Abstract
We study the impact of sky-based calibration errors from source mismodelling on 21 cm power spectrum measurements with an interferometer and propose a method for suppressing their effects. ...While emission from faint sources that are not accounted for in calibration catalogues is believed to be spectrally smooth, deviations of true visibilities from model visibilities are not, due to the inherent chromaticity of the interferometer's sky response (the ‘wedge'). Thus, unmodelled foregrounds, below the confusion limit of many instruments, introduce frequency structure into gain solutions on the same line-of-sight scales on which we hope to observe the cosmological signal. We derive analytic expressions describing these errors using linearized approximations of the calibration equations and estimate the impact of this bias on measurements of the 21 cm power spectrum during the epoch of reionization. Given our current precision in primary beam and foreground modelling, this noise will significantly impact the sensitivity of existing experiments that rely on sky-based calibration. Our formalism describes the scaling of calibration with array and sky-model parameters and can be used to guide future instrument design and calibration strategy. We find that sky-based calibration that downweights long baselines can eliminate contamination in most of the region outside of the wedge with only a modest increase in instrumental noise.
ABSTRACT Realizing the potential of 21 cm tomography to statistically probe the intergalactic medium before and during the Epoch of Reionization requires large telescopes and precise control of ...systematics. Next-generation telescopes are now being designed and built to meet these challenges, drawing lessons from first-generation experiments that showed the benefits of densely packed, highly redundant arrays-in which the same mode on the sky is sampled by many antenna pairs-for achieving high sensitivity, precise calibration, and robust foreground mitigation. In this work, we focus on the Hydrogen Epoch of Reionization Array (HERA) as an interferometer with a dense, redundant core designed following these lessons to be optimized for 21 cm cosmology. We show how modestly supplementing or modifying a compact design like HERA's can still deliver high sensitivity while enhancing strategies for calibration and foreground mitigation. In particular, we compare the imaging capability of several array configurations, both instantaneously (to address instrumental and ionospheric effects) and with rotation synthesis (for foreground removal). We also examine the effects that configuration has on calibratability using instantaneous redundancy. We find that improved imaging with sub-aperture sampling via "off-grid" antennas and increased angular resolution via far-flung "outrigger" antennas is possible with a redundantly calibratable array configuration.
We present limits on the 21 cm power spectrum from the Epoch of Reionization using data from the 64 antenna configuration of the Donald C. Backer Precision Array for Probing the Epoch of Reionization ...(PAPER) analyzed through a power spectrum pipeline independent from previous PAPER analyses. Previously reported results from PAPER have been found to contain significant signal loss. Several lossy steps from previous PAPER pipelines have not been included in this analysis, namely delay-based foreground filtering, optimal fringe-rate filtering, and empirical covariance-based estimators. Steps that remain in common with previous analyses include redundant calibration and local sidereal time (LST) binning. The power spectra reported here are effectively the result of applying a linear Fourier transform analysis to the calibrated, LST-binned data. This analysis also uses more data than previous publications, including the complete available redshift range of z ∼ 7.5 to 11. In previous PAPER analyses, many power spectrum measurements were found to be detections of noncosmological power at levels of significance ranging from two to hundreds of times the theoretical noise. Here, excess power is examined using redundancy between baselines and power spectrum jackknives. The upper limits we find on the 21 cm power spectrum from reionization are , , , , , and at redshifts z = 10.87, 9.93, 8.68, 8.37, 8.13, and 7.48, respectively. For reasons described in Cheng et al., these limits supersede all previous PAPER results.
We study the behavior of internal signal chain reflections and antenna cross coupling as systematics for 21 cm cosmological surveys. We outline the mathematics for how these systematics appear in ...interferometric visibilities and describe their phenomenology. We then describe techniques for modeling and removing these systematics without attenuating the 21 cm signal in the data. This has critical implications for low-frequency radio surveys aiming to characterize the 21 cm signal from the Epoch of Reionization (EoR) and Cosmic Dawn, as systematics can cause bright foreground emission to contaminate the EoR window and prohibit a robust detection. We also quantify the signal loss properties of the systematic modeling algorithms, and show that our techniques demonstrate resistance against EoR signal loss. In a companion paper, we demonstrate these methods on data from the Hydrogen Epoch of Reionization Array as a proof-of-concept.
ABSTRACT The Murchison Widefield Array (MWA) has collected hundreds of hours of Epoch of Reionization (EoR) data and now faces the challenge of overcoming foreground and systematic contamination to ...reduce the data to a cosmological measurement. We introduce several novel analysis techniques, such as cable reflection calibration, hyper-resolution gridding kernels, diffuse foreground model subtraction, and quality control methods. Each change to the analysis pipeline is tested against a two-dimensional power spectrum figure of merit to demonstrate improvement. We incorporate the new techniques into a deep integration of 32 hours of MWA data. This data set is used to place a systematic-limited upper limit on the cosmological power spectrum of mK2 at k = 0.27 h Mpc−1 and z = 7.1, consistent with other published limits, and a modest improvement (factor of 1.4) over previous MWA results. From this deep analysis, we have identified a list of improvements to be made to our EoR data analysis strategies. These improvements will be implemented in the future and detailed in upcoming publications.
We use the Fisher matrix formalism and seminumerical simulations to derive quantitative predictions of the constraints that power spectrum measurements on next-generation interferometers, such as the ...Hydrogen Epoch of Reionization Array (HERA) and the Square Kilometre Array (SKA), will place on the characteristics of the X-ray sources that heated the high-redshift intergalactic medium. Incorporating observations between z = 5 and 25, we find that the proposed 331 element HERA and SKA phase 1 will be capable of placing ≲ 10 per cent constraints on the spectral properties of these first X-ray sources, even if one is unable to perform measurements within the foreground contaminated ‘wedge’ or the FM band. When accounting for the enhancement in power spectrum amplitude from spin temperature fluctuations, we find that the observable signatures of reionization extend well beyond the peak in the power spectrum usually associated with it. We also find that lower redshift degeneracies between the signatures of heating and reionization physics lead to errors on reionization parameters that are significantly greater than previously predicted. Observations over the heating epoch are able to break these degeneracies and improve our constraints considerably. For these two reasons, 21-cm observations during the heating epoch significantly enhance our understanding of reionization as well.
The Epoch of Reionization (EoR) is an uncharted era in our universe's history during which the birth of the first stars and galaxies led to the ionization of neutral hydrogen in the intergalactic ...medium. There are many experiments investigating the EoR by tracing the 21 cm line of neutral hydrogen. Because this signal is very faint and difficult to isolate, it is crucial to develop analysis techniques that maximize sensitivity and suppress contaminants in data. It is also imperative to understand the trade-offs between different analysis methods and their effects on power spectrum estimates. Specifically, with a statistical power spectrum detection in HERA's foreseeable future, it has become increasingly important to understand how certain analysis choices can lead to the loss of the EoR signal. In this paper, we focus on signal loss associated with power spectrum estimation. We describe the origin of this loss using both toy models and data taken by the 64-element configuration of the Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER). In particular, we highlight how detailed investigations of signal loss have led to a revised, higher 21 cm power spectrum upper limit from PAPER-64. Additionally, we summarize errors associated with power spectrum error estimation that were previously unaccounted for. We focus on a subset of PAPER-64 data in this paper; revised power spectrum limits from the PAPER experiment are presented in a forthcoming paper by Kolopanis et al. and supersede results from previously published PAPER analyses.
We present techniques for bridging the gap between idealized inverse covariance weighted quadratic estimation of 21 cm power spectra and the real-world challenges presented universally by ...interferometric observation. By carefully evaluating various estimators and adapting our techniques for large but incomplete data sets, we develop a robust power spectrum estimation framework that preserves the so-called "Epoch of Reionization (EoR) window" and keeps track of estimator errors and covariances. We apply our method to observations from the 32-tile prototype of the Murchinson Widefield Array to demonstrate the importance of a judicious analysis technique. Lastly, we apply our method to investigate the dependence of the clean EoR window on frequency-especially the frequency dependence of the so-called "wedge" feature-and establish upper limits on the power spectrum from z = 6.2 to z = 11.7. Our lowest limit is Delta (k) < 0.3 Kelvin at 95% confidence at a comoving scale k = 0.046 Mpc super(-1) and z = 9.5.
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Abstract
We report upper limits on the Epoch of Reionization 21 cm power spectrum at redshifts 7.9 and 10.4 with 18 nights of data (∼36 hr 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 ∼10
9
with respect to the peak foreground power. This yields a 95% confidence upper limit on the 21 cm power spectrum of
Δ
21
2
≤
(
30.76
)
2
mK
2
at
k
= 0.192
h
Mpc
−1
at
z
= 7.9, and also
Δ
21
2
≤
(
95.74
)
2
mK
2
at
k
= 0.256
h
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
∥
modes, at high
k
∥
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 subreflections, 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.
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