumes, however, on antenna elements with identical primary beams placed precisely on a redundant grid. In this work, we review the detailed implementation of the algorithms enabling redundant-baseline calibration and report results with HERA data.We quantify the effects of real-world non-redundancy and how they compare to the idealized scenario in which redundant measurements differ only in their noise realizations. Finally, we study how non-redundancy can produce spurious temporal structure in our calibration solutions-both in data and in simulations-and present strategies for mitigating that structure.

Radio frequency interference (RFI) is an ever-present limiting factor among radio telescopes even in the most remote observing locations. When looking to retain the maximum amount of sensitivity and reduce contamination for Epoch of Reionization studies, the identification and removal of RFI is especially important. In addition to improved RFI identification, we must also take into account computational efficiency of the RFI-Identification algorithm as radio interferometer arrays such as the Hydrogen Epoch of Reionization Array (HERA) grow larger in number of receivers. To address this, we present a deep fully convolutional neural network (DFCN) that is comprehensive in its use of interferometric data, where both amplitude and phase information are used jointly for identifying RFI. We train the network using simulated HERA visibilities containing mock RFI, yielding a known ‘ground truth’ data set for evaluating the accuracy of various RFI algorithms. Evaluation of the DFCN model is performed on observations from the 67 dish build-out, HERA-67, and achieves a data throughput of 1.6 × 105 HERA time-ordered 1024 channelled visibilities per hour per GPU. We determine that relative to an amplitude only network including visibility phase adds important adjacent time–frequency context which increases discrimination between RFI and non-RFI. The inclusion of phase when predicting achieves a recall of 0.81, precision of 0.58, and F2 score of 0.75 as applied to our HERA-67 observations.

Foreground power dominates the measurements of interferometers that seek a statistical detection of highly-redshifted H i emission from the Epoch of Reionization (EoR). The chromaticity of the instrument creates a boundary in the Fourier transform of frequency (proportional to k ∥) between spectrally smooth emission, characteristic of the strong synchrotron foreground (the "wedge"), and the spectrally structured emission from H i in the EoR (the "EoR window"). Faraday rotation can inject spectral structure into otherwise smooth polarized foreground emission, which through instrument effects or miscalibration could possibly pollute the EoR window. For instruments pursuing a "foreground avoidance" strategy of simply measuring in the EoR window, and not attempting to model and remove foregrounds, as is the plan for the first stage of the Hydrogen Epoch of Reionization Array (HERA), characterizing the intrinsic instrument polarization response is particularly important. Using data from the HERA 19-element commissioning array, we investigate the polarization response of this new instrument in the power-spectrum domain. We perform a simple image-based calibration based on the unpolarized diffuse emission of the Global Sky Model, and show that it achieves qualitative redundancy between the nominally redundant baselines of the array and reasonable amplitude accuracy. We construct power spectra of all fully polarized coherencies in all pseudo-Stokes parameters, and discuss the achieved isolation of foreground power due to the intrinsic spectral smoothness of the foregrounds, the instrument chromaticity, and the calibration. We compare to simulations based on an unpolarized diffuse sky model and detailed electromagnetic simulations of the dish and feed, confirming that in Stokes I, the calibration does not add significant spectral structure beyond that expected from the interferometer array configuration and the modeled primary beam response. Furthermore, this calibration is stable over the 8 days of observations considered. Excess power is seen in the power spectra of the linear polarization Stokes parameters, which is not easily attributable to leakage via the primary beam, and results from some combination of residual calibration errors and actual polarized emission. Stokes V is found to be highly discrepant from the expectation of zero power, strongly pointing to the need for more accurate polarized calibration.

In this erratum, we retract the upper limits on the 21 cm power spectrum presented in the published article. The published article reported an upper limit on δ 212(k ) of (22.4 mK)2 at z= 8.4 in the range 0.15 < k < 0.5h Mpc-1. This analysis underestimated the level of signal loss, or attenuation of the target cosmological 21 cm signal associated with the chosen power spectrum estimator, and also underestimated the statistical error on those estimates. A revised result, with a new analysis, is presented in M. K. Kolopanis et al. (2018, in preparation). Below, we briefly summarize the errors in the original analysis and how they are corrected. For an indepth analysis and discussion of the errors, we refer the reader to Cheng et al. (2018). Signal loss was expected in the original analysis because the covariance matrices, C, used to weight the un-normalized bandpower estimates, qa, in (Formula Presented) were empirically estimated from a time-averaged finite ensemble of the data, x, such that (Formula Presented). While the true covariance C leads to an inherently unbiased lossless estimator of the power spectrum, using an empirically estimated Ĉ can lead to signal loss. Specifically, weighting data by an empirically estimated covariance carries the risk of overfitting and downweighting EoR fluctuations that are coupled to the data. In Cheng et al. (2018), it is shown that these couplings are especially strong in the fringe-rate filtered PAPER-64 data set. The first and most impactful error relates to the method by which signal loss was estimated. To assess signal loss from the empirically estimated covariance matrix, different realizations of mock cosmological signals e of known amplitudes are added to the original data to form a new data vector, (Formula Presented). New covariance matrices, (Formula Presented) are used to estimate un-normalized bandpowers (Formula Presented), which can be written as (Formula Presented). The normalized power estimate can then be compared to the known injected power in e to estimate signal loss. The key error in the previous analysis was to assume that, since e was statistically independent of x, that the two middle crossterms in Equation (2) would average to zero in an ensemble. However, as shown in Cheng et al. (2018) and Switzer et al. (2015), these cross-terms can contain significant negative power because Ĉr contains information that correlates the two vectors. Ignoring these cross-terms leads to a significant underestimate of signal loss. As a result, we presented negligible signal loss in our original analysis, when in fact approximately 99.99% of the signal was removed (Cheng et al. 2018). Correcting for the actual signal loss is the biggest factor revising the upper limit on 21 D2 . The second mistake made in the original analysis was to underestimate the statistical errors in the reported power spectrum estimates. The original analysis used a bootstrap resampling technique on power spectral measurements over the baseline and time axes. However, fringe-rate filtering introduces significant correlations in the data along the time axis. As is discussed in Cheng et al. (2018), bootstrapping across correlated samples can result in a significant underestimate of the variation in the data if the number of resamplings is not equal to the number of independent samples in the data, as in the case of the original analysis. The error bars associated with this oversampling were underestimated by approximately a factor of 2 (in mK). The revised analysis in M. K. Kolopanis et al. (2018, in preparation) only applies bootstrap resampling across the baseline axis to avoid this problem. The mistake in estimating the statistical errors should have become apparent when comparing results to our theoretical thermal noise sensitivity. Unfortunately, a third miscalculation was made in estimating the thermal noise sensitivity. As detailed in Cheng et al. (2018), this miscalculation stemmed from numerous small mismatches between the idealized analysis pipeline used to estimate sensitivity and the actual analysis applied to the data. As a result, our estimated thermal noise sensitivity was approximately a factor of 3 low (in mK), leading to the mistaken impression that our error bars were consistent with the level of thermal noise. In summary, we retract the power spectrum results shown in Figures 18 and 20 in the published article. Results that relied on the original limits, including those presented in Figure 21, are retracted. Additionally, the companion paper to the original manuscript, Pober et al. (2015), used the original limits to place constraints on the spin temperature of the intergalactic medium (IGM) at z=8.4. Our revised limits do not place significant constraints on the IGM temperature, and the results of Figure 4 from Pober et al. (2015) should be disregarded. However, we note that their analysis would still be relevant should a future experiment place constraints on the 21 cm signal similar to those claimed in the published article. An updated analysis of this same data set is presented in M. K. Kolopanis et al. (2018, in preparation), where these revised results are put into context with measurements at other redshifts.

21 cm cosmology is a promising new probe of the evolution of visible matter in our universe, especially during the poorly constrained Cosmic Dawn and Epoch of Reionization. However, in order to separate the 21 cm signal from bright astrophysical foregrounds, we need an exquisite understanding of our telescopes so as to avoid adding spectral structure to spectrally smooth foregrounds. One powerful calibration method relies on repeated simultaneous measurements of the same interferometric baseline to solve for the sky signal and for instrumental parameters simultaneously. However, certain degrees of freedom are not constrained by asserting internal consistency between redundant measurements. In this paper, we review the origin of these degeneracies of redundant-baseline calibration and demonstrate how they can source unwanted spectral structure in our measurement and show how to eliminate that additional, artificial structure. We also generalize redundant calibration to dual-polarization instruments, derive the degeneracy structure, and explore the unique challenges to calibration and preserving spectral smoothness presented by a polarized measurement.

Spectral structures due to the instrument response is the current limiting factor for the experiments attempting to detect the redshifted 21 cm signal from the Epoch of Reionization (EoR). Recent advances in the delay spectrum methodology for measuring the redshifted 21 cm EoR power spectrum brought new attention to the impact of an antenna’s frequency response on the viability of making this challenging measurement. The delay spectrum methodology provides a somewhat straightforward relationship between the time-domain response of an instrument that can be directly measured and the power spectrum modes accessible to a 21 cm EoR experiment. In this paper, we derive the explicit relationship between antenna reflection coefficient (S11) measurements made by a Vector Network Analyzer (VNA) and the extent of additional foreground contaminations in delay space. In the light of this mathematical framework, we examine the chromaticity of a prototype antenna element that will constitute the Hydrogen Epoch of Reionization Array (HERA) between 100 and 200 MHz. These reflectometry measurements exhibit additional structures relative to electromagnetic simulations, but we find that even without any further design improvement, such an antenna element will support measuring spatial k modes with line-of-sight components of k∥ > 0.2h Mpc− 1. We also find that when combined with the powerful inverse covariance weighting method used in optimal quadratic estimation of redshifted 21 cm power spectra the HERA prototype elements can successfully measure the power spectrum at spatial modes as low as k∥ > 0.1h Mpc− 1. This work represents a major step toward understanding the HERA antenna element and highlights a straightforward method for characterizing instrument response for future experiments designed to detect the 21 cm EoR power spectrum.

We present constraints on both the kinetic temperature of the intergalactic medium (IGM) at z = 8.4, and on models for heating the IGM at high-redshift with X-ray emission from the first collapsed objects. These constraints are derived using a semi-analytic method to explore the new measurements of the 21 cm power spectrum from the Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER), which were presented in a companion paper, Ali et al. Twenty-one cm power spectra with amplitudes of hundreds of mK2 can be generically produced if the kinetic temperature of the IGM is significantly below the temperature of the cosmic microwave background (CMB); as such, the new results from PAPER place lower limits on the IGM temperature at z = 8.4. Allowing for the unknown ionization state of the IGM, our measurements find the IGM temperature to be above ≈5 K for neutral fractions between 10% and 85%, above ≈7 K for neutral fractions between 15% and 80%, or above ≈10 K for neutral fractions between 30% and 70%. We also calculate the heating of the IGM that would be provided by the observed high redshift galaxy population, and find that for most models, these galaxies are sufficient to bring the IGM temperature above our lower limits. However, there are significant ranges of parameter space that could produce a signal ruled out by the PAPER measurements; models with a steep drop-off in the star formation rate density at high redshifts or with relatively low values for the X-ray to star formation rate efficiency of high redshift galaxies are generally disfavored. The PAPER measurements are consistent with (but do not constrain) a hydrogen spin temperature above the CMB temperature, a situation which we find to be generally predicted if galaxies fainter than the current detection limits of optical/NIR surveys are included in calculations of X-ray heating.

In this paper, we report new limits on 21 cm emission from cosmic reionization based on a 135 day observing campaign with a 64-element deployment of the Donald C. Backer Precision Array for Probing the Epoch of Reionization in South Africa. This work extends the work presented in Parsons et al. with more collecting area, a longer observing period, improved redundancy-based calibration, improved fringe-rate filtering, and updated power-spectral analysis using optimal quadratic estimators. The result is a new 2σ upper limit on Δ2(k) of (22.4 mK)2 in the range < k < 0.5h Mpc-1 at z = 8.4. This represents a three-fold improvement over the previous best upper limit. As we discuss in more depth in a forthcoming paper, this upper limit supports and extends previous evidence against extremely cold reionization scenarios. We conclude with a discussion of implications for future 21 cm reionization experiments, including the newly funded Hydrogen Epoch of Reionization Array.