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We present an analysis of Epoch of Reionization (EoR) data from Phase II of the Murchison Widefield Array using the simpleds delay spectrum pipeline. Prior work analysed the same observations using the fhd/εppsilon imaging pipeline, and so the present analysis represents the first time that both principal types of 21 cm cosmology power spectrum estimation approaches have been applied to the same data set. Our limits on the 21 cm power spectrum amplitude span a range in k space of $|k| \lt 1 \, h_{100}\, {\rm Mpc}^{-1}$ with a lowest measurement of Δ2(k) ≤ 4.58 × 103 mK2 at $k = 0.190\, h_{100}\, \rm {Mpc}^{-1}$ and z = 7.14. In order to achieve these limits, we need to mitigate a previously unidentified common mode systematic in the data set. If not accounted for, this systematic introduces an overall negative bias that can make foreground contaminated measurements appear as stringent, noise-limited constraints on the 21 cm signal amplitude. The identification of this systematic highlights the risk in modelling systematics as positive-definite contributions to the power spectrum and in ‘conservatively’ interpreting all measurements as upper limits.

Measurements of the one-point probability distribution function and higher-order moments (variance, skewness, and kurtosis) of the high-redshift 21-cm fluctuations are among the most direct statistical probes of the non-Gaussian nature of structure formation and evolution during re-ionization. However, contamination from astrophysical foregrounds and instrument systematics pose significant challenges in measuring these statistics in real observations. In this work, we use forward modelling to investigate the feasibility of measuring 21-cm one-point statistics through a foreground avoidance strategy. Leveraging the characteristic wedge-shape of the foregrounds in k-space, we apply a wedge-cut filtre that removes the foreground contaminated modes from a mock data set based on the Hydrogen Epoch of Re-ionization Array (HERA) instrument, and measure the one-point statistics from the image-space representation of the remaining non-contaminated modes. We experiment with varying degrees of wedge-cutting over different frequency bandwidths and find that the centre of the band is the least susceptible to bias from wedge-cutting. Based on this finding, we introduce a rolling filtre method that allows reconstruction of an optimal wedge-cut 21-cm intensity map over the full bandwidth using outputs from wedge-cutting over multiple sub-bands. We perform Monte Carlo simulations to show that HERA should be able to measure the risemore »in skewness and kurtosis near the end of re-ionization with the rolling wedge-cut method if foreground leakage from the Fourier transform window function can be controlled.

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-HERAmore »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.

Low-frequency radio observatories are reaching unprecedented levels of sensitivity in an effort to detect the 21 cm signal from the Cosmic Dawn. High precision is needed because the expected signal is overwhelmed by foreground contamination, largely from so-called diffuse emission—a nonlocalized glow comprising Galactic synchrotron emission and radio galaxies. The impact of this diffuse emission on observations may be better understood through detailed simulations, which evaluate the Radio Interferometry Measurement Equation (RIME) for a given instrument and sky model. Evaluating the RIME involves carrying out an integral over the full sky, which is naturally discretized for point sources but must be approximated for diffuse emission. The choice of integration scheme can introduce errors that must be understood and isolated from the instrumental effects under study. In this paper, we present several analytically defined patterns of unpolarized diffuse sky emission for which the RIME integral is manageable, yielding closed-form or series visibility functions. We demonstrate the usefulness of these RIME solutions for validation by comparing them to simulated data and show that the remaining differences behave as expected with varied sky resolution and baseline orientation and length.

We present a broad-band map of polarized diffuse emission at 167–198 MHz developed from data from the Murchison Widefield Array (MWA). The map is designed to improve visibility simulation and precision calibration for 21 cm Epoch of Reionization (EoR) experiments. It covers a large swath – 11 000 sq. deg. – of the Southern hemisphere sky in all four Stokes parameters and captures emission on angular scales of 1–9°. The band-averaged diffuse structure is pre-dominantly unpolarized but has significant linearly polarized structure near RA  = 0 h. We evaluate the accuracy of the map by combining it with the GLEAM catalogue and simulating an observation from the MWA, demonstrating that the accuracy of the short baselines (6.1–50 wavelengths) now approaches the accuracy of the longer baselines typically used for EoR calibration. We discuss how to use the map for visibility simulation for a variety of interferometric arrays. The map has potential to improve calibration accuracy for experiments such as the Hydrogen Epoch of Reionization Array and the forthcoming Square Kilometre Array as well as the MWA.

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 usingmore »visibility intensities, or related.

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 themore »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.

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.

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 relationshipmore »between soft X-ray luminosity and star formation and thus requires heating driven by evolved low-metallicity stars.

Motivated by the desire for wide-field images with well-defined statistical properties for 21 cm cosmology, we implement an optimal mapping pipeline that computes a maximum likelihood estimator for the sky using the interferometric measurement equation. We demonstrate this “direct optimal mapping” with data from the Hydrogen Epoch of Reionization (HERA) Phase I observations. After validating the pipeline with simulated data, we develop a maximum likelihood figure-of-merit for comparing four sky models at 166 MHz with a bandwidth of 100 kHz. The HERA data agree with the GLEAM catalogs to < 10%. After subtracting the GLEAM point sources, the HERA data discriminate between the different continuum sky models, providing most support for the model of Byrne et al. We report the computation cost for mapping the HERA Phase I data and project the computation for the HERA 320-antenna data; both are feasible with a modern server. The algorithm is broadly applicable to other interferometers and is valid for wide-field and noncoplanar arrays.