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Abstract We introduce DAYENU, a linear, spectral filter for HI intensity mapping that achieves the desirable foreground mitigation and error minimization properties of inverse co-variance weighting with minimal modeling of the underlying data. Beyond 21 cm power-spectrum estimation, our filter is suitable for any analysis where high dynamic-range removal of spectrally smooth foregrounds in irregularly (or regularly) sampled data is required, something required by many other intensity mapping techniques. Our filtering matrix is diagonalized by Discrete Prolate Spheroidal Sequences which are an optimal basis to model band-limited foregrounds in 21 cm intensity mapping experiments in the sense that they maximally concentrate power within a finite region of Fourier space. We show that DAYENU enables the access of large-scale line-of-sight modes that are inaccessible to tapered DFT estimators. Since these modes have the largest SNRs, DAYENU significantly increases the sensitivity of 21 cm analyses over tapered Fourier transforms. Slight modifications allow us to use DAYENU as a linear replacement for iterative delay CLEANing (DAYENUREST). We refer readers to the Code section at the end of this paper for links to examples and code. 

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. 

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. 

ABSTRACT The key challenge in the observation of the redshifted 21-cm signal from cosmic reionization is its separation from the much brighter foreground emission. Such separation relies on the different spectral properties of the two components, although, in real life, the foreground intrinsic spectrum is often corrupted by the instrumental response, inducing systematic effects that can further jeopardize the measurement of the 21-cm signal. In this paper, we use Gaussian Process Regression to model both foreground emission and instrumental systematics in ∼2 h of data from the Hydrogen Epoch of Reionization Array. We find that a simple co-variance model with three components matches the data well, giving a residual power spectrum with white noise properties. These consist of an ‘intrinsic’ and instrumentally corrupted component with a coherence scale of 20 and 2.4 MHz, respectively (dominating the line-of-sight power spectrum over scales k∥ ≤ 0.2 h cMpc−1) and a baseline-dependent periodic signal with a period of ∼1 MHz (dominating over k∥ ∼ 0.4–0.8 h cMpc−1), which should be distinguishable from the 21-cm Epoch of Reionization signal whose typical coherence scale is ∼0.8 MHz.