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Register a new userCharacterizing Signal Loss in the 21 cm Reionization Power Spectrum: A Revised Study of PAPER-64
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The Epoch of Reionization (EoR) is an uncharted era in our Universes 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 21cm 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 HERAs 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 21cm 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. (in prep.) and supersede results from previously published PAPER analyses.
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21 cm Epoch of Reionization observations promise to transform our understanding of galaxy formation, but these observations are impossible without unprecedented levels of instrument calibration. We present end-to-end simulations of a full EoR power spectrum analysis including all of the major components of a real data processing pipeline: models of astrophysical foregrounds and EoR signal, frequency-dependent instrument effects, sky-based antenna calibration, and the full PS analysis. This study reveals that traditional sky-based per-frequency antenna calibration can only be implemented in EoR measurement analyses if the calibration model is unrealistically accurate. For reasonable levels of catalog completeness, the calibration introduces contamination in otherwise foreground-free power spectrum modes, precluding a PS measurement. We explore the origin of this contamination and potential mitigation techniques. We show that there is a strong joint constraint on the precision of the calibration catalog and the inherent spectral smoothness of antennae, and that this has significant implications for the instrumental design of the SKA and other future EoR observatories.
The non-Gaussian nature of the epoch of reionization (EoR) 21-cm signal has a significant impact on the error variance of its power spectrum $P({bf textit{k}})$. We have used a large ensemble of semi-numerical simulations and an analytical model to estimate the effect of this non-Gaussianity on the entire error-covariance matrix ${mathcal{C}}_{ij}$. Our analytical model shows that ${mathcal{C}}_{ij}$ has contributions from two sources. One is the usual variance for a Gaussian random field which scales inversely of the number of modes that goes into the estimation of $P({bf textit{k}})$. The other is the trispectrum of the signal. Using the simulated 21-cm signal ensemble, an ensemble of the randomized signal and ensembles of Gaussian random ensembles we have quantified the effect of the trispectrum on the error variance ${mathcal{C}}_{ij}$. We find that its relative contribution is comparable to or larger than that of the Gaussian term for the $k$ range $0.3 leq k leq 1.0 ,{rm Mpc}^{-1}$, and can be even $sim 200$ times larger at $k sim 5, {rm Mpc}^{-1}$. We also establish that the off-diagonal terms of ${mathcal{C}}_{ij}$ have statistically significant non-zero values which arise purely from the trispectrum. This further signifies that the error in different $k$ modes are not independent. We find a strong correlation between the errors at large $k$ values ($ge 0.5 ,{rm Mpc}^{-1}$), and a weak correlation between the smallest and largest $k$ values. There is also a small anti-correlation between the errors in the smallest and intermediate $k$ values. These results are relevant for the $k$ range that will be probed by the current and upcoming EoR 21-cm experiments.
We present the 21 cm power spectrum analysis approach of the Murchison Widefield Array Epoch of Reionization project. In this paper, we compare the outputs of multiple pipelines for the purpose of validating statistical limits cosmological hydrogen at redshifts between 6 and 12. Multiple, independent, data calibration and reduction pipelines are used to make power spectrum limits on a fiducial night of data. Comparing the outputs of imaging and power spectrum stages highlights differences in calibration, foreground subtraction and power spectrum calculation. The power spectra found using these different methods span a space defined by the various tradeoffs between speed, accuracy, and systematic control. Lessons learned from comparing the pipelines range from the algorithmic to the prosaically mundane; all demonstrate the many pitfalls of neglecting reproducibility. We briefly discuss the way these different methods attempt to handle the question of evaluating a significant detection in the presence of foregrounds.
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 HERAs 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.
A proposed method for dealing with foreground emission in upcoming 21-cm observations from the epoch of reionization is to limit observations to an uncontaminated window in Fourier space. Foreground emission can be avoided in this way, since it is limited to a wedge-shaped region in $k_{parallel}, k_{perp}$ space. However, the power spectrum is anisotropic owing to redshift-space distortions from peculiar velocities. Consequently, the 21-cm power spectrum measured in the foreground avoidance window---which samples only a limited range of angles close to the line-of-sight direction---differs from the full spherically-averaged power spectrum which requires an average over emph{all} angles. In this paper, we calculate the magnitude of this wedge bias for the first time. We find that the bias is strongest at high redshifts, where measurements using foreground avoidance will over-estimate the power spectrum by around 100 per cent, possibly obscuring the distinctive rise and fall signature that is anticipated for the spherically-averaged 21-cm power spectrum. In the later stages of reionization, the bias becomes negative, and smaller in magnitude ($lesssim 20$ per cent). The effect shows only a weak dependence on spatial scale and reionization topology.
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