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Register a new userMethods of Error Estimation for Delay Power Spectra in $21,textrm{cm}$ Cosmology
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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.
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Detection of 21~cm emission of HI from the epoch of reionization, at redshifts z>6, is limited primarily by foreground emission. We investigate the signatures of wide-field measurements and an all-sky foreground model using the delay spectrum technique that maps the measurements to foreground object locations through signal delays between antenna pairs. We demonstrate interferometric measurements are inherently sensitive to all scales, including the largest angular scales, owing to the nature of wide-field measurements. These wide-field effects are generic to all observations but antenna shapes impact their amplitudes substantially. A dish-shaped antenna yields the most desirable features from a foreground contamination viewpoint, relative to a dipole or a phased array. Comparing data from recent Murchison Widefield Array observations, we demonstrate that the foreground signatures that have the largest impact on the HI signal arise from power received far away from the primary field of view. We identify diffuse emission near the horizon as a significant contributing factor, even on wide antenna spacings that usually represent structures on small scales. For signals entering through the primary field of view, compact emission dominates the foreground contamination. These two mechanisms imprint a characteristic pitchfork signature on the foreground wedge in Fourier delay space. Based on these results, we propose that selective down-weighting of data based on antenna spacing and time can mitigate foreground contamination substantially by a factor ~100 with negligible loss of sensitivity.
Contamination from instrumental effects interacting with bright astrophysical sources is the primary impediment to measuring Epoch of Reionization and BAO 21 cm power spectra---an effect called mode-mixing. In this paper we identify four fundamental power spectrum shapes produced by mode-mixing that will affect all upcoming observations. We are able, for the first time, to explain the wedge-like structure seen in advanced simulations and to forecast the shape of an EoR window that is mostly free of contamination. Understanding the origins of these contaminations also enables us to identify calibration and foreground subtraction errors below the imaging limit, providing a powerful new tool for precision observations.
Calibration precision is currently a limiting systematic in 21 cm cosmology experiments. While there are innumerable calibration approaches, most can be categorized as either `sky-based, relying on an extremely accurate model of astronomical foreground emission, or `redundant, requiring a precisely regular array with near-identical antenna response patterns. Both of these classes of calibration are inflexible to the realities of interferometric measurement. In practice, errors in the foreground model, antenna position offsets, and beam response inhomogeneities degrade calibration performance and contaminate the cosmological signal. Here we show that sky-based and redundant calibration can be unified into a highly general and physically motivated calibration framework based on a Bayesian statistical formalism. Our new framework includes sky and redundant calibration as special cases but can additionally support relaxing the rigid assumptions implicit in those approaches. Furthermore, we present novel calibration techniques such as redundant calibration for arrays with no redundant baselines, representing an alternative calibration method for imaging arrays such as the MWA Phase I. These new calibration approaches could mitigate systematics and reduce calibration error, thereby improving the precision of cosmological measurements.
Detecting a signal from the Epoch of Reionisation (EoR) requires an exquisite understanding of galactic and extra-galactic foregrounds, low frequency radio instruments, instrumental calibration, and data analysis pipelines. In this work we build upon existing work that aims to understand the impact of calibration errors on 21-cm power spectrum (PS) measurements. It is well established that calibration errors have the potential to inhibit EoR detections by introducing additional spectral features that mimic the structure of EoR signals. We present a straightforward way to estimate the impact of a wide variety of modelling residuals in EoR PS estimation. We apply this framework to the specific case of broken dipoles in Murchison Widefield Array (MWA) to understand its effect and estimate its impact on PS estimation. Combining an estimate of the percentage of MWA tiles that have at least one broken dipole (15%-40%) with an analytic description of beam errors induced by such dipoles, we compute the residuals of the foregrounds after calibration and source subtraction. We find that that incorrect beam modelling introduces bias in the 2D-PS on the order of $sim 10^3, mathrm{mK}^2 ,h^{-3}, mathrm{Mpc}^{3}$. Although this is three orders of magnitude lower than current lowest limits, it is two orders of magnitude higher than the expected signal. Determining the accuracy of both current beam models and direction dependent calibration pipelines is therefore crucial in our search for an EoR signal.
We analyse the accuracy of radio interferometric gridding of visibilities with the aim to quantify the Epoch of Reionization (EoR) 21-cm power spectrum bias caused by gridding, ultimately to determine the suitability of different imaging algorithms and gridding settings for 21-cm power spectrum analysis. We simulate realistic LOFAR data, and construct power spectra with convolutional gridding and w-stacking, w-projection, image domain gridding and without w-correction. These are compared against directly Fourier transformed data. The influence of oversampling, kernel size, w-quantization, kernel windowing function and image padding are quantified. The gridding excess power is measured with a foreground subtraction strategy, for which foregrounds have been subtracted using Gaussian progress regression, as well as with a foreground avoidance strategy. Constructing a power spectrum that has a bias significantly lower compared to the expected EoR signals is possible with the tested methods, but requires a kernel oversampling factor > 4000 and, when using w-correction, > 500 w-quantization levels. These values are higher than typical values used for imaging, but are computationally feasible. The kernel size and padding factor parameters are less crucial. Among the tested methods, image domain gridding shows the highest accuracy with the lowest imaging time. LOFAR 21-cm power spectrum results are not affected by gridding. Image domain gridding is overall the most suitable algorithm for 21-cm EoR experiments, including for future SKA EoR analyses. Nevertheless, convolutional gridding with tuned parameters results in sufficient accuracy. This holds also for w-stacking for wide-field imaging. The w-projection algorithm is less suitable because of the kernel oversampling requirements, and a faceting approach is unsuitable due to the resulting spatial discontinuities.
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