21 cm cosmology is a promising new probe of the evolution of visible matter in our universe, especially during the poorly constrained Cosmic Dawn and Epoch of Reionization. However, in order to separate the 21 cm signal from bright astrophysical foregrounds, we need an exquisite understanding of our telescopes so as to avoid adding spectral structure to spectrally smooth foregrounds. One powerful calibration method relies on repeated simultaneous measurements of the same interferometric baseline to solve for the sky signal and for instrumental parameters simultaneously. However, certain degrees of freedom are not constrained by asserting internal consistency between redundant measurements. In this paper, we review the origin of these degeneracies of redundant-baseline calibration and demonstrate how they can source unwanted spectral structure in our measurement and show how to eliminate that additional, artificial structure. We also generalize redundant calibration to dual-polarization instruments, derive the degeneracy structure, and explore the unique challenges to calibration and preserving spectral smoothness presented by a polarized measurement.

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.

Radio frequency interference (RFI) is an ever-present limiting factor among radio telescopes even in the most remote observing locations. When looking to retain the maximum amount of sensitivity and reduce contamination for Epoch of Reionization studies, the identification and removal of RFI is especially important. In addition to improved RFI identification, we must also take into account computational efficiency of the RFI-Identification algorithm as radio interferometer arrays such as the Hydrogen Epoch of Reionization Array (HERA) grow larger in number of receivers. To address this, we present a deep fully convolutional neural network (DFCN) that is comprehensive in its use of interferometric data, where both amplitude and phase information are used jointly for identifying RFI. We train the network using simulated HERA visibilities containing mock RFI, yielding a known ‘ground truth’ data set for evaluating the accuracy of various RFI algorithms. Evaluation of the DFCN model is performed on observations from the 67 dish build-out, HERA-67, and achieves a data throughput of 1.6 × 105 HERA time-ordered 1024 channelled visibilities per hour per GPU. We determine that relative to an amplitude only network including visibility phase adds important adjacent time–frequency context which increases discrimination between RFI and non-RFI. The inclusion of phase when predicting achieves a recall of 0.81, precision of 0.58, and F2 score of 0.75 as applied to our HERA-67 observations.

Spectral structures due to the instrument response is the current limiting factor for the experiments attempting to detect the redshifted 21 cm signal from the Epoch of Reionization (EoR). Recent advances in the delay spectrum methodology for measuring the redshifted 21 cm EoR power spectrum brought new attention to the impact of an antenna’s frequency response on the viability of making this challenging measurement. The delay spectrum methodology provides a somewhat straightforward relationship between the time-domain response of an instrument that can be directly measured and the power spectrum modes accessible to a 21 cm EoR experiment. In this paper, we derive the explicit relationship between antenna reflection coefficient (S11) measurements made by a Vector Network Analyzer (VNA) and the extent of additional foreground contaminations in delay space. In the light of this mathematical framework, we examine the chromaticity of a prototype antenna element that will constitute the Hydrogen Epoch of Reionization Array (HERA) between 100 and 200 MHz. These reflectometry measurements exhibit additional structures relative to electromagnetic simulations, but we find that even without any further design improvement, such an antenna element will support measuring spatial k modes with line-of-sight components of k∥ > 0.2h Mpc− 1. We also find that when combined with the powerful inverse covariance weighting method used in optimal quadratic estimation of redshifted 21 cm power spectra the HERA prototype elements can successfully measure the power spectrum at spatial modes as low as k∥ > 0.1h Mpc− 1. This work represents a major step toward understanding the HERA antenna element and highlights a straightforward method for characterizing instrument response for future experiments designed to detect the 21 cm EoR power spectrum.

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.

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.

Characterizing the epoch of reionization (EoR) at z 6 via the redshifted 21 cm line of neutral Hydrogen (H i) is critical to modern astrophysics and cosmology, and thus a key science goal of many current and planned low-frequency radio telescopes. The primary challenge to detecting this signal is the overwhelmingly bright foreground emission at these frequencies, placing stringent requirements on the knowledge of the instruments and inaccuracies in analyses. Results from these experiments have largely been limited not by thermal sensitivity but by systematics, particularly caused by the inability to calibrate the instrument to high accuracy. The interferometric bispectrum phase is immune to antenna-based calibration and errors therein, and presents an independent alternative to detect the EoR H i fluctuations while largely avoiding calibration systematics. Here, we provide a demonstration of this technique on a subset of data from the Hydrogen Epoch of Reionization Array (HERA) to place approximate constraints on the brightness temperature of the intergalactic medium (IGM). From this limited data, at z=7.7 we infer "1σ"upper limits on the IGM brightness temperature to be ≤ 316 "pseudo"mK at κ =0.33 "pseudo"h Mpc-1 (data-limited) and ≤ 1000 "pseudo"mK at κ =0.875 "pseudo"h Mpc-1 (noise-limited). The "pseudo"units denote only an approximate and not an exact correspondence to the actual distance scales and brightness temperatures. By propagating models in parallel to the data analysis, we confirm that the dynamic range required to separate the cosmic H i signal from the foregrounds is similar to that in standard approaches, and the power spectrum of the bispectrum phase is still data-limited (at 106 dynamic range) indicating scope for further improvement in sensitivity as the array build-out continues.