Informing antenna design for sky-averaged 21-cm experiments using a simulated Bayesian data analysis pipeline

Detecting the faint 21-cm signal from the Cosmic Dawn and the Epoch of Reionization is one of the ultimate goals of modern cosmology, but it is an endeavour fraught with immense observational challenges. In our paper, 2106.10193, we introduce a robust methodology to guide the design of radio antennae for these exacting experiments, ensuring they are optimized not just for sensitivity, but for the ability to distinguish the cosmological signal from overwhelming astrophysical foregrounds.

The Challenge of Antenna Chromaticity

The primary obstacle in global 21-cm experiments is the presence of galactic synchrotron and free-free emission, which are orders of magnitude brighter than the predicted cosmological signal. A common strategy to separate these components relies on the spectral smoothness of the foregrounds. However, this is complicated by the antenna itself. No real-world wideband antenna has a perfectly uniform response across all frequencies—an effect known as chromaticity. This frequency-dependent beam pattern couples the spatial structure of the sky into the frequency domain, introducing complex, non-smooth distortions that can easily be mistaken for, or completely obscure, the 21-cm signal. This issue has been a central point of discussion following the tentative detection by the EDGES experiment (10.1038/nature25792) and the subsequent scrutiny regarding potential uncorrected systematic effects (10.1038/s41586-018-0796-5).

Simply minimizing chromaticity may not be the optimal strategy. An antenna’s performance depends on the nature of its chromatic distortions and whether they can be accurately modelled and separated from the signal. An antenna with a simple, regular chromatic pattern might be preferable to a more achromatic one whose residual distortions are degenerate with the 21-cm signal.

A Bayesian Pipeline for Antenna Evaluation

To address this complexity, this work, led by Dominic Anstey in collaboration with Eloy de Lera Acedo and Will Handley, develops an end-to-end simulation framework to rigorously test antenna designs. Our method moves beyond simple metrics and evaluates an antenna’s performance within the context of a full Bayesian data analysis pipeline. The process involves:

1. Simulated Observations: We create realistic mock datasets by convolving electromagnetic simulations of an antenna’s beam with a physically motivated, spatially varying model of the radio sky.
2. Signal Injection: A variety of plausible Gaussian-shaped 21-cm signals, with different amplitudes and central frequencies, are injected into these mock datasets.
3. Bayesian Recovery: We then employ the REACH data analysis pipeline, further detailed in 10.1093/mnras/stab1765, to analyse the data. This pipeline uses the nested sampling algorithm PolyChord (10.1093/mnras/stv1911) to simultaneously fit a model for the foregrounds (including chromatic effects) and the cosmological signal.
4. Model Comparison: By comparing the Bayesian evidence of models with and without a 21-cm signal, we can quantify the confidence with which a given signal can be detected and the accuracy of its reconstruction.

Comparing Candidate Designs for REACH

We applied this powerful simulation pipeline to five candidate antenna designs for the Radio Experiment for the Analysis of Cosmic Hydrogen (REACH):

• A conical log spiral antenna
• An inverted conical sinuous antenna
• Three dipole designs: polygonal, rectangular, and elliptical-bladed

Our results revealed a clear hierarchy in performance that would not have been apparent from superficial characterizations of beam chromaticity alone.

• The Winner: Conical Log Spiral: This design performed exceptionally well, consistently recovering every injected 21-cm signal—even those with very low amplitudes (0.05 K)—with high accuracy and statistical confidence. Its regular chromatic structure was effectively modelled by our pipeline.
• The Runner-Up: Polygonal Dipole: This antenna also performed robustly, successfully detecting most signals. Its main limitation was an inability to confidently identify signals with both very low amplitudes and low central frequencies.
• The Laggard: Conical Sinuous: Surprisingly, this antenna, which has a relatively low degree of chromaticity, performed the worst. It was only able to detect the highest-amplitude signals and, more problematically, produced confident but biased or entirely false detections for weaker signals. This demonstrates that its irregular chromatic pattern creates distortions that are highly degenerate with the 21-cm signal, fooling the analysis pipeline.

This work provides a crucial demonstration that a holistic, simulation-based approach is essential for designing next-generation 21-cm experiments. By integrating realistic instrument models with advanced Bayesian inference, we can make informed design choices that maximize the potential for a definitive detection of signals from our cosmic dawn.

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