skip to main content

Title: Redundant-baseline calibration of the hydrogen epoch of reionization array
ABSTRACT In 21-cm cosmology, precision calibration is key to the separation of the neutral hydrogen signal from very bright but spectrally smooth astrophysical foregrounds. The Hydrogen Epoch of Reionization Array (HERA), an interferometer specialized for 21-cm cosmology and now under construction in South Africa, was designed to be largely calibrated using the self-consistency of repeated measurements of the same interferometric modes. This technique, known as redundant-baseline calibration resolves most of the internal degrees of freedom in the calibration problem. It assumes, however, on antenna elements with identical primary beams placed precisely on a redundant grid. In this work, we review the detailed implementation of the algorithms enabling redundant-baseline calibration and report results with HERA data. We quantify the effects of real-world non-redundancy and how they compare to the idealized scenario in which redundant measurements differ only in their noise realizations. Finally, we study how non-redundancy can produce spurious temporal structure in our calibration solutions – both in data and in simulations – and present strategies for mitigating that structure.
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more » ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; « less
Award ID(s):
1636646 1701536
Publication Date:
NSF-PAR ID:
10204061
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
499
Issue:
4
Page Range or eLocation-ID:
5840 to 5861
ISSN:
0035-8711
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    The Canadian Hydrogen Intensity Mapping Experiment (CHIME) is a drift scan radio telescope operating across the 400–800 MHz band. CHIME is located at the Dominion Radio Astrophysical Observatory near Penticton, BC, Canada. The instrument is designed to map neutral hydrogen over the redshift range 0.8–2.5 to constrain the expansion history of the universe. This goal drives the design features of the instrument. CHIME consists of four parallel cylindrical reflectors, oriented north–south, each 100 m × 20 m and outfitted with a 256-element dual-polarization linear feed array. CHIME observes a two-degree-wide stripe covering the entire meridian at any given moment, observing three-quarters of the sky every day owing to Earth’s rotation. An FX correlator utilizes field-programmable gate arrays and graphics processing units to digitize and correlate the signals, with different correlation products generated for cosmological, fast radio burst, pulsar, very long baseline interferometry, and 21 cm absorber back ends. For the cosmology back end, theNfeed2correlation matrix is formed for 1024 frequency channels across the band every 31 ms. A data receiver system applies calibration and flagging and, for our primary cosmological data product, stacks redundant baselines and integrates for 10 s. We present an overview of themore »instrument, its performance metrics based on the first 3 yr of science data, and we describe the current progress in characterizing CHIME’s primary beam response. We also present maps of the sky derived from CHIME data; we are using versions of these maps for a cosmological stacking analysis, as well as for investigation of Galactic foregrounds.

    « less
  2. ABSTRACT

    High-fidelity radio interferometric data calibration that minimizes spurious spectral structure in the calibrated data is essential in astrophysical applications, such as 21 cm cosmology, which rely on knowledge of the relative spectral smoothness of distinct astrophysical emission components to extract the signal of interest. Existing approaches to radio interferometric calibration have been shown to impart spurious spectral structure to the calibrated data if the sky model used to calibrate the data is incomplete. In this paper, we introduce BayesCal: a novel solution to the sky-model incompleteness problem in interferometric calibration, designed to enable high-fidelity data calibration. The BayesCal data model supplements the a priori known component of the forward model of the sky with a statistical model for the missing and uncertain flux contribution to the data, constrained by a prior on the power in the model. We demonstrate how the parameters of this model can be marginalized out analytically, reducing the dimensionality of the parameter space to be sampled from and allowing one to sample directly from the posterior probability distribution of the calibration parameters. Additionally, we show how physically motivated priors derived from theoretical and measurement-based constraints on the spectral smoothness of the instrumental gains can be usedmore »to constrain the calibration solutions. In a companion paper, we apply this algorithm to simulated observations with a HERA-like array and demonstrate that it enables up to four orders of magnitude suppression of power in spurious spectral fluctuations relative to standard calibration approaches.

    « less
  3. null (Ed.)
    ABSTRACT Precision calibration poses challenges to experiments probing the redshifted 21-cm signal of neutral hydrogen from the Cosmic Dawn and Epoch of Reionization (z ∼ 30–6). In both interferometric and global signal experiments, systematic calibration is the leading source of error. Though many aspects of calibration have been studied, the overlap between the two types of instruments has received less attention. We investigate the sky based calibration of total power measurements with a HERA dish and an EDGES-style antenna to understand the role of autocorrelations in the calibration of an interferometer and the role of sky in calibrating a total power instrument. Using simulations we study various scenarios such as time variable gain, incomplete sky calibration model, and primary beam model. We find that temporal gain drifts, sky model incompleteness, and beam inaccuracies cause biases in the receiver gain amplitude and the receiver temperature estimates. In some cases, these biases mix spectral structure between beam and sky resulting in spectrally variable gain errors. Applying the calibration method to the HERA and EDGES data, we find good agreement with calibration via the more standard methods. Although instrumental gains are consistent with beam and sky errors similar in scale to those simulated,more »the receiver temperatures show significant deviations from expected values. While we show that it is possible to partially mitigate biases due to model inaccuracies by incorporating a time-dependent gain model in calibration, the resulting errors on calibration products are larger and more correlated. Completely addressing these biases will require more accurate sky and primary beam models.« less
  4. ABSTRACT

    In a companion paper, we presented bayescal, a mathematical formalism for mitigating sky-model incompleteness in interferometric calibration. In this paper, we demonstrate the use of bayescal to calibrate the degenerate gain parameters of full-Stokes simulated observations with a HERA-like hexagonal close-packed redundant array, for three assumed levels of completeness of the a priori known component of the calibration sky model. We compare the bayescal calibration solutions to those recovered by calibrating the degenerate gain parameters with only the a priori known component of the calibration sky model both with and without imposing physically motivated priors on the gain amplitude solutions and for two choices of baseline length range over which to calibrate. We find that bayescal provides calibration solutions with up to 4 orders of magnitude lower power in spurious gain amplitude fluctuations than the calibration solutions derived for the same data set with the alternate approaches, and between ∼107 and ∼1010 times smaller than in the mean degenerate gain amplitude, on the full range of spectral scales accessible in the data. Additionally, we find that in the scenarios modelled only bayescal has sufficiently high fidelity calibration solutions for unbiased recovery of the 21-cm power spectrum on large spectralmore »scales (k∥ ≲ 0.15 hMpc−1). In all other cases, in the completeness regimes studied, those scales are contaminated.

    « less
  5. ABSTRACT

    Measurements of the one-point probability distribution function and higher-order moments (variance, skewness, and kurtosis) of the high-redshift 21-cm fluctuations are among the most direct statistical probes of the non-Gaussian nature of structure formation and evolution during re-ionization. However, contamination from astrophysical foregrounds and instrument systematics pose significant challenges in measuring these statistics in real observations. In this work, we use forward modelling to investigate the feasibility of measuring 21-cm one-point statistics through a foreground avoidance strategy. Leveraging the characteristic wedge-shape of the foregrounds in k-space, we apply a wedge-cut filtre that removes the foreground contaminated modes from a mock data set based on the Hydrogen Epoch of Re-ionization Array (HERA) instrument, and measure the one-point statistics from the image-space representation of the remaining non-contaminated modes. We experiment with varying degrees of wedge-cutting over different frequency bandwidths and find that the centre of the band is the least susceptible to bias from wedge-cutting. Based on this finding, we introduce a rolling filtre method that allows reconstruction of an optimal wedge-cut 21-cm intensity map over the full bandwidth using outputs from wedge-cutting over multiple sub-bands. We perform Monte Carlo simulations to show that HERA should be able to measure the risemore »in skewness and kurtosis near the end of re-ionization with the rolling wedge-cut method if foreground leakage from the Fourier transform window function can be controlled.

    « less