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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.

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.

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.

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.

Observations with radio arrays that target the 21-cm signal originating from the early Universe suffer from a variety of systematic effects. An important class of these is reflections and spurious couplings between antennas. We apply a Hamiltonian Monte Carlo sampler to the modelling and mitigation of these systematics in simulated Hydrogen Epoch of Reionization Array (HERA) data. This method allows us to form statistical uncertainty estimates for both our models and the recovered visibilities, which is an important ingredient in establishing robust upper limits on the epoch of reionization (EoR) power spectrum. In cases where the noise is large compared to the EoR signal, this approach can constrain the systematics well enough to mitigate them down to the noise level for both systematics studied. Incoherently averaging the recovered power spectra can further reduce the noise and improve recovery. Where the noise level is lower than the EoR, our modelling can mitigate the majority of the reflections and coupling with there being only a minor level of residual systematics. Our approach performs similarly to existing filtering/fitting techniques used in the HERA pipeline, but with the added benefit of rigorously propagating uncertainties. In all cases it does not significantly attenuate the underlying signal. [ABSTRACT FROM AUTHOR]

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.

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 H 0 tension. [ABSTRACT FROM AUTHOR]

Observation of redshifted 21-cm signal from the Epoch of Reionization (EoR) is challenging due to contamination from the bright foreground sources that exceed the signal by several orders of magnitude. Removal of this very high foreground relies on accurate calibration to keep the intrinsic property of the foreground with frequency. Commonly employed calibration techniques for these experiments are the sky model-based and the redundant baseline-based calibration approaches, which can suffer from sky-modelling error and array redundancy imperfection respectively. In this work, we introduce the hybrid correlation calibration (CorrCal) scheme, which aims to bridge the gap between redundant and sky-based calibration by relaxing redundancy of the array and including sky information into the calibration formalisms. We apply the CorrCal to the data of Precision Array for Probing the Epoch of Reionization (PAPER) experiment, which was pre-calibrated using redundant baseline calibration. We show about |$6\%$| suppression at the bin right on the horizon limit of the foreground wedge-like structure, relative to the pre-calibrated power spectra. This small improvement of the foreground power spectra around the wedge limit could be suggestive of reduced spectral structure in the data after CorrCal calibration, which lays the foundation for future improvement of the calibration algorithm and implementation method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 k ∥-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. [ABSTRACT FROM AUTHOR]