🔭 astrophysics

Impact of Antenna Structure and Orientation on Forward-Modelled Global 21 cm Signal Recovery

This study quantifies how antenna structural and orientation mismodelling biases the recovery of the global 21 cm signal in forward-modelled analyses, demonstrating that while orientation errors as small as 0.25 degrees significantly skew parameter inference, Bayesian evidence can precisely infer orientation and partial signal recovery remains feasible even with imperfect beam models.

Original authors: Joe H. N. Pattison, John M. Cumner, Dominic J. Anstey, Saurabh Pegwal, Wessel Croukamp, Dirk I. L. de Villiers, Eloy de Lera Acedo

Published 2026-03-26

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Joe H. N. Pattison, John M. Cumner, Dominic J. Anstey, Saurabh Pegwal, Wessel Croukamp, Dirk I. L. de Villiers, Eloy de Lera Acedo

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Cosmic "Static" and the Perfect Antenna

Imagine the early Universe as a giant, dark room. For hundreds of thousands of years after the Big Bang, it was pitch black. Then, the first stars flickered on, and the gas in the room began to heat up and cool down in a specific rhythm. Scientists believe this rhythm left a faint "echo" or "whisper" in the form of radio waves, known as the Global 21 cm signal.

Finding this whisper is like trying to hear a single person whispering in a stadium full of people screaming. The "screaming" is the bright radio noise from our own galaxy (the foreground), which is millions of times louder than the cosmic whisper.

To hear the whisper, scientists use a special radio antenna (the REACH experiment) and a super-smart computer program that tries to mathematically subtract the screaming to reveal the whisper. This paper is about how tiny mistakes in how we build or aim that antenna can ruin the whole experiment.

The Problem: The "Imperfect" Antenna

The REACH antenna isn't just a simple stick; it's a complex structure sitting on a raised, serrated metal ground plane (like a jagged metal rug).

In the real world, things aren't perfect:

The Ground: The metal ground plane isn't perfectly flat. The wind, the sun, and the weight of the antenna might warp it slightly, like a trampoline that's been sat on unevenly.
The Angle: The antenna might be pointing a tiny fraction of a degree off from where the engineers thought it was pointing.

The scientists in this paper asked: "If our computer model thinks the antenna is perfect, but the real antenna is slightly warped or tilted, will we still hear the cosmic whisper?"

The Analogy: The Flashlight and the Wall

Imagine you are trying to read a tiny, faint message written on a wall in a dark room. You have a flashlight (the antenna) to shine on the wall.

The Ideal Scenario: You know exactly where the flashlight is pointing and exactly how the light beam spreads out. You can perfectly calculate the brightness of the wall and subtract it to find the message.
The Real Scenario: The flashlight is slightly bent, or you are holding it at a slightly wrong angle. The beam of light hits the wall differently than you thought.

If you don't account for this bend or angle, your calculation of the wall's brightness will be wrong. You might think the "noise" of the wall is actually the "message" you are looking for, or you might accidentally erase the real message.

What the Scientists Found

The team ran simulations using different versions of the antenna: one perfect, one with a warped ground, and one tilted slightly. Here is what they discovered:

1. The "Tilt" is Dangerous (Orientation)
Even a tiny tilt—about 0.25 degrees (roughly the width of a pencil held at arm's length)—is enough to mess up the results.

The "Galaxy Up" vs. "Galaxy Down": When the bright center of our galaxy is high in the sky (like a spotlight shining directly on your flashlight), a tiny tilt causes a huge error. It's like trying to read a note while someone is shining a laser pointer in your eyes; a tiny movement makes the glare unbearable.
The Solution: However, the scientists found a clever trick. Because the computer program uses "Bayesian Evidence" (a way of scoring how well a model fits the data), they can actually use the data itself to figure out the correct angle. It's like adjusting your flashlight until the glare disappears and the note becomes clear. The computer can "learn" the correct angle if it tries enough different possibilities.

2. The "Warped Rug" (Structure)
When the ground plane is warped (bumpy instead of flat), the radio signal gets distorted.

The Good News: If you only look at a small slice of the radio spectrum (a narrow band of frequencies), you can still figure out when the event happened (the frequency) and how long it lasted (the width). It's like being able to tell when the whisper happened, even if you can't hear it clearly.
The Bad News: You cannot accurately measure how loud the whisper was (the depth/strength). The warping of the antenna makes the signal look deeper or shallower than it really is. This is a big problem because the "loudness" tells us how hot or cold the early Universe was.

The Takeaway

This paper is a reality check for scientists trying to hear the first whispers of the Universe. It tells us:

Precision Matters: We need to know the exact angle and shape of our antennas. A "good enough" guess isn't good enough; we need millimeter and fraction-of-a-degree precision.
Strategy Matters: If we can't build a perfect antenna, we can choose when to observe (when the galaxy is below the horizon) to make the errors smaller.
Smart Math Helps: Even if our antenna isn't perfect, our computer models are smart enough to sometimes "self-correct" and find the right answer, but only if we are careful about what parts of the signal we trust.

In short, to hear the faintest echo of the Big Bang, we need to build our listening devices with extreme care and know exactly how they are shaped. If we get the shape wrong, we might hear a ghost instead of history.

1. Problem Statement

The detection of the global 21 cm signal from cosmic neutral hydrogen (the "Dark Ages" and "Epoch of Reionization") is hindered by the signal's extreme faintness (depth $\le$ 500 mK) compared to bright galactic foregrounds. While the REACH experiment employs a fully Bayesian, forward-modelled data analysis pipeline to separate systematics from the cosmological signal, this approach relies heavily on precise knowledge of the instrument's physical properties.

The core problem addressed is antenna mismodelling. In practice, the physical realization of an antenna (specifically the REACH hexagonal bladed dipole on a serrated ground plane) inevitably deviates from its idealized design due to:

Manufacturing tolerances and assembly errors.
Environmental factors (e.g., thermal expansion/contraction in the Karoo desert causing ground plane warping).
Orientation errors relative to true north.

The authors investigate how discrepancies between the simulated antenna beam used in data generation and the modelled beam used in signal recovery bias the inference of cosmological parameters.

2. Methodology

A. Instrument Characterization

The authors performed rigorous on-site measurements of the REACH radiometer in the Karoo Radio Reserve, South Africa:

Orientation: Measured using magnetic compasses and corrected via the 2025 World Magnetic Model. The dipole was found to be rotated $\sim$ 3.5° west of true north, with an uncertainty of 0.5–1.5°.
Topography: A custom measuring device (plumb bob and dumpy level) was used to map the ground plane's surface. They found the ground plane was not perfectly flat, with height variations (warping) of up to $\sim$ 8 cm (standard deviation 1.27 cm) relative to the dipole blades.

B. Antenna Modelling (CEM Simulations)

Using CST Microwave Studio, the authors generated four layers of antenna models to simulate increasing complexity:

FIS (Flat, Ideal, Straight): Idealized flat ground plane, ideal serrations, dipole aligned with the ground plane.
FRS (Flat, Realistic, Straight): Ground plane serrations match on-site measurements; dipole remains straight.
FRA (Flat, Realistic, Angled): Includes realistic serrations and the measured dipole rotation ( $\sim$ 3°).
BRA (Bumpy, Realistic, Angled): Includes realistic serrations, dipole rotation, and the measured ground plane topography (warping).

C. Data Analysis Pipeline

The study utilized the REACH Bayesian pipeline:

Data Generation: Simulated antenna temperatures were generated using the Global Sky Model (GSM), injecting a known 21 cm signal (Gaussian or flattened Gaussian) and noise.
Signal Recovery: The pipeline uses nested sampling (Polychord) to fit a likelihood function comparing observed data against a foreground model + 21 cm signal model.
Testing Strategy: The authors simulated observations under two conditions:
- "Galaxy Up": Galactic center above the horizon (high foreground anisotropy).
- "Galaxy Down": Galactic center below the horizon (lower anisotropy).
  They then attempted to recover the signal using models with varying degrees of antenna complexity and orientation mismatches.

3. Key Contributions

Quantification of Orientation Sensitivity: The study establishes that orientation mismatches as small as 0.25° can significantly bias signal recovery, particularly when the galactic center is visible.
Bayesian Evidence for Orientation Calibration: The authors demonstrate that Bayesian evidence decreases monotonically as the orientation mismatch increases. This suggests a method to infer the true antenna orientation by scanning model realizations, potentially achieving precision better than physical compass measurements ( $\pm$ 0.25°).
Parameter-Specific Sensitivity: The paper distinguishes between the sensitivity of different signal parameters:
- Frequency and Width: Can be robustly recovered even with imperfect beam models, especially when restricting analysis to specific frequency bands.
- Signal Depth: Highly sensitive to beam errors; incorrect modelling drives the depth parameter to prior boundaries or biases it significantly.
Ground Plane Impact: Quantified that centimeter-scale ground plane deformations (warping) cause antenna temperature differences on the order of Kelvin, which can mask the 21 cm signal if not modelled.

4. Key Results

Orientation Mismatch:
- In "Galaxy Up" scenarios, a rotation $>1^\circ$ causes temperature mismatches $>1000$ ppm. Even $0.25^\circ$ causes $>300$ ppm errors.
- In "Galaxy Down" scenarios, the system is more forgiving ( $<100$ ppm for $<1^\circ$ ), but a 0.25° mismatch still biases the recovered signal beyond 3 $\sigma$ , saturating priors and preventing reliable inference.
- Conclusion: Orientation must be modelled to $<0.25^\circ$ precision for unbiased broadband recovery.
Structural Mismodelling:
- Moving from ideal (FIS) to realistic (BRA) models introduces frequency-dependent ripples in the gain pattern.
- Broadband Recovery: Fitting the full frequency band with a mismodelled beam (e.g., using FRA to fit BRA data) leads to parameter saturation (bias) for signal depth and width.
- Partial Recovery: When restricting the analysis to lower frequencies (e.g., $<80$ MHz) where beam-induced spectral structure is minimized, the center frequency and width of an EDGES-like signal can be accurately recovered even with a mismodelled ground plane. However, the signal depth remains heavily biased.
Evidence as a Metric:
- The log-evidence of the fit serves as a robust metric for identifying the correct antenna orientation and structural complexity. The model with the highest evidence corresponds to the best match with the true physical state.

5. Significance and Implications

For Instrument Design: The results highlight the need for symmetric, zenith-oriented beams and stable mechanical structures to minimize beam-sky coupling. It underscores that "simple" antennas still require high-precision manufacturing and environmental stability.
For Observing Strategy: Observing when the galactic center is below the horizon ("Galaxy Down") significantly reduces sensitivity to orientation errors, offering a strategic mitigation path.
For Data Analysis:
- Forward-modelled approaches offer superior interpretability over polynomial foreground removal but impose stricter requirements on instrument knowledge.
- The study validates a workflow where Bayesian evidence is used to self-calibrate antenna orientation and structural parameters, potentially overcoming the limitations of physical surveying tools.
- It suggests that while full broadband recovery of all parameters requires perfect beam knowledge, partial recovery of key astrophysical features (timing of reionization via frequency/width) is possible with imperfect models, provided the analysis is frequency-restricted.

In summary, this paper provides a critical quantitative framework for the REACH experiment and future global 21 cm missions, demonstrating that while antenna mismodelling is a severe systematic, it is quantifiable and potentially correctable through rigorous Bayesian inference and strategic observing.