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  1. Abstract We report upper limits on the Epoch of Reionization 21 cm power spectrum at redshifts 7.9 and 10.4 with 18 nights of data (∼36 hr of integration) from Phase I of the Hydrogen Epoch of Reionization Array (HERA). The Phase I data show evidence for systematics that can be largely suppressed with systematic models down to a dynamic range of ∼10 9 with respect to the peak foreground power. This yields a 95% confidence upper limit on the 21 cm power spectrum of Δ 21 2 ≤ ( 30.76 ) 2 mK 2 at k = 0.192 h Mpc −1 at z = 7.9, and also Δ 21 2 ≤ ( 95.74 ) 2 mK 2 at k = 0.256 h Mpc −1 at z = 10.4. At z = 7.9, these limits are the most sensitive to date by over an order of magnitude. While we find evidence for residual systematics at low line-of-sight Fourier k ∥ modes, at high k ∥ modes we find our data to be largely consistent with thermal noise, an indicator that the system could benefit from deeper integrations. The observed systematics could be due to radio frequency interference, cable subreflections, or residual instrumental cross-coupling, and warrant further study. This analysis emphasizes algorithms that have minimal inherent signal loss, although we do perform a careful accounting in a companion paper of the small forms of loss or bias associated with the pipeline. Overall, these results are a promising first step in the development of a tuned, instrument-specific analysis pipeline for HERA, particularly as Phase II construction is completed en route to reaching the full sensitivity of the experiment. 
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  2. Abstract We describe the validation of the HERA Phase I software pipeline by a series of modular tests, building up to an end-to-end simulation. The philosophy of this approach is to validate the software and algorithms used in the Phase I upper-limit analysis on wholly synthetic data satisfying the assumptions of that analysis, not addressing whether the actual data meet these assumptions. We discuss the organization of this validation approach, the specific modular tests performed, and the construction of the end-to-end simulations. We explicitly discuss the limitations in scope of the current simulation effort. With mock visibility data generated from a known analytic power spectrum and a wide range of realistic instrumental effects and foregrounds, we demonstrate that the current pipeline produces power spectrum estimates that are consistent with known analytic inputs to within thermal noise levels (at the 2 σ level) for k > 0.2 h Mpc −1 for both bands and fields considered. Our input spectrum is intentionally amplified to enable a strong “detection” at k ∼ 0.2 h Mpc −1 —at the level of ∼25 σ —with foregrounds dominating on larger scales and thermal noise dominating at smaller scales. Our pipeline is able to detect this amplified input signal after suppressing foregrounds with a dynamic range (foreground to noise ratio) of ≳10 7 . Our validation test suite uncovered several sources of scale-independent signal loss throughout the pipeline, whose amplitude is well-characterized and accounted for in the final estimates. We conclude with a discussion of the steps required for the next round of data analysis. 
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    ABSTRACT Precision calibration poses challenges to experiments probing the redshifted 21-cm signal of neutral hydrogen from the Cosmic Dawn and Epoch of Reionization (z ∼ 30–6). In both interferometric and global signal experiments, systematic calibration is the leading source of error. Though many aspects of calibration have been studied, the overlap between the two types of instruments has received less attention. We investigate the sky based calibration of total power measurements with a HERA dish and an EDGES-style antenna to understand the role of autocorrelations in the calibration of an interferometer and the role of sky in calibrating a total power instrument. Using simulations we study various scenarios such as time variable gain, incomplete sky calibration model, and primary beam model. We find that temporal gain drifts, sky model incompleteness, and beam inaccuracies cause biases in the receiver gain amplitude and the receiver temperature estimates. In some cases, these biases mix spectral structure between beam and sky resulting in spectrally variable gain errors. Applying the calibration method to the HERA and EDGES data, we find good agreement with calibration via the more standard methods. Although instrumental gains are consistent with beam and sky errors similar in scale to those simulated, the receiver temperatures show significant deviations from expected values. While we show that it is possible to partially mitigate biases due to model inaccuracies by incorporating a time-dependent gain model in calibration, the resulting errors on calibration products are larger and more correlated. Completely addressing these biases will require more accurate sky and primary beam models. 
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  5. 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 KT¯S630 K (2.3 KT¯S640 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 ofLr,ν/SFR > 4 × 1024W Hz−1M1yr andLX/SFR < 7.6 × 1039erg s−1M1yr. 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.

     
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    ABSTRACT 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. 
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