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Through a very careful analysis Kolopanis and collaborators identified a negative power spectrum (PS) systematic. The 21 cm cosmology community has assumed that any observational systematics would add power, as negative PS are non-physical. In addition to the mystery of their origin, negative PS systematics raise the spectre of artificially lowering upper limits on the 21 cm PS. It appears that the source of the negative PS systematics is a subtle interaction between choices in how the PS estimate is calculated and baseline-dependent systematic power. In this paper, we present a statistical model of baseline dependent systematics to explore how negative PS systematics can appear and their statistical characteristics. This leads us to recommendations on when and how to consider negative PS systematics when reporting observational 21 cm cosmology upper limits.

We explore how chromatic radio frequency interference (RFI) flags affect 21-cm power spectrum measurements. We particularly study flags that are coarser than the analysis resolution. We find that such RFI flags produce excess power in the EoR window in much the same way as residual RFI. We use Fast Holographic Deconvolution (fhd) simulations to explain this as a result of chromatic disruptions in the interferometric sampling function of the array. We also use these simulations in conjunction with Error Propagated Power Spectrum with InterLeaved Observed Noise to show that without modifying current flagging strategies or implementing extremely accurate and complete foreground subtraction, 21-cm EoR experiments will fail to make a significant detection. As a mitigation strategy, we find that circumventing the chromatic structure altogether by flagging the entire analysis band when RFI is detected is simple to implement and highly successful. This demands a detection strategy with a low false-positive rate in order to prevent excessive data loss.

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.

ABSTRACT Calibration precision is currently a limiting systematic in 21 cm cosmology experiments. While there are innumerable calibration approaches, most can be categorized as either ‘sky-based,’ relying on an extremely accurate model of astronomical foreground emission, or ‘redundant,’ requiring a precisely regular array with near-identical antenna response patterns. Both of these classes of calibration are inflexible to the realities of interferometric measurement. In practice, errors in the foreground model, antenna position offsets, and beam response inhomogeneities degrade calibration performance and contaminate the cosmological signal. Here, we show that sky-based and redundant calibration can be unified into a highly general and physically motivated calibration framework based on a Bayesian statistical formalism. Our new framework includes sky-based and redundant calibration as special cases but can additionally support relaxing the rigid assumptions implicit in those approaches. We present simulation results demonstrating that, in a simple case, working in an intermediate regime between sky-based and redundant calibration improves calibration performance. Our framework is highly general and encompasses novel calibration approaches including techniques for calibrating compact non-redundant arrays, calibrating to incomplete sky models, and constraining calibration solutions across frequency.

ABSTRACT We quantify the effect of radio frequency interference (RFI) on measurements of the 21-cm power spectrum during the Epoch of Reionization (EoR). Specifically, we investigate how the frequency structure of RFI source emission generates contamination in higher order wave modes, which is much more problematic than smooth-spectrum foreground sources. Using a relatively optimistic EoR model, we find that even a single relatively dim RFI source can overwhelm the EoR power spectrum signal of $\sim 10\, {\rm mK}^2$ for modes $0.1 \ \lt k \lt 2 \, h\, {\rm Mpc}^{-1}$. If the total apparent RFI flux density in the final power spectrum integration is kept below 1 mJy, an EoR signal resembling this optimistic model should be detectable for modes $k \lt 0.9\, h\, {\rm Mpc}^{-1}$, given no other systematic contaminants and an error tolerance as high as 10 per cent. More pessimistic models will be more restrictive. These results emphasize the need for highly effective RFI mitigation strategies for telescopes used to search for the EoR.

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.

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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.

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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.

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