Redundant Array Configurations for 21 cm Cosmology

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.Comment: 19 pages, 11 figures. Revised to match the accepted ApJ versio

Detecting the 21 cm Forest in the 21 cm Power Spectrum

We describe a new technique for constraining the radio loud population of active galactic nuclei at high redshift by measuring the imprint of 21 cm spectral absorption features (the 21 cm forest) on the 21 cm power spectrum. Using semi-numerical simulations of the intergalactic medium and a semi-empirical source population we show that the 21 cm forest dominates a distinctive region of $k$-space, $k \gtrsim 0.5 \text{Mpc}^{-1}$. By simulating foregrounds and noise for current and potential radio arrays, we find that a next generation instrument with a collecting area on the order of $\sim 0.1\text{km}^2$ (such as the Hydrogen Epoch of Reionization Array) may separately constrain the X-ray heating history at large spatial scales and radio loud active galactic nuclei of the model we study at small ones. We extrapolate our detectability predictions for a single radio loud active galactic nuclei population to arbitrary source scenarios by analytically relating the 21 cm forest power spectrum to the optical depth power spectrum and an integral over the radio luminosity function.Comment: 20 pages, 17 figures, accepted for publication in MNRA

Constraining High Redshift X-ray Sources with Next Generation 21 cm Power Spectrum Measurements

We use the Fisher matrix formalism and semi-numerical 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 $z=25$, we find that the proposed 331 element HERA and SKA phase 1 will be capable of placing $\lesssim 10\%$ 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.Comment: 15 pages, 10 figures, Accepted to MNRA

The impact of modelling errors on interferometer calibration for 21 cm power spectra

We study the impact of sky-based calibration errors from source mismodeling 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 catalogs 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, unmodeled 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 (EoR). Given our current precision in primary beam and foreground modeling, 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 down-weights long baselines can eliminate contamination in most of the region outside of the wedge with only a modest increase in instrumental noise.Comment: 24 pages, 8 figures, 1 table, accepted for publication in MNRAS. Matches published versio

Polarized Redundant-Baseline Calibration for 21 cm Cosmology Without Adding Spectral Structure

21 cm cosmology is a promising new probe of the evolution of visible matter in our universe, especially during the poorly-constrained Cosmic Dawn and Epoch of Reionization. However, in order to separate the 21 cm signal from bright astrophysical foregrounds, we need an exquisite understanding of our telescopes so as to avoid adding spectral structure to spectrally-smooth foregrounds. One powerful calibration method relies on repeated simultaneous measurements of the same interferometric baseline to solve for the sky signal and for instrumental parameters simultaneously. However, certain degrees of freedom are not constrained by asserting internal consistency between redundant measurements. In this paper, we review the origin of these "degeneracies" of redundant-baseline calibration and demonstrate how they can source unwanted spectral structure in our measurement and show how to eliminate that additional, artificial structure. We also generalize redundant calibration to dual-polarization instruments, derive the degeneracy structure, and explore the unique challenges to calibration and preserving spectral smoothness presented by a polarized measurement.Comment: 12 pages, 3 figures, updated to match the published MNRAS versio

Spectral Redundancy for Calibrating Interferometers and Suppressing the Foreground Wedge in 21\,cm Cosmology

Observations of 21\,cm line from neutral hydrogen promise to be an exciting new probe of astrophysics and cosmology during the Cosmic Dawn and through the Epoch of Reionization (EoR) to when dark energy accelerates the expansion of the Universe. At each of these epochs, separating bright foregrounds from the cosmological signal is a primary challenge that requires exquisite calibration. In this paper, we present a new calibration method called \textsc{nucal} that extends redundant-baseline calibration, allowing spectral variation in antenna responses to be solved for by using correlations between visibilities measuring the same angular Fourier modes at different frequencies. By modeling the chromaticity of the beam-weighted sky with a tunable set of discrete prolate spheroidal sequences (DPSS), we develop a calibration loop that optimizes for spectrally smooth calibrated visibilities. Crucially, this technique does not require explicit models of the sky or the primary beam. With simulations that incorporate realistic source and beam chromaticity, we show that this method solves for unsmooth bandpass features, exposes narrowband interference systematics, and suppresses smooth-spectrum foregrounds below the level of 21\,cm reionization models, even within much of the so-called "wedge" region where current foreground mitigation techniques struggle. We show that this foreground subtraction can be performed with minimal cosmological signal loss for certain well-sampled angular Fourier modes, making spectral-redundant calibration a promising technique for current and next-generation 21\,cm intensity mapping experiments.Comment: 22 pages, 10 figures, Submitted to MNRA