Direct Optimal Mapping Image Power Spectrum and its Window Functions

The key to detecting neutral hydrogen during the epoch of reionization (EoR) is to separate the cosmological signal from the dominating foreground radiation. We developed direct optimal mapping (Xu et al. 2022) to map interferometric visibilities; it contains only linear operations, with full knowledge of point spread functions from visibilities to images. Here we present an FFT-based image power spectrum and its window functions based on direct optimal mapping. We use noiseless simulation, based on the Hydrogen Epoch of Reionization Array (HERA) Phase I configuration, to study the image power spectrum properties. The window functions show $<10^{-11}$ power leakage from the foreground-dominated region into the EoR window; the 2D and 1D power spectra also verify the separation between the foregrounds and the EoR. Furthermore, we simulated visibilities from a $uv$-complete array and calculated its image power spectrum. The result shows that the foreground--EoR leakage is further suppressed below $10^{-12}$, dominated by the tapering function sidelobes; the 2D power spectrum does not show signs of the horizon wedge. The $uv$-complete result provides a reference case for future 21cm cosmology array designs.Comment: Submitted to Ap

Bayesian jackknife tests with a small number of subsets: Application to HERA 21cm power spectrum upper limits

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

Direct Optimal Mapping for 21cm Cosmology: A Demonstration with the Hydrogen Epoch of Reionization Array

Motivated by the desire for wide-field images with well-defined statistical properties for 21cm 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 166MHz with a bandwidth of 100kHz. 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. 2021. 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 non-coplanar arrays.Comment: 16 pages, 10 figures, 2 tables, published on Ap

Characterization Of Inpaint Residuals In Interferometric Measurements of the Epoch Of Reionization

Radio Frequency Interference (RFI) is one of the systematic challenges preventing 21cm interferometric instruments from detecting the Epoch of Reionization. To mitigate the effects of RFI on data analysis pipelines, numerous inpaint techniques have been developed to restore RFI corrupted data. We examine the qualitative and quantitative errors introduced into the visibilities and power spectrum due to inpainting. We perform our analysis on simulated data as well as real data from the Hydrogen Epoch of Reionization Array (HERA) Phase 1 upper limits. We also introduce a convolutional neural network that capable of inpainting RFI corrupted data in interferometric instruments. We train our network on simulated data and show that our network is capable at inpainting real data without requiring to be retrained. We find that techniques that incorporate high wavenumbers in delay space in their modeling are best suited for inpainting over narrowband RFI. We also show that with our fiducial parameters Discrete Prolate Spheroidal Sequences (DPSS) and CLEAN provide the best performance for intermittent ``narrowband'' RFI while Gaussian Progress Regression (GPR) and Least Squares Spectral Analysis (LSSA) provide the best performance for larger RFI gaps. However we caution that these qualitative conclusions are sensitive to the chosen hyperparameters of each inpainting technique. We find these results to be consistent in both simulated and real visibilities. We show that all inpainting techniques reliably reproduce foreground dominated modes in the power spectrum. Since the inpainting techniques should not be capable of reproducing noise realizations, we find that the largest errors occur in the noise dominated delay modes. We show that in the future, as the noise level of the data comes down, CLEAN and DPSS are most capable of reproducing the fine frequency structure in the visibilities of HERA data.Comment: 26 pages, 18 figure

What does an interferometer really measure? Including instrument and data characteristics in the reconstruction of the 21cm power spectrum

Combining the visibilities measured by an interferometer to form a cosmological power spectrum is a complicated process in which the window functions play a crucial role. In a delay-based analysis, the mapping between instrumental space, made of per-baseline delay spectra, 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 spectrum measured by an interferometer, we assess the impact of instrument characteristics and analysis choices on the estimator by deriving its exact window functions, outside of the delay approximation. Focusing on HERA as a case study, we find that observations made with long baselines tend to correspond to enhanced low-k tails of the window functions, which facilitate foreground leakage outside the wedge, whilst the choice of bandwidth and frequency taper can help narrow them down. With the help of simple test cases and more realistic visibility simulations, we show that, apart from tracing mode mixing, the window functions can accurately reconstruct the power spectrum estimator of simulated visibilities. We note that the window functions depend strongly on the chromaticity of the beam, 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 in this work correspond to the latest HERA upper limits for the full Phase I data. They allow an accurate reconstruction of the power spectrum measured by the instrument and can be used in future analyses to confront theoretical models and data directly in cylindrical space.Comment: 18 pages, 18 figures, submitted to MNRAS. Comments welcome

Search for the Epoch of Reionisation with HERA: Upper Limits on the Closure Phase Delay Power Spectrum

Radio interferometers aiming to measure the power spectrum of the redshifted 21 cm line during the Epoch of Reionisation (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% confidence that the 21 cm EoR brightness temperature is $\le$(372)$^2$ "pseudo" mK$^2$ at 1.14 "pseudo" $h$ Mpc$^{-1}$, where the "pseudo" emphasises 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 using visibility intensities, or related.Comment: 16 pages, 14 figures, accepted for publication by MNRA

Improved Constraints on the 21 cm EoR Power Spectrum and the X-Ray Heating of the IGM with HERA Phase I Observations

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 (HERA Collaboration 2022a), we find at 95% confidence that $\Delta^2(k = 0.34$ $h$ Mpc$^{-1}$) $\leq 457$ mK$^2$ at $z = 7.9$ and that $\Delta^2 (k = 0.36$ $h$ Mpc$^{-1}) \leq 3,496$ mK$^2$ at $z = 10.4$, an improvement by a factor of 2.1 and 2.6 respectively. These limits are mostly consistent with thermal noise over a wide range of $k$ after 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 (2022b), we find that the intergalactic medium must have been heated above the adiabatic cooling limit at least as early as $z = 10.4$, 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 relationship between soft X-ray luminosity and star formation and thus requires heating driven by evolved low-metallicity stars.Comment: 57 pages, 37 figures. Updated to match the accepted ApJ version. Corresponding author: Joshua S. Dillo

Hydrogen Epoch of Reionization Array (HERA) Phase II Deployment and Commissioning

This paper presents the design and deployment of the Hydrogen Epoch of Reionization Array (HERA) phase II system. HERA is designed as a staged experiment targeting 21 cm emission measurements of the Epoch of Reionization. First results from the phase I array are published as of early 2022, and deployment of the phase II system is nearing completion. We describe the design of the phase II system and discuss progress on commissioning and future upgrades. As HERA is a designated Square Kilometre Array pathfinder instrument, we also show a number of “case studies” that investigate systematics seen while commissioning the phase II system, which may be of use in the design and operation of future arrays. Common pathologies are likely to manifest in similar ways across instruments, and many of these sources of contamination can be mitigated once the source is identified

Direct Optimal Mapping Image Power Spectrum and its Window Functions

Abstract The key to detecting neutral hydrogen during the epoch of reionization (EoR) is to separate the cosmological signal from the dominating foreground radiation. We developed direct optimal mapping (DOM) to map interferometric visibilities; it contains only linear operations, with full knowledge of point spread functions from visibilities to images. Here, we demonstrate a fast Fourier transform-based image power spectrum and its window functions computed from the DOM images. We use noiseless simulation, based on the Hydrogen Epoch of Reionization Array Phase I configuration, to study the image power spectrum properties. The window functions show &lt;10−11 of the integrated power leaks from the foreground-dominated region into the EoR window; the 2D and 1D power spectra also verify the separation between the foregrounds and the EoR.</jats:p