Hydrogen Epoch Of Reionization Array Research Articles

Mitigating calibration errors from mutual coupling with time-domain filtering of 21 cm cosmological radio observations

Abstract The 21 cm transition from neutral Hydrogen promises to be the best observational probe of the Epoch of Reionisation (EoR). This has led to the construction of low-frequency radio interferometric arrays, such as the Hydrogen Epoch of Reionization Array (HERA), aimed at systematically mapping this emission for the first time. Precision calibration, however, is a requirement in 21 cm radio observations. Due to the spatial compactness of HERA, the array is prone to the effects of mutual coupling, which inevitably lead to non-smooth calibration errors that contaminate the data. When unsmooth gains are used in calibration, intrinsically spectrally-smooth foreground emission begins to contaminate the data in a way that can prohibit a clean detection of the cosmological EoR signal. In this paper, we show that the effects of mutual coupling on calibration quality can be reduced by applying custom time-domain filters to the data prior to calibration. We find that more robust calibration solutions are derived when filtering in this way, which reduces the observed foreground power leakage. Specifically, we find a reduction of foreground power leakage by 2 orders of magnitude at k∥ ≈ 0.5 h Mpc−1.

Effects of feedback-free starburst galaxies on the 21-cm signal and reionization history

ABSTRACT Different star formation models at Cosmic Dawn produce detectable signatures in the observables of upcoming 21-cm experiments. In this work, we consider the physical scenario of feedback-free starbursts (FFB), according to which the star formation efficiency (SFE) is enhanced in sufficiently massive haloes at early enough times, thus explaining the indication from the JWST for an excess of bright galaxies at $z \ge 10$. We model the contribution of FFBs to popII SFE and compute the impact these have on the 21-cm global signal and power spectrum. We show that FFBs affect the evolution of the brightness temperature and the 21-cm power spectrum, but they only have a limited effect on the neutral hydrogen fraction. We investigate how the observables are affected by changes in the underlying star formation model and by contribution from popIII stars. Finally, we forecast the capability of next-generation Hydrogen Epoch of Reionization Array (HERA) to detect the existence of FFB galaxies via power spectrum measurements. Our results show the possibility of a significant detection, provided that popII stars are the main drivers of lowering the spin temperature. Efficient popIII star formation will make the detection more challenging.

Disentangling the anisotropic radio sky: Fisher forecasts for 21 cm arrays

ABSTRACT The existence of a radio synchrotron background (RSB) excess is implied by a number of measurements, including excess emission seen by the Absolute Radiometer for Cosmology, Astrophysics, and Diffuse Emission (ARCADE 2) and Long Wavelength Array (LWA) experiments. Highly sensitive wideband radio arrays, of the kind used to measure the cosmic 21 cm signal, provide a promising way to further constrain the RSB excess through its anisotropy, providing additional insight into its origin. We present a framework for evaluating the potential of 21 cm arrays to disentangle different components of the diffuse radio sky based on the combination of their frequency spectrum and angular power spectrum. The formalism is designed to calculate uncertainties due to the intrinsic cosmic variance alone or together with instrumental noise. In particular, we predict the potential for measuring the anisotropy of a broad generalized class of excess radio background models using the low-frequency Hydrogen Epoch of Reionization Array (HERA) as an example. We find that a HERA-like array can distinguish an RSB excess from other sky components based on its angular clustering and spectral dependence, even if these are quite similar to one or more of the other components – but only in the case that the RSB excess is relatively bright.

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.

High-dimensional inference of radio interferometer beam patterns I: parametric model of the HERA beams

ABSTRACT Accurate modelling of the primary beam is an important but difficult task in radio astronomy. For high dynamic range problems such as 21 cm intensity mapping, small modelling errors in the sidelobes, and spectral structure of the beams can translate into significant systematic errors. Realistic beams exhibit complex spatial and spectral structure, presenting a major challenge for beam measurement and calibration methods. In this paper series, we present a Bayesian framework to infer per-element beam patterns from the interferometric visibilities for large arrays with complex beam structure, assuming a particular (but potentially uncertain) sky model and calibration solution. In this first paper, we develop a compact basis for the beam so that the Bayesian computation is tractable with high-dimensional sampling methods. We use the Hydrogen Epoch of Reionization Array (HERA) as an example, verifying that the basis is capable of describing its single-element E-field beam (i.e. without considering array effects like mutual coupling) with a relatively small number of coefficients. We find that 32 coefficients per feed, incident polarization, and frequency, are sufficient to give percent-level and $\sim$10 per cent errors in the mainlobe and sidelobes, respectively, for the current HERA Vivaldi feeds, improving to $\sim 0.1{{\ \rm per\ cent}}$ and $\sim 1{{\ \rm per\ cent}}$ for 128 coefficients.

21cm signal sensitivity to dark matter decay

The redshifted 21cm signal from the Cosmic Dawn is expected to provide unprecedented insights into early Universe astrophysics and cosmology. Here we explore how dark matter can heat the intergalactic medium before the first galaxies, leaving a distinctive imprint in the 21cm power spectrum. We provide the first dedicated Fisher matrix forecasts on the sensitivity of the Hydrogen Epoch of Reionization Array (HERA) telescope to dark matter decays. We show that with 1000 hours of observation, HERA has the potential to improve current cosmological constraints on the dark matter decay lifetime by up to three orders of magnitude. Even in extreme scenarios with strong X-ray emission from early-forming, metal-free galaxies, the bounds on the decay lifetime would be improved by up to two orders of magnitude. Overall, HERA shall improve on existing limits for dark matter masses below 2 GeV/c 2 for decays into e+e- and below few MeV/c 2 for decays into photons.

21cmemu: an emulator of 21cmfast summary observables

ABSTRACT Recent years have witnessed rapid progress in observations of the epoch of reionization (EoR). These have enabled high-dimensional inference of galaxy and intergalactic medium (IGM) properties during the first billion years of our Universe. However, even using efficient, seminumerical simulations, traditional inference approaches that compute 3D lightcones on-the-fly can take 105 core hours. Here we present 21cmemu: an emulator of several summary observables from the popular 21cmfast simulation code. 21cmemu takes as input nine parameters characterizing EoR galaxies, and outputs the following summary statistics: (i) the IGM mean neutral fraction; (ii) the 21-cm power spectrum; (iii) the mean 21-cm spin temperature; (iv) the sky-averaged (global) 21-cm signal; (vi) the ultraviolet (UV) luminosity functions (LFs); and (vii) the Thomson scattering optical depth to the cosmic microwave background (CMB). All observables are predicted with sub- per cent median accuracy, with a reduction of the computational cost by a factor of over 104. After validating inference results, we showcase a few applications, including: (i) quantifying the relative constraining power of different observational data sets; (ii) seeing how recent claims of a late EoR impact previous inferences; and (iii) forecasting upcoming constraints from the sixth observing season of the Hydrogen Epoch of Reionization Array (HERA) telescope. 21cmemu is publicly available, and is included as an alternative simulator in the public 21cmmc sampler.

Joint analysis constraints on the physics of the first galaxies with low-frequency radio astronomy data

ABSTRACT The first billion years of cosmic history remains largely unobserved. We demonstrate, using a novel machine learning technique, how combining upper limits on the spatial fluctuations in the 21-cm signal with observations of the sky-averaged 21-cm signal from neutral hydrogen can improve our understanding of this epoch. By jointly analysing data from the Shaped Antenna measurement of the background RAdio Spectrum (SARAS3, redshift z ≈ 15−25) and limits from the Hydrogen Epoch of Reionization Array (HERA, z ≈ 8 and 10), we show that such a synergetic analysis provides tighter constraints on the astrophysics of galaxies 200 million years after the big bang than can be achieved with the individual data sets. Although our constraints are weak, this is the first time data from a sky-averaged 21-cm experiment and power spectrum experiment have been analysed together. In synergy, the two experiments leave only $64.9^{+0.3}_{-0.1}$ per cent of the explored broad theoretical parameter space to be consistent with the joint data set, in comparison to $92.3^{+0.3}_{-0.1}$ per cent for SARAS3 and $79.0^{+0.5}_{-0.2}$ per cent for HERA alone. We use the joint analysis to constrain star formation efficiency, minimum halo mass for star formation, X-ray luminosity of early emitters, and the radio luminosity of early galaxies. The joint analysis disfavours at 68 per cent confidence a combination of galaxies with X-ray emission that is ≲33 and radio emission that is ≳32 times as efficient as present day galaxies. We disfavour at 95 per cent confidence scenarios in which power spectra are ≥126 mK2 at z = 25 and the sky-averaged signals are ≤−277 mK.

Cross Correlation of Pencil-beam Galaxy Surveys and Line-intensity Maps: An Application of the James Webb Space Telescope

Line-intensity mapping (IM) experiments seek to perform statistical measurements of large-scale structure with spectral lines such as 21 cm, CO, and Lyα. A challenge in these observations is to ensure that astrophysical foregrounds, such as galactic synchrotron emission in 21 cm measurements, are properly removed. One method that has the potential to reduce foreground contamination is to cross correlate with a galaxy survey that overlaps with the IM volume. However, telescopes sensitive to high-redshift galaxies typically have small field of views compared to IM surveys. Thus, a galaxy survey for cross correlation would necessarily consist of pencil beams that sparsely fill the IM volume. In this paper, we develop the formalism to forecast the sensitivity of cross correlations between IM experiments and pencil-beam galaxy surveys. We find that a random distribution of pencil beams leads to very similar overall sensitivity as a lattice spaced across the IM survey and derive a simple formula for random configurations that agrees with the Fisher matrix formalism. We explore examples of combining high-redshift James Webb Space Telescope (JWST) observations with both an SPHEREx-like Lyα IM survey and a 21 cm experiment based on the Hydrogen Epoch of Reionization Array (HERA). We find that the JWST-SPHEREx case is promising, leading to a total signal-to-noise ratio of ∼5 after 100 total hours of JWST (at z = 7). We find that HERA is not well-suited for this approach owing to its drift-scan strategy, but that a similar experiment that can integrate down on one field could be.

The Impact of Beam Variations on Power Spectrum Estimation for 21 cm Cosmology. II. Mitigation of Foreground Systematics for HERA

One key challenge in detecting a 21 cm cosmological signal at z > 6 is to separate the cosmological signal from foreground emission. This can be studied in a power spectrum space where the foreground is confined to low delay (or, equivalently, k ∥) modes, whereas the cosmological signal can spread out to high delay modes. When there is a calibration error, however, the chromaticity of the gain errors propagates to the power spectrum estimate and contaminates the modes for cosmological detection. The Hydrogen Epoch of Reionization Array (HERA) employs a high-precision calibration scheme using redundancy in measurements. In this study, we focus on the gain errors induced by nonredundancies arising from a feed offset relative to HERA’s 14 m parabolic dish element and investigate how to mitigate the chromatic gain errors using three different methods: restricting baseline lengths for calibration, smoothing the antenna gains, and applying a temporal filter prior to calibration. With 2 cm/2° perturbations for translation/tilting motions, a level achievable under normal HERA operating conditions, the combination of the baseline cut and temporal filtering indicates that the spurious gain feature due to nonredundancies is significantly reduced, and the power spectrum recovers the clean foreground-free region. We found that the mitigation technique works even for large feed motions, but in order to keep a stable calibration process, the feed positions need to be constrained to 2 cm for translation motions and 2° for tilting offset relative to the dish’s vertex.

Statistical Recovery of 21 cm Visibilities and Their Power Spectra with Gaussian-constrained Realizations and Gibbs Sampling

Radio interferometers designed to probe the 21 cm signal from Cosmic Dawn and the Epoch of Reionization must contend with systematic effects that make it difficult to achieve sufficient dynamic range to separate the 21 cm signal from foreground emission and other effects. For instance, the instrument’s chromatic response modulates the otherwise spectrally smooth foregrounds, making them difficult to model, while a significant fraction of the data must be excised due to the presence of radio-frequency interference, leaving gaps in the data. Errors in modeling the (modulated and gappy) foregrounds can easily generate spurious contamination of what should otherwise be 21 cm signal-dominated modes. Various approaches have been developed to mitigate these issues by, for example, using nonparametric reconstruction of the foregrounds, in-painting the gaps, and weighting the data to reduce the level of contamination. We present a Bayesian statistical method that combines these approaches, using the coupled techniques of Gaussian-constrained realizations and Gibbs sampling. This provides a way of drawing samples from the joint posterior distribution of the 21 cm signal modes and their power spectrum in the presence of gappy data and an uncertain foreground model in a computationally scalable manner. The data are weighted by an inverse covariance matrix that is estimated as part of the inference, along with a foreground model that can then be marginalized over. We demonstrate the application of this technique on a simulated Hydrogen Epoch of Reionization Array–like delay spectrum analysis, comparing three different approaches for accounting for the foreground components.

Studying the multifrequency angular power spectrum of the cosmic dawn 21-cm signal

ABSTRACT The light-cone (LC) anisotropy arises due to cosmic evolution of the cosmic dawn (CD) 21-cm signal along the line-of-sight (LoS) axis of the observation volume. The LC effect makes the signal statistically non-ergodic along the LoS axis. The multifrequency angular power spectrum (MAPS) provides an unbiased alternative to the popular three-dimensional (3D) power spectrum as it does not assume statistical ergodicity along every direction in the signal volume. Unlike the 3D power spectrum which mixes the cosmic evolution of the 21-cm signal along the LoS k modes, MAPS keeps the evolution information disentangled. Here, we first study the impact of different underlying physical processes during CD on the behaviour of the 21-cm MAPS using simulations of various different scenarios and models. We also make error predictions in 21-cm MAPS measurements considering only the system noise and cosmic variance for mock observations of Hydrogen Epoch of Reionization Array (HERA), NenuFAR, and SKA-Low. We find that 100 h of HERA observations will be able to measure 21-cm MAPS at ≥3σ for ℓ ≲ 1000 with $0.1\, {\rm MHz}$ channel-width. The better sensitivity of SKA-Low allows reaching this sensitivity up to ℓ ≲ 3000. Note that due to the difference in the frequency coverage of the various experiments, the CD–epoch of reionization model considered for NenuFAR is different than those used for the HERA and SKA-Low predictions. Considering NenuFAR with the new model, measurements ≥2σ are possible only for ℓ ≲ 600 with $0.2\, {\rm MHz}$ channel-width and for a 10 times longer observation time of tobs = 1000 h. However, for the range 300 ≲ ℓ ≲ 600 and tobs = 1000 h more than 3σ measurements are still possible for NenuFAR when combining consecutive frequency channels within a 5 MHz band.

On the use of temporal filtering for mitigating galactic synchrotron calibration bias in 21 cm reionization observations

ABSTRACT Precision antenna calibration is required for mitigating the impact of foreground contamination in 21 cm cosmological radio surveys. One widely studied source of error is the effect of missing point sources in the calibration sky model; however, poorly understood diffuse galactic emission also creates a calibration bias that can complicate the clean separation of foregrounds from the 21 cm signal. In this work, we present a technique for suppressing this bias with temporal filtering of radio interferometric visibilities observed in a drift-scan mode. We demonstrate this technique on mock simulations of the Hydrogen Epoch of Reionization Array (HERA) experiment. Inspecting the recovered calibration solutions, we find that our technique reduces spurious errors by over an order of magnitude. This improved accuracy approaches the required accuracy needed to make a fiducial detection of the 21 cm signal with HERA, but is dependent on a number of external factors that we discuss. We also explore different types of temporal filtering techniques and discuss their relative performance and trade-offs.

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, we find at 95% confidence that Δ2(k = 0.34 h Mpc−1) ≤ 457 mK2 at z = 7.9 and that Δ2(k = 0.36 h Mpc−1) ≤ 3496 mK2 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, 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.

Search for the Epoch of Reionization with HERA: upper limits on the closure phase delay power spectrum

ABSTRACT Radio interferometers aiming to measure the power spectrum of the redshifted 21 cm line during the Epoch of Reionization (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 per cent confidence that the 21 cm EoR brightness temperature is ≤(372)2 ‘pseudo’ mK2 at 1.14 ‘pseudo’ h Mpc−1, where the ‘pseudo’ emphasizes 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.

Characterization of inpaint residuals in interferometric measurements of the epoch of reionization

ABSTRACTTo mitigate the effects of Radio Frequency Interference (RFI) on the data analysis pipelines of 21 cm interferometric instruments, numerous inpaint techniques have been developed. In this paper, 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 is capable of inpainting RFI corrupted data. We train our network on simulated data and show that our network is capable of inpainting real data without requiring to be retrained. We find that techniques that incorporate high wavenumbers in delay space in their modelling are best suited for inpainting over narrowband RFI. We show that with our fiducial parameters discrete prolate spheroidal sequences (dpss) and clean provide the best performance for intermittent 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 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 as the noise level of the data comes down, clean and dpss are most capable of reproducing the fine frequency structure in the visibilities.

Prospects for 21 cm Galaxy Cross-correlations with HERA and the Roman High-latitude Survey

The cross-correlation between the 21 cm field and the galaxy distribution is a potential probe of the Epoch of Reionization (EoR). The 21 cm signal traces neutral gas in the intergalactic medium and, on large spatial scales, this should be anticorrelated with the high-redshift galaxy distribution, which partly sources and tracks the ionized gas. In the near future, interferometers such as the Hydrogen Epoch of Reionization Array (HERA) are projected to provide extremely sensitive measurements of the 21 cm power spectrum. At the same time, the Nancy Grace Roman Space Telescope (Roman) will produce the most extensive catalog to date of bright galaxies from the EoR. Using seminumeric simulations of reionization, we explore the prospects for measuring the cross-power spectrum between the 21 cm and galaxy fields during the EoR. We forecast a 12σ detection between HERA and Roman, assuming an overlapping survey area of 500 deg2, redshift uncertainties of σ z = 0.01 (as expected for the high-latitude spectroscopic survey of Lyα-emitting galaxies), and an effective Lyα emitter duty cycle of f LAE = 0.1. Thus the HERA–Roman cross-power spectrum may be used to help verify 21 cm detections from HERA. We find that the shot-noise in the galaxy distribution is a limiting factor for detection, and so supplemental observations using Roman should prioritize deeper observations, rather than covering a wider field of view. We have made a public GitHub repository containing key parts of the calculation, which accompanies this paper: https://github.com/plaplant/21cm_gal_cross_correlation.

Impact of instrument and data characteristics in the interferometric reconstruction of the 21 cm power spectrum

ABSTRACT 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.

Effective bias expansion for 21-cm cosmology in redshift space

A near-future detection of the 21-cm signal from the epoch of reionization will provide unique opportunities to probe the underlying cosmology, provided that such cosmological information can be extracted with precision. To this end, we further develop effective field theory (EFT) inspired techniques for the 21-cm brightness temperature field during the epoch of reionization, incorporating renormalized bias and a treatment of redshift space distortions. Notably, we confirm that in redshift space, measures of the 21-cm brightness, e.g., the power spectrum, should have irreducible contributions that lack a bias coefficient and therefore contain direct, astrophysics-free information about the cosmological density field; in this work, we study this effect beyond linear order. To validate our theoretical treatment, we fit the predicted EFT Fourier-space shapes to the thesan suite of hydrodynamical simulations of reionization at the field level, where the considerable number of modes prevents overfitting. We find agreement at the level of a few percent between the 21-cm power spectrum from the EFT fits and simulations over the wave number range $k\ensuremath{\lesssim}0.8\text{ }\text{ }\mathrm{h}/\mathrm{Mpc}$ and neutral fraction ${x}_{\mathrm{HI}}\ensuremath{\gtrsim}0.4$, which is imminently measurable by the Hydrogen Epoch of Reionization Array and future experiments. The ability of the EFT to describe the 21-cm signal extends to simulations that have different astrophysical prescriptions for reionization as well as simulations with interacting dark matter.

The Impact of Beam Variations on Power Spectrum Estimation for 21 cm Cosmology. I. Simulations of Foreground Contamination for HERA

Detecting cosmological signals from the Epoch of Reionization (EoR) requires high-precision calibration to isolate the cosmological signals from foreground emission. In radio interferometry, the perturbed primary beams of antenna elements can disrupt the precise calibration, which results in the contamination of the foreground-free region, or the EoR window, in the cylindrically averaged power spectrum. For the Hydrogen Epoch of Reionization Array (HERA), we simulate and characterize the perturbed primary beams that are induced by feed motions, such as axial, lateral, and tilting motions, above the 14 m dish. To understand the effect of the perturbed beams, visibility measurements are modeled with two different foreground components, point sources and diffuse sources, and we find that different feed motions present a different reaction to each type of sky source. HERA’s redundant baseline calibration in the presence of nonredundant antenna beams due to feed motions introduces chromatic errors in the gain solutions, producing foreground power leakage into the EoR window. The observed leakage from the vertical feed motions comes predominantly from point sources around the zenith. Furthermore, the observed leakage from the horizontal and tilting feed motions comes predominantly from the diffuse components near the horizon. Mitigation of the chromatic gain errors will be necessary for robust detections of the EoR signals with minimal foreground bias, and this will be discussed in a subsequent paper.