Search

In 2018 the EDGES experiment claimed the first detection of the global cosmic 21cm signal, which featured an absorption trough centered around $z \sim 17$ with a depth of approximately -500mK. This amplitude is deeper than the standard prediction (in which the radio background is determined by the cosmic microwave background) by a factor of two and potentially hints at the existence of a radio background excess. While this result was obtained by fitting the data with a phenomenological flattened-Gaussian shape for the cosmological signal, here we develop a physical model for the inhomogeneous radio background sourced by the first galaxies hosting population III stars. Star formation in these galaxies is quenched at lower redshifts due to various feedback mechanisms, so they serve as a natural candidate for the excess radio background hinted by EDGES, without violating present day measurements by ARCADE2. We forward-model the EDGES sky temperature data, jointly sampling our physical model for the cosmic signal, a foreground model, and residual calibration errors. We compare the Bayesian evidences obtained by varying the complexity and prior ranges for the systematics. We find that the data is best explained by a model with seven log-polynomial foreground terms, and that it requires calibration residuals. Interestingly, the presence of a cosmic 21cm signal with a non-standard depth is decisively disfavored. This is contrary to previous EDGES analysis in the context of extra radio background models, serving as a caution against using a ''pseudo-likelihood'' built on a model (flattened Gaussian) that is different from the one being used for inference. We make our simulation code and associated emulator publicly-available., Comment: 17 pages, 9 figures, 1 table, version submitted to A&A

The 21cm line of neutral hydrogen is a powerful probe of the high-redshift universe (Cosmic Dawn and the Epoch of Reionization), with an unprecedented potential to inform us about key processes of early galaxy formation, the first stars and even cosmology and structure formation, via intensity mapping. It is the subject of a number of current and upcoming low-frequency radio experiments. This paper presents 21cmSense v2.0, which is a Python package that provides a modular framework for calculating the sensitivity of these experiments, in order to enhance the process of their design and forecasting their power for parameter inference. Version 2.0 of 21cmSense has been re-written from the ground up to be more modular and extensible than its venerable predecessor (Pober et al., 2013, 2014), and to provide a more user-friendly interface. The package is freely available both to use and contribute towards at https://github.com/rasg-affiliates/21cmSense., Comment: 2 figures. Published in JOSS. Comments and contributions very welcome!

Radio interferometers targeting the 21cm brightness temperature fluctuations at high redshift are subject to systematic effects that operate over a range of different timescales. These can be isolated by designing appropriate Fourier filters that operate in fringe-rate (FR) space, the Fourier pair of local sidereal time (LST). Applications of FR filtering include separating effects that are correlated with the rotating sky vs. those relative to the ground, down-weighting emission in the primary beam sidelobes, and suppressing noise. FR filtering causes the noise contributions to the visibility data to become correlated in time however, making interpretation of subsequent averaging and error estimation steps more subtle. In this paper, we describe fringe rate filters that are implemented using discrete prolate spheroidal sequences, and designed for two different purposes -- beam sidelobe/horizon suppression (the `mainlobe' filter), and ground-locked systematics removal (the `notch' filter). We apply these to simulated data, and study how their properties affect visibilities and power spectra generated from the simulations. Included is an introduction to fringe-rate filtering and a demonstration of fringe-rate filters applied to simple situations to aid understanding., Comment: 21 pages, 18 figures, submitted to Monthly Notices of the Royal Astronomical Society

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 Kilometer Array (SKA) 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.

Detection of the faint 21 cm line emission from the Cosmic Dawn and Epoch of Reionisation will require not only exquisite control over instrumental calibration and systematics to achieve the necessary dynamic range of observations but also validation of analysis techniques to demonstrate their statistical properties and signal loss characteristics. A key ingredient in achieving this is the ability to perform high-fidelity simulations of the kinds of data that are produced by the large, many-element, radio interferometric arrays that have been purpose-built for these studies. The large scale of these arrays presents a computational challenge, as one must simulate a detailed sky and instrumental model across many hundreds of frequency channels, thousands of time samples, and tens of thousands of baselines for arrays with hundreds of antennas. In this paper, we present a fast matrix-based method for simulating radio interferometric measurements (visibilities) at the necessary scale. We achieve this through judicious use of primary beam interpolation, fast approximations for coordinate transforms, and a vectorised outer product to expand per-antenna quantities to per-baseline visibilities, coupled with standard parallelisation techniques. We validate the results of this method, implemented in the publicly-available matvis code, against a high-precision reference simulator, and explore its computational scaling on a variety of problems., Comment: 25 pages, 20 figures, submitted to RAS Techniques and Instruments, matvis is publicly available at https://github.com/HERA-Team/matvis

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 are 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 Reionisation 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 Reionisation (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. Where the noise is smaller than the EoR, our modelling can mitigate the majority of the reflections with there being only a minor level of residual systematics, while cross-coupling sees essentially complete mitigation. 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., Comment: 19 pages, 14 figures, submitted to MNRAS

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 $<10^{-11}$ 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., Comment: Published in ApJ

Diffuse radio recombination lines (RRLs) in the Galaxy are possible foregrounds for redshifted 21~cm experiments. We use EDGES drift scans centered at $-26.7^o$~declination to characterize diffuse RRLs across the southern sky. We find RRLs averaged over the large antenna beam ($ 72^o \times 110^o $) reach minimum amplitudes between right ascensions~2-6~h. In this region, the C$\alpha$ absorption amplitude is $33\pm11$~mK (1$\sigma$) averaged over 50-87~MHz ($27\gtrsim z \gtrsim15$ for the 21~cm line) and increases strongly as frequency decreases. C$\beta$ and H$\alpha$ lines are consistent with no detection with amplitudes of $13\pm14$ and $12\pm10$~mK (1$\sigma$), respectively. At 108-124.5~MHz ($z\approx11$) in the same region, we find no evidence for carbon or hydrogen lines at the noise level of 3.4~mK (1$\sigma$). Conservatively assuming observed lines come broadly from the diffuse interstellar medium, as opposed to a few compact regions, these amplitudes provide upper limits on the intrinsic diffuse lines. The observations support expectations that Galactic RRLs can be neglected as significant foregrounds for a large region of sky until redshifted 21~cm experiments, particularly those targeting Cosmic Dawn, move beyond the detection phase. We fit models of the spectral dependence of the lines averaged over the large beam of EDGES, which may contain multiple line sources with possible line blending, and find that including degrees of freedom for expected smooth, frequency-dependent deviations from local thermodynamic equilibrium (LTE) is preferred over simple LTE assumptions for C$\alpha$ and H$\alpha$ lines. For C$\alpha$ we estimate departure coefficients $0.79

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 MNRAS

Scattering from objects near an antenna produce correlated signals from strong compact radio sources in a manner similar to those used by the Sea Interferometer to measure the radio source positions using the fine frequency structure in the total power spectrum of a single antenna. These fringes or ripples due to correlated signal interference are present at a low level in the spectrum of any single antenna and are a major source of systematics in systems used to measure the global redshifted 21-cm signal from the early universe. In the Sea Interferometer a single antenna on a cliff above the sea is used to add the signal from the direct path to the signal from the path reflected from the sea thereby forming an interferometer. This was used for mapping radio sources with a single antenna by Bolton and Slee in the 1950s. In this paper we derive analytic expressions to determine the level of these ripples and compare these results in a few simple cases with electromagnetic modeling software to verify that the analytic calculations are sufficient to obtain the magnitude of the scattering effects on the measurements of the global 21-cm signal. These analytic calculations are needed to evaluate the magnitude of the effects in cases that are either too complex or take too much time to be modeled using software.

Accurately accounting for spectral structure in spectrometer data induced by instrumental chromaticity on scales relevant for detection of the 21-cm signal is among the most significant challenges in global 21-cm signal analysis. In the publicly available EDGES low-band data set, this complicating structure is suppressed using beam-factor based chromaticity correction (BFCC), which works by dividing the data by a sky-map-weighted model of the spectral structure of the instrument beam. Several analyses of this data have employed models that start with the assumption that this correction is complete. However, while BFCC mitigates the impact of instrumental chromaticity on the data, given realistic assumptions regarding the spectral structure of the foregrounds, the correction is only partial. This complicates the interpretation of fits to the data with intrinsic sky models (models that assume no instrumental contribution to the spectral structure of the data). In this paper, we derive a BFCC data model from an analytic treatment of BFCC and demonstrate using simulated observations that, in contrast to using an intrinsic sky model for the data, the BFCC data model enables unbiased recovery of a simulated global 21-cm signal from beam-factor chromaticity corrected data in the limit that the data is corrected with an error-free beam-factor model., Comment: 26 pages, 8 figures; accepted for publication in MNRAS

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. Dillon

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 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 will be used in future analyses to confront theoretical models and data directly in cylindrical space., Comment: 18 pages, 19 figures, accepted for publication in MNRAS

We develop a Bayesian model that jointly constrains receiver calibration, foregrounds and cosmic 21cm signal for the EDGES global 21\,cm experiment. This model simultaneously describes calibration data taken in the lab along with sky-data taken with the EDGES low-band antenna. We apply our model to the same data (both sky and calibration) used to report evidence for the first star formation in 2018. We find that receiver calibration does not contribute a significant uncertainty to the inferred cosmic signal (<1%), though our joint model is able to more robustly estimate the cosmic signal for foreground models that are otherwise too inflexible to describe the sky data. We identify the presence of a significant systematic in the calibration data, which is largely avoided in our analysis, but must be examined more closely in future work. Our likelihood provides a foundation for future analyses in which other instrumental systematics, such as beam corrections and reflection parameters, may be added in a modular manner., Comment: 18 pages + 3 for appendices. 13 figures. Accepted to MNRAS

The Multi-frequency Angular Power Spectrum (MAPS) is an alternative to spherically-averaged power spectra, and computes local fluctuations in the angular power spectrum without need for line-of-sight spectral transform. To test different approaches to MAPS and treatment of the foreground contamination, and compare with the spherically-averaged power spectrum, and the single-frequency angular power spectrum. We apply the MAPS to 110~hours of data in $z=6.2-7.5$ obtained for the Murchison Widefield Array Epoch of Reionisation experiment to compute the statistical power of 21~cm brightness temperature fluctuations. In the presence of bright foregrounds, a filter is applied to remove large-scale modes prior to MAPS application, significantly reducing MAPS power due to systematics. The MAPS shows a contrast of 10$^2$--10$^3$ to a simulated 21~cm cosmological signal for spectral separations of 0--4~MHz after application of the filter, reflecting results for the spherically-averaged power spectrum. The single-frequency angular power spectrum is also computed. At $z=7.5$ and $l=200$, we find an angular power of 53~mK$^2$, exceeding a simulated cosmological signal power by a factor of one thousand. Residual spectral structure, inherent to the calibrated data, and not spectral leakage from large-scale modes, is the dominant source of systematic power bias. The single-frequency angular power spectrum yields slightly poorer results compared with the spherically-averaged power spectrum, having applied a spectral filter to reduce foregrounds. Exploration of other filters may improve this result, along with consideration of wider bandwidths., Comment: 9 pages, 9 figures; accepted for publication in Astronomy & Astrophysics

Preparing for the first detection of the cosmic 21-cm signal from large-scale interferometer experiments requires rigorous testing of the data analysis and reduction pipelines. To validate that these pipelines do not erroneously remove or add features that can mimic the cosmic signal (e.g. from side-lobes or large-scale power leakage), we require reionisation simulations larger than the experiments primary field of view. For an experiment such as the MWA, with a field of view of $\sim25^{2}$ deg.$^{2}$, this would require a simulation of several Gpcs, which is currently infeasible. To overcome this, we developed a simplified version of the semi-numerical reionisation simulation code 21CMFAST preferencing large volumes over some physical accuracy by assuming linear theory for structure formation. With this, we constructed a 7.5 Gpc comoving volume with voxel resolution of $\sim1.17$ cMpc tailored specifically to the binned spectral resolution of the MWA. This simulation was used for validating the pipelines for the 2020 MWA 21-cm power spectrum (PS) upper limits (Trott et al.). We then use this large-volume simulation to explore: (i) whether smaller volume simulations are biased by the missing large-scale modes, (ii) non-Gaussianity in estimates of the cosmic variance, (iii) biases in the recovered 21-cm PS following foreground wedge removal and (iv) the impact of tiling smaller volume simulations to achieve extremely large volumes. In summary, we find: (i) no biases from missing large-scale power, (ii) significant contribution from non-Gaussianity in the cosmic variance as expected following Mondal et al. (iii) an over-estimate of the 21-cm PS of 10-20 per cent following wedge mode excision for our particular model and (iv) tiling smaller volume simulations under-estimates the large-scale power and also the estimated cosmic variance., Comment: 13 pages, 9 figures and 1 table. Submitted to MNRAS, comments welcome

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 ApJ

Measurements of the one-point probability distribution function and higher-order moments (variance, skewness, and kurtosis) of the high-redshift 21 cm fluctuations are among the most direct statistical probes of the non-Gaussian nature of structure formation and evolution during reionization. However, contamination from astrophysical foregrounds and instrument systematics pose significant challenges in measuring these statistics in real observations. In this work, we use forward modelling to investigate the feasibility of measuring 21 cm one-point statistics through a foreground avoidance strategy. Leveraging the characteristic wedge-shape of the foregrounds in k-space, we apply a wedge-cut filter that removes the foreground contaminated modes from a mock data set based on the Hydrogen Epoch of Reionization Array (HERA) instrument, and measure the one-point statistics from the image-space representation of the remaining non-contaminated modes. We experiment with varying degrees of wedge-cutting over different frequency bandwidths and find that the centre of the band is the least susceptible to bias from wedge-cutting. Based on this finding, we introduce a rolling filter method that allows reconstruction of an optimal wedge-cut 21~cm intensity map over the full bandwidth using outputs from wedge-cutting over multiple sub-bands. We perform Monte Carlo simulations to show that HERA should be able to measure the rise in skewness and kurtosis near the end of reionization with the rolling wedge-cut method if foreground leakage from the Fourier transform window function can be controlled., Comment: 13 pages, 10 figures, Accepted to MNRAS

The light-cone effect breaks the periodicity and statistical homogeneity (ergodicity) along the line-of-sight direction of cosmological emission/absorption line surveys. The spherically averaged power spectrum (SAPS), which by definition assumes ergodicity and periodicity in all directions, can only quantify some of the second-order statistical information in the 3D light-cone signals and therefore gives a biased estimate of the true statistics. The multi-frequency angular power spectrum (MAPS), by extracting more information from the data, does not rely on these assumptions. It is therefore better aligned with the properties of the signal. We have compared the performance of the MAPS and SAPS metrics for parameter estimation for a mock 3D light-cone observation of the 21-cm signal from the Epoch of Reionization. Our investigation is based on a simplified 3-parameter 21cmFAST model. We find that the MAPS produces parameter constraints which are a factor of $\sim 2$ more stringent than when the SAPS is used. The significance of this result does not change much even in the presence of instrumental noise expected for 128 hours of SKA-Low observations. Our results therefore suggest that a parameter estimation framework based on the MAPS metric would yield superior results over one using the SAPS metric., Comment: Published in MNRAS Letters

Cross-correlating 21cm and Ly$\alpha$ intensity maps of the Epoch of Reionization (EoR) promises to be a powerful tool for exploring the properties of the first galaxies. Next-generation intensity mapping experiments such as the Hydrogen Epoch of Reionization Array (HERA) and SPHEREx will individually probe reionization through the power spectra of the 21cm and Ly$\alpha$ lines respectively, but will be limited by bright foregrounds and instrumental systematics. Cross-correlating these measurements could reduce systematics, potentially tightening constraints on the inferred astrophysical parameters. In this study, we present forecasts of cross-correlation taking into account the effects of exact uv-sampling and foreground filtering to estimate the feasibility of HERAxSPHEREx making a detection of the 21cm-Ly$\alpha$ cross-power spectrum. We also project the sensitivity of a cross-power spectrum between HERA and the proposed next-generation Cosmic Dawn Intensity Mapper. By isolating the sources of uncertainty, we explore the impacts of experimental limitations such as foreground filtering and Ly$\alpha$ thermal noise uncertainty have on making a detection of the cross-power spectrum. We then implement this strategy in a simulation of the cross-power spectrum and observational error to identify redshifts where fiducial 21cmFAST models predict the highest signal-to-noise detection ($z \sim 8$). We conclude that detection of the SPHEREx-HERA cross-correlation will require an optimistic level of 21cm foreground filtering, as well as deeper thermal noise integrations due to a lack of overlapping sensitive modes but for CDIM with its larger range of scales and lower noise forecast detection levels, may be possible even with stricter 21cm foreground filtering., Comment: 11 pages, 6 figures, Accepted by MNRAS

A limiting systematic effect in 21-cm interferometric experiments is the chromaticity due to the coupling between the sky and the instrument. This coupling is sourced by the instrument primary beam; therefore it is important to know the beam to extremely high precision. Here we demonstrate how known beam uncertainties can be characterized using databases of beam models. In this introductory work, we focus on beam errors arising from physically offset and/or broken antennas within a station. We use the public code OSKAR to generate an "ideal" SKA beam formed from 256 antennas regularly-spaced in a 35-m circle, as well as a large database of "perturbed" beams sampling distributions of broken/offset antennas. We decompose the beam errors ("ideal" minus "perturbed") using Principal Component Analysis (PCA) and Kernel PCA (KPCA). Using 20 components, we find that PCA/KPCA can reduce the residual of the beam in our datasets by 60-90% compared with the assumption of an ideal beam. Using a simulated observation of the cosmic signal plus foregrounds, we find that assuming the ideal beam can result in 1% error in the EoR window and 10% in the wedge of the 2D power spectrum. When PCA/KPCA is used to characterize the beam uncertainties, the error in the power spectrum shrinks to below 0.01% in the EoR window and <1% in the wedge. Our framework can be used to characterize and then marginalize over uncertainties in the beam for robust next-generation 21-cm parameter estimation., Comment: 12 pages, 9 main figures

Low-frequency radio observatories are reaching unprecedented levels of sensitivity in an effort to detect the 21 cm signal from the Cosmic Dawn. High precision is needed because the expected signal is overwhelmed by foreground contamination, largely from so-called diffuse emission -- a non-localized glow comprising Galactic synchrotron emission and radio galaxies. The impact of this diffuse emission on observations may be better understood through detailed simulations, which evaluate the Radio Interferometry Measurement Equation (RIME) for a given instrument and sky model. Evaluating the RIME involves carrying out an integral over the full sky, which is naturally discretized for point sources but must be approximated for diffuse emission. The choice of integration scheme can introduce errors that must be understood and isolated from the instrumental effects under study. In this paper, we present several analytically-defined patterns of unpolarized diffuse sky emission for which the RIME integral is manageable, yielding closed-form or series visibility functions. We demonstrate the usefulness of these RIME solutions for validation by comparing them to simulated data, and show that the remaining differences behave as expected with varied sky resolution and baseline orientation and length., Comment: 28 pages, 13 figures

The formation of the first galaxies during cosmic dawn and reionization (at redshifts $z=5-30$), triggered the last major phase transition of our universe, as hydrogen evolved from cold and neutral to hot and ionized. The 21-cm line of neutral hydrogen will soon allow us to map these cosmic milestones and study the galaxies that drove them. To aid in interpreting these observations, we upgrade the publicly available code {\tt 21cmFAST}. We introduce a new, flexible parametrization of the additive feedback from: an inhomogeneous, $H_2$-dissociating (Lyman-Werner; LW) background; and dark matter -- baryon relative velocities; which recovers results from recent, small-scale hydrodynamical simulations with both effects. We perform a large, "best-guess" simulation as the 2021 installment of the Evolution of 21-cm Structure (EOS) project. This improves the previous release with a galaxy model that reproduces the observed UV luminosity functions (UVLFs), and by including a population of molecular-cooling galaxies. The resulting 21-cm global signal and power spectrum are significantly weaker, primarily due to a more rapid evolution of the star-formation rate density required to match the UVLFs. Nevertheless, we forecast high signal-to-noise detections for both HERA and the SKA. We demonstrate how the stellar-to-halo mass relation of the unseen, first galaxies can be inferred from the 21-cm evolution. Finally, we show that the spatial modulation of X-ray heating due to relative velocities provides a unique acoustic signature that is detectable at $z \approx 10-15$ in our fiducial model. Ours are the first public simulations with joint inhomogeneous LW and relative-velocity feedback across the entire cosmic dawn and reionization., Comment: 23+3 pages, 23+3 figures. Matches accepted version. Simulation output available at https://www.dropbox.com/sh/dqh9r6wb0s68jfo/AACc9ZCqsN0SQ_JJN7GRVuqDa?dl=0

We present a framework for identifying and flagging malfunctioning antennas in large radio interferometers. We outline two distinct categories of metrics designed to detect outliers along known failure modes of large arrays: cross-correlation metrics, based on all antenna pairs, and auto-correlation metrics, based solely on individual antennas. We define and motivate the statistical framework for all metrics used, and present tailored visualizations that aid us in clearly identifying new and existing systematics. We implement these techniques using data from 105 antennas in the Hydrogen Epoch of Reionization Array (HERA) as a case study. Finally, we provide a detailed algorithm for implementing these metrics as flagging tools on real data sets., Comment: 31 pages, 17 figures

We report upper-limits on the Epoch of Reionization (EoR) 21 cm power spectrum at redshifts 7.9 and 10.4 with 18 nights of data ($\sim36$ hours 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 $\sim10^9$ with respect to the peak foreground power. This yields a 95% confidence upper limit on the 21 cm power spectrum of $\Delta^2_{21} \le (30.76)^2\ {\rm mK}^2$ at $k=0.192\ h\ {\rm Mpc}^{-1}$ at $z=7.9$, and also $\Delta^2_{21} \le (95.74)^2\ {\rm mK}^2$ at $k=0.256\ h\ {\rm Mpc}^{-1}$ 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 $k_\parallel$ modes, at high $k_\parallel$ 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 sub-reflections, 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., Comment: Accepted to ApJ. https://reionization.org/science/public-data-release-1/

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 auto-correlations 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., Comment: 16 pages, 13 figures, 1 table; accepted for publication in MNRAS main journal

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 sigma level) for k > 0.2 h/Mpc for both bands and fields considered. Our input spectrum is intentionally amplified to enable a strong `detection' at k ~0.2 h/Mpc -- at the level of ~25 sigma -- 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., Comment: 32 pages, 20 figures. Submitted to the Astrophysical Journal

Precise measurements of the 21 cm power spectrum are crucial for understanding the physical processes of hydrogen reionization. Currently, this probe is being pursued by low-frequency radio interferometer arrays. As these experiments come closer to making a first detection of the signal, error estimation will play an increasingly important role in setting robust measurements. Using the delay power spectrum approach, we have produced a critical examination of different ways that one can estimate error bars on the power spectrum. We do this through a synthesis of analytic work, simulations of toy models, and tests on small amounts of real data. We find that, although computed independently, the different error bar methodologies are in good agreement with each other in the noise-dominated regime of the power spectrum. For our preferred methodology, the predicted probability distribution function is consistent with the empirical noise power distributions from both simulated and real data. This diagnosis is mainly in support of the forthcoming HERA upper limit, and also is expected to be more generally applicable., Comment: 35 Pages, 9 Figures, 4 Tables. Replaced with accepted ApJ version; some clarifying text added in response to referee comments with no changes to results

The response of the antenna is a source of uncertainty in measurements with the Experiment to Detect the Global EoR Signature (EDGES). We aim to validate the beam model of the low-band (50-100 MHz) dipole antenna with comparisons between models and against data. We find that simulations of a simplified model of the antenna over an infinite perfectly conducting ground plane are, with one exception, robust to changes of numerical electromagnetic solver code or algorithm. For simulations of the antenna with the actual finite ground plane and realistic soil properties, we find that two out of three numerical solvers agree well. Applying our analysis pipeline to a simulated driftscan observation from an early EDGES low-band instrument that had a 10 m $\times$ 10 m ground plane, we find residual levels after fitting and removing a five-term foreground model to data binned in Local Sidereal Time (LST) average about 250 mK with $\pm$40 mK variation between numerical solvers. A similar analysis of the primary 30 m $\times$ 30 m sawtooth ground plane reduced the LST-averaged residuals to about 90 mK with $\pm$10 mK between the two viable solvers. More broadly we show that larger ground planes generally perform better than smaller ground planes. Simulated data have a power which is within 4$\%$ of real observations, a limitation of net accuracy of the sky and beam models. We observe that residual spectral structures after foreground model fits match qualitatively between simulated data and observations, suggesting that the frequency dependence of the beam is reasonably represented by the models. We find that soil conductivity of 0.02 Sm$^{-1}$ and relative permittivity of 3.5 yield good agreement between simulated spectra and observations. This is consistent with the soil properties reported by Sutinjo et al. (2015) for the Murchison Radio-astronomy Observatory, where EDGES is located., Comment: 19 pages, 17 figures

We use EDGES measurements to determine scale and zero-level corrections to the diffuse radio surveys by Guzm\'an et al. at $45$ MHz and Landecker & Wielebinski at $150$ MHz. We find that the Guzm\'an et al. map requires a scale correction of $1.076 \pm 0.034$ ($2\sigma$) and a zero-level correction of $-160 \pm 78$ K ($2\sigma$) to best-fit the EDGES data. For the Landecker & Wielebinski map, the scale correction is $1.112 \pm 0.023$ ($2\sigma$) and the zero-level correction is $0.7 \pm 6.0$ K ($2\sigma$). The correction uncertainties are dominated by systematic effects, of which the most significant are uncertainty in the calibration of the EDGES receivers, antenna pointing, and tropospheric and ionospheric effects. We propagate the correction uncertainties to estimate the uncertainties in the corrected maps themselves and find that the $2\sigma$ uncertainty in the map brightness temperature is in the range $3.2-7.5\%$ for the Guzm\'an et al. map and $2.1-9.0\%$ for the Landecker & Wielebinski map, with the largest percent uncertainties occurring at high Galactic latitudes. The corrected maps could be used to improve existing diffuse low-frequency radio sky models, which are essential tools in analyses of cosmological $21$ cm observations, as well as to investigate the existence of a radio monopole excess above the cosmic microwave background and known Galactic and extragalactic contributions., Comment: Accepted for publication in ApJ

This brief code paper presents a new Python-wrapped version of the popular 21cm cosmology simulator, 21cmFAST. The new version, v3+, maintains the same core functionality of previous versions of 21cmFAST, but features a simple and intuitive interface, and a great deal more flexibility. This evolution represents the work of a formalized collaboration, and the new version, available publicly on GitHub, provides a single point-of-reference for all future upgrades and community-added features. In this paper, we describe simple usage of 21cmFAST, some of its new features, and provide a simple performance benchmark., Comment: 6 pages, 3 figures, published in JOSS

We present a new halo model of neutral hydrogen (HI) calibrated to galaxy formation simulations at redshifts $z\sim0.1$ and $z\sim1.0$ that we employ to investigate the constraining power of interferometric HI intensity mapping on HI astrophysics. We demonstrate that constraints on the small-scale HI power spectrum can break the degeneracy between the HI density $\Omega_{\rm HI}$ and the HI bias $b_{\rm HI}$. For $z\sim0.1$, we forecast that an accurate measurement of $\Omega_{\rm HI}$ up to 6% level precision and the large-scale HI bias $b_{\rm HI}^0$ up to 1% level precision can be achieved using Square Kilometre Array (SKA) pathfinder data from MeerKAT and Australian SKA Pathfinder (ASKAP). We also propose a new description of the HI shot noise in the halo model framework in which a scatter of the relation between the HI mass of galaxies and their host halo mass is taken into account. Furthermore, given the number density of HI galaxies above a certain HI mass threshold, future surveys will also be able to constrain the HI mass function using only the HI shot noise. This will lead to constraints at the 10% level using the standard Schechter function. This technique will potentially provide a new way of measuring the HI Mass Function, independent from existing methods. We predict that the SKA will be able to further improve the low-redshift constraints by a factor of 3, as well as pioneering measurements of HI astrophysics at higher redshifts., Comment: 19 pages, 11 figures and 6 tables. Updated to match the published version in MNRAS. For the computational tool used in this paper see arXiv:2009.14066 and https://halomod.readthedocs.io/en/latest/examples/extension.html

The halo model is a successful framework for describing the distribution of matter in the Universe -- from weak lensing observables to galaxy 2-point correlation functions. We review the basic formulation of the halo model and several of its components in the context of galaxy two-point statistics, developing a coherent framework for its application. We use this framework to motivate the presentation of a new Python tool for simple and efficient calculation of halo model quantities, and their extension to galaxy statistics via a \textit{halo occupation distribution}, called \halomod. This tool is efficient, simple to use, comprehensive and importantly provides a great deal of flexibility in terms of custom extensions. This Python tool is complemented by a new web-application at https://thehalomod.app that supports the generation of many halo model quantities directly from the browser -- useful for educators, students, theorists and observers., Comment: 39 pages (32 w/o refs and appendices), 13 figures, accepted to Astronomy and Computing (v2 is the accepted version)

We discuss absolute calibration strategies for Phase I of the Hydrogen Epoch of Reionization Array (HERA), which aims to measure the cosmological 21 cm signal from the Epoch of Reionization (EoR). HERA is a drift-scan array with a 10 degree wide field of view, meaning bright, well-characterized point source transits are scarce. This, combined with HERA's redundant sampling of the uv plane and the modest angular resolution of the Phase I instrument, make traditional sky-based and self-calibration techniques difficult to implement with high dynamic range. Nonetheless, in this work we demonstrate calibration for HERA using point source catalogues and electromagnetic simulations of its primary beam. We show that unmodeled diffuse flux and instrumental contaminants can corrupt the gain solutions, and present a gain smoothing approach for mitigating their impact on the 21 cm power spectrum. We also demonstrate a hybrid sky and redundant calibration scheme and compare it to pure sky-based calibration, showing only a marginal improvement to the gain solutions at intermediate delay scales. Our work suggests that the HERA Phase I system can be well-calibrated for a foreground-avoidance power spectrum estimator by applying direction-independent gains with a small set of degrees of freedom across the frequency and time axes., Comment: Accepted to ApJ

We present a study of internal reflection and cross coupling systematics in Phase I of the Hydrogen Epoch of Reionization Array (HERA). In a companion paper, we outlined the mathematical formalism for such systematics and presented algorithms for modeling and removing them from the data. In this work, we apply these techniques to data from HERA's first observing season as a method demonstration. The data show evidence for systematics that, without removal, would hinder a detection of the 21 cm power spectrum for the targeted EoR line-of-sight modes in the range 0.2 < k_parallel < 0.5\ h^-1 Mpc. After systematic removal, we find we can recover these modes in the power spectrum down to the integrated noise-floor of a nightly observation, achieving a dynamic range in the EoR window of 10^-6 in power (mK^2 units) with respect to the bright galactic foreground signal. In the absence of other systematics and assuming the systematic suppression demonstrated here continues to lower noise levels, our results suggest that fully-integrated HERA Phase I may have the capacity to set competitive upper limits on the 21 cm power spectrum. For future observing seasons, HERA will have upgraded analog and digital hardware to better control these systematics in the field., Comment: Submitted to ApJ

In this white paper, we lay out a US roadmap for high-redshift 21 cm cosmology (30 < z < 6) in the 2020s. Beginning with the currently-funded HERA and MWA Phase II projects and advancing through the decade with a coordinated program of small-scale instrumentation, software, and analysis projects targeting technology development, this roadmap incorporates our current best understanding of the systematics confronting 21 cm cosmology into a plan for overcoming them, enabling next-generation, mid-scale 21 cm arrays to be proposed late in the decade. Submitted for consideration by the Astro2020 Decadal Survey Program Panel for Radio, Millimeter, and Submillimeter Observations from the Ground as a Medium-Sized Project., Comment: 10 pages (plus a cover page and references), 6 figures. Submitted as a APC White Paper for Astro2020

This paper presents \textsc{hankel}, a pure-python code for solving Hankel-type integrals and transforms. Such transforms are common in the physical sciences, especially appearing as the radial solution to angularly symmetric Fourier Transforms in arbitrary dimensions. The code harnesses the advantages of solving such transforms via the one-dimensional Hankel transform -- an increase in conceptual simplicity and efficiency -- and implements them in the user-friendly and flexible Python language. We discuss several limitations of the adopted method, and point to the code's extensive documentation for further examples.

The 2D power spectrum is a cornerstone of the modern toolkit for analysis of the low-frequency radio interferometric observations of the 21 cm signal arising from the early Universe. Its familiar form disentangles a great deal of systematic information concerning both the sky and telescope, and displays as a foreground-dominated `brick' and `wedge' on large line-of-sight scales, and a complementary `window' on smaller scales. This paper builds on many previous works in the literature which seek to elucidate the varied instrumental and foreground factors which contribute to these familiar structures in the 2D power spectrum. In particular, we consider the effects of $uv$-sampling on the emergence of the wedge. Our results verify the expectation that arbitrarily dense instrument layouts in principal restore the missing information that leads to mode-mixing, and can therefore mitigate the wedge feature. We derive rule-of-thumb estimates for the required baseline density for complete wedge mitigation, showing that these will be unachievable in practice. We also discuss the optimal shape of the layout, showing that logarithmic regularity in the radial separation of baselines is favourable. While complete suppression of foreground leakage into the wedge is practically unachievable, we find that designing layouts which promote radial density and regularity is able to reduce the amplitude of foreground power by 1-3 orders of magnitude., Comment: 21 pages + 4 Appendix Pages, 16 figures, Accepted to ApJ

Powerbox is a pure-Python package for creating and measuring structured fields with homogeneous and isotropic power spectra., Comment: The powerbox software can be found here: https://github.com/steven-murray/powerbox

The halo mass function, encoding the comoving number density of dark matter halos of a given mass, plays a key role in understanding the formation and evolution of galaxies. As such, it is a key goal of current and future deep optical surveys to constrain the mass function down to mass scales which typically host $L_\star$ galaxies. Motivated by the proven accuracy of Press-Schechter-type mass functions, we introduce a related but purely empirical form consistent with standard formulae to better than 4\% in the medium-mass regime, $10^{10}-10^{13} h^{-1}M_\odot$. In particular, our form consists of 4 parameters, each of which has a simple interpretation, and can be directly related to parameters of the galaxy distribution, such as $L_\star$. Using this form within a hierarchical Bayesian likelihood model, we show how individual mass-measurement errors can be successfully included in a typical analysis whilst accounting for Eddington bias. We apply our form to a question of survey design in the context of a semi-realistic data model, illustrating how it can be used to obtain optimal balance between survey depth and angular coverage for constraints on mass function parameters. Open-source {\tt Python} and {\tt R} codes to apply our new form are provided at \url{http://mrpy.readthedocs.org} and \url{https://cran.r-project.org/web/packages/tggd/index.html} respectively., Comment: 23 pages, 11 figures, accepted to ApJ

We present a general modified maximum likelihood (MML) method for inferring generative distribution functions from uncertain and biased data. The MML estimator is identical to, but easier and many orders of magnitude faster to compute than the solution of the exact Bayesian hierarchical modelling of all measurement errors. As a key application, this method can accurately recover the mass function (MF) of galaxies, while simultaneously dealing with observational uncertainties (Eddington bias), complex selection functions and unknown cosmic large-scale structure. The MML method is free of binning and natively accounts for small number statistics and non-detections. Its fast implementation in the R-package "dftools" is equally applicable to other objects, such as haloes, groups and clusters, as well as observables other than mass. The formalism readily extends to multi-dimensional distribution functions, e.g. a Choloniewski function for the galaxy mass-angular momentum distribution, also handled by dftools. The code provides uncertainties and covariances for the fitted model parameters and approximate Bayesian evidences. We use numerous mock surveys to illustrate and test the MML method, as well as to emphasise the necessity of accounting for observational uncertainties in MFs of modern galaxy surveys., Comment: 24 pages, 22 figures

We present a sophisticated statistical point-source foreground model for low-frequency radio Epoch of Reionization (EoR) experiments using the 21 cm neutral hydrogen emission line. Motivated by our understanding of the low-frequency radio sky, we enhance the realism of two model components compared with existing models: the source count distributions as a function of flux density and spatial position (source clustering), extending current formalisms for the foreground covariance of 2D power spectral modes in 21 cm EoR experiments. The former we generalise to an arbitrarily broken power-law, and the latter to an arbitrary isotropically-correlated field. This paper presents expressions for the modified covariance under these extensions, and shows that for a more realistic source spatial distribution, extra covariance arises in the EoR window which was previously unaccounted for. Failure to include this contribution can yield bias in the final power spectrum and under-estimate uncertainties, potentially leading to a false detection of signal. The extent of this effect is uncertain, owing to ignorance of physical model parameters, but we show that it is dependent on the relative abundance of faint sources, to the effect that our extension will become more important for future deep surveys. Finally, we show that under some parameter choices, ignoring source clustering can lead to false detections on large scales, due to both the induced bias and an artificial reduction in the estimated measurement uncertainty., Comment: 18 pages, 10 figures, accepted in ApJ

We present a simple method of generating approximate synthetic halo catalogues: HALOGEN. This method uses a combination of $2^{nd}$-order Lagrangian Perturbation Theory (2LPT) in order to generate the large-scale matter distribution, analytical mass functions to generate halo masses, and a single-parameter stochastic model for halo bias to position haloes. HALOGEN represents a simplification of similar recently published methods. Our method is constrained to recover the 2-point function at intermediate ($10Mpc/h