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Abstract Measuring one-point statistics in redshifted 21 cm intensity maps offers an opportunity to explore non-Gaussian features of the early Universe. We assess the impact of instrumental effects on measurements made with the Hydrogen Epoch of Reionization Array (HERA) by forward modeling observational and simulation data. Using HERA Phase I observations over 94 nights, we examine the second (m₂, variance) and third (m₃) moments of images. We employ theDAYENU-filtering method for foreground removal and reduce simulated foreground residuals to 10% of the 21 cm signal residuals. In noiseless cosmological simulations, the amplitudes of one-point statistics measurements are significantly reduced by the instrument response and further reduced by wedge-filtering. Analyses with wedge-filtered observational data, along with expected noise simulations, show that systematics alter the probability distribution of the map pixels. A likelihood analysis based on the observational data showsm₂measurements disfavor the cold reionization model characterized by inefficient X-ray heating, in line with other power spectra measurements. Small signals inm₃due to the instrument response of the Phase I observation and wedge-filtering make it challenging to use these non-Gaussian statistics to explore model parameters. Forecasts with the full HERA array predict high signal-to-noise ratios form₂,m₃, andS₃assuming no foregrounds, but wedge-filtering drastically reduces these ratios. This work demonstrates conclusively that a comprehensive understanding of instrumental effects onm₂andm₃is essential for their use as a cosmological probe, given their dependence on the underlying model. 

ABSTRACT Interferometric experiments designed to detect the highly redshifted 21-cm signal from neutral hydrogen are producing increasingly stringent constraints on the 21-cm power spectrum, but some k-modes remain systematics-dominated. Mutual coupling is a major systematic that must be overcome in order to detect the 21-cm signal, and simulations that reproduce effects seen in the data can guide strategies for mitigating mutual coupling. In this paper, we analyse 12 nights of data from the Hydrogen Epoch of Reionization Array and compare the data against simulations that include a computationally efficient and physically motivated semi-analytic treatment of mutual coupling. We find that simulated coupling features qualitatively agree with coupling features in the data; however, coupling features in the data are brighter than the simulated features, indicating the presence of additional coupling mechanisms not captured by our model. We explore the use of fringe-rate filters as mutual coupling mitigation tools and use our simulations to investigate the effects of mutual coupling on a simulated cosmological 21-cm power spectrum in a ‘worst case’ scenario where the foregrounds are particularly bright. We find that mutual coupling contaminates a large portion of the ‘EoR Window’, and the contamination is several orders-of-magnitude larger than our simulated cosmic signal across a wide range of cosmological Fourier modes. While our fiducial fringe-rate filtering strategy reduces mutual coupling by roughly a factor of 100 in power, a non-negligible amount of coupling cannot be excised with fringe-rate filters, so more sophisticated mitigation strategies are required. 

ABSTRACT Observations of 21 cm line from neutral hydrogen promise to be an exciting new probe of astrophysics and cosmology during the Cosmic Dawn and through the Epoch of Reionization (EoR) to when dark energy accelerates the expansion of our Universe. At each of these epochs, separating bright foregrounds from the cosmological signal is a primary challenge that requires exquisite calibration. In this paper, we present a new calibration method called nucal that extends redundant-baseline calibration, allowing spectral variation in antenna responses to be solved for by using correlations between visibilities measuring the same angular Fourier modes at different frequencies. By modelling the chromaticity of the beam-weighted sky with a tunable set of discrete prolate spheroidal sequences, we develop a calibration loop that optimizes for spectrally smooth calibrated visibilities. Crucially, this technique does not require explicit models of the sky or the primary beam. With simulations that incorporate realistic source and beam chromaticity, we show that this method solves for unsmooth bandpass features, exposes narrow-band interference systematics, and suppresses smooth-spectrum foregrounds below the level of 21 cm reionization models, even within much of the so-called wedge region where current foreground mitigation techniques struggle. We show that this foreground subtraction can be performed with minimal cosmological signal loss for certain well-sampled angular Fourier modes, making spectral-redundant calibration a promising technique for current and next-generation 21 cm intensity mapping experiments. 

ABSTRACT To mitigate the effects of Radio Frequency Interference (RFI) on the data analysis pipelines of 21 cm interferometric instruments, numerous inpaint techniques have been developed. In this paper, we examine the qualitative and quantitative errors introduced into the visibilities and power spectrum due to inpainting. We perform our analysis on simulated data as well as real data from the Hydrogen Epoch of Reionization Array (HERA) Phase 1 upper limits. We also introduce a convolutional neural network that is capable of inpainting RFI corrupted data. We train our network on simulated data and show that our network is capable of inpainting real data without requiring to be retrained. We find that techniques that incorporate high wavenumbers in delay space in their modelling are best suited for inpainting over narrowband RFI. We show that with our fiducial parameters discrete prolate spheroidal sequences (dpss) and clean provide the best performance for intermittent RFI while Gaussian progress regression (gpr) and least squares spectral analysis (lssa) provide the best performance for larger RFI gaps. However, we caution that these qualitative conclusions are sensitive to the chosen hyperparameters of each inpainting technique. We show that all inpainting techniques reliably reproduce foreground dominated modes in the power spectrum. Since the inpainting techniques should not be capable of reproducing noise realizations, we find that the largest errors occur in the noise dominated delay modes. We show that as the noise level of the data comes down, clean and dpss are most capable of reproducing the fine frequency structure in the visibilities. 

ABSTRACT Radio interferometers aiming to measure the power spectrum of the redshifted 21 cm line during the Epoch of Reionization (EoR) need to achieve an unprecedented dynamic range to separate the weak signal from overwhelming foreground emissions. Calibration inaccuracies can compromise the sensitivity of these measurements to the effect that a detection of the EoR is precluded. An alternative to standard analysis techniques makes use of the closure phase, which allows one to bypass antenna-based direction-independent calibration. Similarly to standard approaches, we use a delay spectrum technique to search for the EoR signal. Using 94 nights of data observed with Phase I of the Hydrogen Epoch of Reionization Array (HERA), we place approximate constraints on the 21 cm power spectrum at z = 7.7. We find at 95 per cent confidence that the 21 cm EoR brightness temperature is ≤(372)2 ‘pseudo’ mK2 at 1.14 ‘pseudo’ h Mpc−1, where the ‘pseudo’ emphasizes that these limits are to be interpreted as approximations to the actual distance scales and brightness temperatures. Using a fiducial EoR model, we demonstrate the feasibility of detecting the EoR with the full array. Compared to standard methods, the closure phase processing is relatively simple, thereby providing an important independent check on results derived using visibility intensities, or related. 

ABSTRACT We present a Bayesian jackknife test for assessing the probability that a data set contains biased subsets, and, if so, which of the subsets are likely to be biased. The test can be used to assess the presence and likely source of statistical tension between different measurements of the same quantities in an automated manner. Under certain broadly applicable assumptions, the test is analytically tractable. We also provide an open-source code, chiborg, that performs both analytic and numerical computations of the test on general Gaussian-distributed data. After exploring the information theoretical aspects of the test and its performance with an array of simulations, we apply it to data from the Hydrogen Epoch of Reionization Array (HERA) to assess whether different sub-seasons of observing can justifiably be combined to produce a deeper 21 cm power spectrum upper limit. We find that, with a handful of exceptions, the HERA data in question are statistically consistent and this decision is justified. We conclude by pointing out the wide applicability of this test, including to CMB experiments and the H0 tension. 

ABSTRACT Cross-correlating 21cm and Lyα intensity maps of the Epoch of Reionization promises to be a powerful tool for exploring the properties of the first galaxies. Next-generation intensity mapping experiments such as the Hydrogen Epoch of Reionization Array (HERA) and SPHEREx will individually probe reionization through the power spectra of the 21cm and Lyα lines respectively, but will be limited by bright foregrounds and instrumental systematics. Cross-correlating these measurements could reduce systematics, potentially tightening constraints on the inferred astrophysical parameters. In this study, we present forecasts of cross-correlation taking into account the effects of exact uv-sampling and foreground filtering to estimate the feasibility of HERAxSPHEREx making a detection of the 21cm-Lyα cross-power spectrum. We also project the sensitivity of a cross-power spectrum between HERA and the proposed next-generation Cosmic Dawn Intensity Mapper. By isolating the sources of uncertainty, we explore the impacts of experimental limitations such as foreground filtering and Lyα thermal noise uncertainty have on making a detection of the cross-power spectrum. We then implement this strategy in a simulation of the cross-power spectrum and observational error to identify redshifts where fiducial 21cmFAST models predict the highest signal-to-noise detection (z ∼ 8). We conclude that detection of the SPHEREx-HERA cross-correlation will require an optimistic level of 21cm foreground filtering, as well as deeper thermal noise integrations due to a lack of overlapping sensitive modes but for CDIM with its larger range of scales and lower noise forecast detection levels, may be possible even with stricter 21cm foreground filtering. 

ABSTRACT Combining the visibilities measured by an interferometer to form a cosmological power spectrum is a complicated process. In a delay-based analysis, the mapping between instrumental and cosmological space is not a one-to-one relation. Instead, neighbouring modes contribute to the power measured at one point, with their respective contributions encoded in the window functions. To better understand the power measured by an interferometer, we assess the impact of instrument characteristics and analysis choices on these window functions. Focusing on the Hydrogen Epoch of Reionization Array (HERA) as a case study, we find that long-baseline observations correspond to enhanced low-k tails of the window functions, which facilitate foreground leakage, whilst an informed choice of bandwidth and frequency taper can reduce said tails. With simple test cases and realistic simulations, we show that, apart from tracing mode mixing, the window functions help accurately reconstruct the power spectrum estimator of simulated visibilities. The window functions depend strongly on the beam chromaticity and less on its spatial structure – a Gaussian approximation, ignoring side lobes, is sufficient. Finally, we investigate the potential of asymmetric window functions, down-weighting the contribution of low-k power to avoid foreground leakage. The window functions presented here correspond to the latest HERA upper limits for the full Phase I data. They allow an accurate reconstruction of the power spectrum measured by the instrument and will be used in future analyses to confront theoretical models and data directly in cylindrical space. 

Abstract We report the most sensitive upper limits to date on the 21 cm epoch of reionization power spectrum using 94 nights of observing with Phase I of the Hydrogen Epoch of Reionization Array (HERA). Using similar analysis techniques as in previously reported limits, we find at 95% confidence that Δ²(k= 0.34hMpc⁻¹) ≤ 457 mK²atz= 7.9 and that Δ²(k= 0.36hMpc⁻¹) ≤ 3496 mK²atz= 10.4, an improvement by a factor of 2.1 and 2.6, respectively. These limits are mostly consistent with thermal noise over a wide range ofkafter our data quality cuts, despite performing a relatively conservative analysis designed to minimize signal loss. Our results are validated with both statistical tests on the data and end-to-end pipeline simulations. We also report updated constraints on the astrophysics of reionization and the cosmic dawn. Using multiple independent modeling and inference techniques previously employed by HERA Collaboration, we find that the intergalactic medium must have been heated above the adiabatic cooling limit at least as early asz= 10.4, ruling out a broad set of so-called “cold reionization” scenarios. If this heating is due to high-mass X-ray binaries during the cosmic dawn, as is generally believed, our result’s 99% credible interval excludes the local relationship between soft X-ray luminosity and star formation and thus requires heating driven by evolved low-metallicity stars. 

Abstract Recently, the Hydrogen Epoch of Reionization Array (HERA) has produced the experiment’s first upper limits on the power spectrum of 21 cm fluctuations atz∼ 8 and 10. Here, we use several independent theoretical models to infer constraints on the intergalactic medium (IGM) and galaxies during the epoch of reionization from these limits. We find that the IGM must have been heated above the adiabatic-cooling threshold byz∼ 8, independent of uncertainties about IGM ionization and the radio background. Combining HERA limits with complementary observations constrains the spin temperature of thez∼ 8 neutral IGM to 27 K $〈{\overline{T}}_S〉$630 K (2.3 K $〈{\overline{T}}_S〉$640 K) at 68% (95%) confidence. They therefore also place a lower bound on X-ray heating, a previously unconstrained aspects of early galaxies. For example, if the cosmic microwave background dominates thez∼ 8 radio background, the new HERA limits imply that the first galaxies produced X-rays more efficiently than local ones. Thez∼ 10 limits require even earlier heating if dark-matter interactions cool the hydrogen gas. If an extra radio background is produced by galaxies, we rule out (at 95% confidence) the combination of high radio and low X-ray luminosities ofL_r,ν/SFR > 4 × 10²⁴W Hz⁻¹ $M_{\odot }^{-1}$yr andL_X/SFR < 7.6 × 10³⁹erg s⁻¹ $M_{\odot }^{-1}$yr. The new HERA upper limits neither support nor disfavor a cosmological interpretation of the recent Experiment to Detect the Global EOR Signature (EDGES) measurement. The framework described here provides a foundation for the interpretation of future HERA results.