🔭 astrophysics

Joint Estimation of Properties of the Lunar Subsurface and Galactic Foregrounds with LuSEE-Night

This paper demonstrates that a Bayesian inference pipeline can successfully and robustly jointly estimate the dielectric properties of the lunar subsurface and galactic foregrounds for the LuSEE-Night mission, leveraging their distinct spectral signatures to overcome calibration challenges caused by subsurface reflections.

Original authors: Fatima Yousuf, Zack Li, Stuart D. Bale, David W. Barker, Jack Burns, Christian H. Bye, Hugo Camacho, Cristina-Maria Cordun, Johnny Dorigo Jones, Adam Fahs, Sonia Ghosh, Keith Goetz, Robert Grimm, Sven

Published 2026-04-24

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CC BY 4.0

Original authors: Fatima Yousuf, Zack Li, Stuart D. Bale, David W. Barker, Jack Burns, Christian H. Bye, Hugo Camacho, Cristina-Maria Cordun, Johnny Dorigo Jones, Adam Fahs, Sonia Ghosh, Keith Goetz, Robert Grimm, Sven Herrmann, Joshua J. Hibbard, Oliver Jeong, Marc Klein-Wolt, Léon V. E. Koopmans, Joel Krajewski, Corentin Louis, Milan Maksimović, Ryan McLean, Raul A. Monsalve, Arnur Nigmetov, Paul O'Connor, Aaron Parsons, Michel Piat, Marc Pulupa, Rugved Pund, David Rapetti, Kaja M. Rotermund, Benjamin Saliwanchik, Anže Slosar, Graham Speedie, Nikolai Stefanov, David Sundkvist, Aritoki Suzuki, Harish K. Vedantham, Philippe Zarka

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

Imagine you are trying to listen to a very faint, ancient whisper from the beginning of the universe. This whisper is the "Dark Ages" signal, a radio hum from when the universe was just a baby. To hear it, you need to go to the Moon, specifically the far side, because Earth's atmosphere and our radio chatter (like Wi-Fi and cell towers) are too loud and block the view.

Enter LuSEE-Night, a new radio telescope scheduled to land on the Moon in 2027. It's like a giant, sensitive ear planted in the lunar dust.

However, there's a problem. The Moon isn't just a flat, empty stage. The ground underneath the telescope is made of lunar soil (regolith) that has unknown electrical properties. Think of the ground as a mysterious mirror.

The Core Problem: The "Muddy Mirror"

When the telescope listens to the sky, the radio waves don't just come from above; they also bounce off the ground.

The Analogy: Imagine you are trying to hear a bird singing in a forest (the galaxy), but you are standing on a floor covered in thick, sticky mud (the lunar subsurface). The mud doesn't just sit there; it soaks up some of the sound and changes how the sound bounces back to your ears.
The Issue: If you don't know exactly how "sticky" or "spongy" the mud is, you can't tell if the sound you hear is the bird singing normally, or if the mud is distorting the sound. This makes it hard to separate the real cosmic signal from the ground's interference.

The Solution: Solving a Puzzle with Two Unknowns

The scientists in this paper asked a tricky question: Can we figure out what the ground is made of AND what the sky sounds like at the same time?

Usually, scientists try to fix one thing before studying the other. But here, they used a clever mathematical trick called Bayesian Inference.

The Analogy: Imagine you are trying to guess the recipe of a soup (the sky) and the type of pot it's being cooked in (the ground) just by tasting the soup.
- If you change the pot (the ground), the soup tastes different in a very specific way: it changes the texture or the crunch right in the middle of the flavor profile.
- If you change the recipe (the sky), the whole flavor profile shifts smoothly from start to finish.

Because the ground messes with the sound in a "bumpy" way (specifically around a certain pitch, like a resonance) and the sky changes the sound in a "smooth" way, the scientists realized they could untangle the two.

What They Did

Built a Virtual Moon: They used powerful computers to simulate the LuSEE-Night telescope on thousands of different types of "virtual moon grounds." Some were spongy, some were hard, some had layers.
Created a "Sound Map": They simulated what the telescope would hear for each type of ground, mixing in a realistic model of the Milky Way galaxy.
The "Magic" Filter: They created a digital "translator" (an emulator) that could predict what the telescope would hear for any combination of ground type and sky sound.
The Test: They fed the computer a fake set of data (a mix of a specific ground type and a specific sky sound) and asked the computer to guess the ingredients.

The Results

The computer was surprisingly good at it!

It successfully guessed the electrical properties of the lunar ground (how deep the layers were and how "conductive" they were).
It simultaneously guessed the characteristics of the galactic radio noise.

Why This Matters

This is a huge step forward. It means that when LuSEE-Night actually lands in 2027, it won't need to wait years to figure out what the ground is made of before it can start studying the universe. It can do both jobs at once.

The Takeaway:
The Moon's ground is like a tricky filter that distorts our view of the cosmos. But because the ground distorts the view in a different "pattern" than the universe changes, we can use math to reverse-engineer both the filter and the picture simultaneously. This ensures that when we finally hear that faint whisper from the Dark Ages, we know exactly what it sounds like and that it wasn't just the lunar mud talking.

1. Problem Statement

The Lunar Surface Electromagnetics Experiment (LuSEE-Night) is a low-frequency radio telescope scheduled for deployment on the lunar far side in 2027. Its primary scientific goal is to detect the faint 21-cm signal from the Cosmic Dark Ages ( $z \sim 30-200$ ). However, this signal is extremely weak (tens of mK) and buried beneath galactic foregrounds that are five orders of magnitude brighter.

A critical challenge for LuSEE-Night is the unknown dielectric properties of the lunar subsurface at the landing site. The lunar regolith acts as a lossy dielectric that interacts with the antenna, causing:

Beam Distortion: Reflections from the subsurface alter the antenna's primary beam pattern by 10–20%.
Impedance Changes: The subsurface affects the antenna's input impedance.
Signal Absorption: A lossy subsurface can absorb significant power from the sky signal.

These effects introduce chromatic (frequency-dependent) distortions to the measured spectrum that can mimic or obscure the spectral signatures of the galactic foregrounds and the cosmological 21-cm signal. Current calibration methods struggle to disentangle these instrumental/subsurface effects from the astrophysical signal.

2. Methodology

The authors propose a joint Bayesian inference framework to simultaneously estimate the dielectric properties of the lunar subsurface and the spectral parameters of the galactic foregrounds.

A. Simulation Pipeline

Antenna Modeling (HFSS):
- The LuSEE-Night instrument (four 3m BeCu monopoles in a cross-dipole configuration) was modeled in Ansys HFSS.
- The lunar subsurface was modeled as a two-layer impedance boundary with varying dielectric constants ( $\epsilon_{r,top}$ , $\epsilon_{r,bottom}$ ) and interface depth ( $L$ ).
- 216 distinct simulations were run across a $6 \times 6 \times 6$ grid of subsurface parameters, covering frequencies from 1–50 MHz.
- Output: Far-field beam patterns and antenna impedance ( $Z_{ant}$ ).
Galactic Foreground Modeling:
- Foregrounds were modeled using a power-law spectrum with curvature, based on the Ultralong-wavelength Sky Model with Absorption (ULSA).
- Parameters included spectral index ( $\beta$ ), curvature ( $\gamma$ ), and amplitude/offset terms ( $k_1, k_2$ ).
Data Generation:
- Simulated voltage power spectral densities (PSD) were generated by convolving the HFSS beam patterns with the foreground maps.
- The simulation included auto-correlations and cross-correlations for all four monopoles over one lunar night (360 hours).
- Emulator Construction: A surrogate model using Radial Basis Functions (RBF) was built to interpolate between the 216 discrete HFSS simulations, allowing for rapid evaluation of the PSD at arbitrary parameter points without re-running expensive electromagnetic simulations.
Inference Engine:
- A Preconditioned Monte Carlo (PMC) algorithm (via pocoMC) was used to perform Bayesian inference.
- The algorithm maximized a Gaussian log-likelihood function comparing the emulator output to a "mock" dataset (simulated measurement with 5% Gaussian noise).
- Parameters Estimated: 7 total parameters ( $\epsilon_{r,top}, \epsilon_{r,bottom}, L, \beta, \gamma, k_1, k_2$ ).

3. Key Contributions

Joint Estimation Framework: Demonstrated that subsurface properties and foreground spectral parameters can be estimated simultaneously rather than treating subsurface effects as a fixed calibration error.
Spectral Orthogonality: Identified that subsurface effects and foreground variations have distinct spectral signatures:
- Foregrounds: Produce smooth, broadband spectral slopes and curvature (dominated by low-frequency synchrotron emission).
- Subsurface: Introduces localized, complex spectral features specifically around the antenna resonance (~30 MHz), affecting amplitude, position, and width.
Eigenmode Analysis: Used Singular Value Decomposition (SVD) on the covariance matrices to show that the dominant eigenmodes for subsurface variations are orthogonal to those of foreground variations, justifying the feasibility of joint fitting.
Voltage PSD vs. Antenna Temperature: Emphasized that for instruments like LuSEE-Night, the observable is the voltage power spectrum, which inherently couples beam pattern and impedance effects. The analysis correctly operates on voltage PSD rather than derived antenna temperature.

4. Results

Parameter Recovery: The PMC algorithm successfully recovered the true input parameters for both the subsurface and foreground models within 5% uncertainty.
- Subsurface parameters ( $\epsilon_{r,top}, \epsilon_{r,bottom}, L$ ) were constrained with standard deviations of $\sim 0.001-0.005$ .
- Foreground parameters ( $\beta, \gamma, k_1$ ) were similarly well-constrained.
- The offset parameter $k_2$ showed larger uncertainty ( $\sim 44$ K), likely due to degeneracy with the absolute calibration.
Correlation Analysis: While some correlations existed (e.g., between $\beta$ and $\gamma$ , or between subsurface parameters), the distinct spectral signatures allowed the Bayesian framework to disentangle them effectively.
Emulator Limitations:
- The $6 \times 6 \times 6$ simulation grid was sufficient for proof-of-concept but insufficient for faithful interpolation at arbitrary off-grid points.
- Appendix A analysis showed that as parameters moved further off the grid, emulator residuals increased, particularly near the 30 MHz resonance. In extreme off-grid cases, errors exceeded the assumed 5% noise level.

5. Significance and Future Work

Robustness of Calibration: The study proves that LuSEE-Night can potentially characterize its own landing site environment (dielectric properties) while observing the sky, removing a major systematic uncertainty for Dark Ages cosmology.
Instrument Design: The results highlight the necessity of modeling the voltage spectrum directly, as subsurface effects modify both the beam and impedance in a coupled manner.
Future Directions:
- Denser Sampling: Future work requires more sophisticated sampling strategies (e.g., Latin Hypercube Sampling) to create a denser parameter grid for accurate interpolation.
- Complex Models: Moving from a 2-layer to multi-layer subsurface models to better represent the complex lunar regolith.
- Analytical Models: Developing analytical approximations for the HFSS results to reduce computational costs.
- Realistic Noise: Incorporating frequency-dependent receiver noise and systematic instrumental effects into the likelihood function.

Conclusion: The paper establishes a viable pathway for LuSEE-Night to self-calibrate against unknown lunar subsurface properties, ensuring that the faint Dark Ages 21-cm signal can be extracted from the overwhelming galactic foregrounds with high fidelity.