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Identifying Exoplanets with Deep Learning VI. Enhancing neural network mitigation of stellar activity RV signals with additional metrics

By training a neural network on six years of HARPS-N solar data augmented with specific stellar activity metrics such as unsigned magnetic flux, TSI derivatives, and chromatic CCFs, the study demonstrates a significant reduction in radial velocity scatter from 147.1 to 93.3 cm/s, highlighting the importance of identifying effective tracers for supergranulation to improve the detection of Earth-like exoplanets.

Original authors: Naomi McWilliam, Zoë L. de Beurs, Andrew Vanderburg, Javier Viaña, Annelies Mortier, Lars A. Buchhave, Andrew Collier Cameron, Rosario Cosentino, Xavier Dumusque, Adriano Ghedina, Ben Lakeland, Marcel

Published 2026-02-23

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Naomi McWilliam, Zoë L. de Beurs, Andrew Vanderburg, Javier Viaña, Annelies Mortier, Lars A. Buchhave, Andrew Collier Cameron, Rosario Cosentino, Xavier Dumusque, Adriano Ghedina, Ben Lakeland, Marcello Lodi, Mercedes López-Morales, Dimitar Sasselov, Alessandro Sozzetti

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" Problem

Imagine you are trying to hear a tiny, distant whisper (an Earth-like planet) while standing next to a roaring, chaotic waterfall (a star like our Sun). The waterfall's roar is so loud and unpredictable that it completely drowns out the whisper.

In astronomy, this "roar" is called stellar activity. Stars aren't perfect, calm spheres; they are turbulent balls of gas with sunspots, magnetic storms, and bubbling surface currents. These activities create "noise" in our measurements, making it incredibly hard to detect the tiny wobble a planet causes as it orbits. For years, scientists have been trying to build better "noise-canceling headphones" to filter out this stellar roar.

The Old Solution: A Smart Filter

Previously, a team of scientists (led by de Beurs et al.) built a digital filter using Artificial Intelligence (AI). They taught a computer to look at the "shape" of the star's light.

Think of the star's light like a fingerprint. When the star is calm, the fingerprint is smooth. When a sunspot or magnetic storm hits, the fingerprint gets a little smudge or a weird curve. The AI learned to recognize these smudges and subtract them from the data, effectively silencing the roar so the whisper could be heard. This worked well, but it was like trying to clean a muddy window using only a cloth; it helped, but some dirt remained.

The New Approach: Giving the AI More Clues

In this new paper, the team asked: "What if we give the AI more than just the fingerprint? What if we give it a whole toolbox of clues?"

They trained a new, smarter AI model using six years of data (double the previous amount) and fed it a variety of "activity metrics," including:

The Sun's Total Brightness (TSI): Like checking if the lightbulb is flickering.
Magnetic Flux: Measuring the strength of the star's invisible magnetic field.
Color Changes: Looking at the star's light in blue, yellow, and red separately (like checking if the smudge is only on the blue part of the fingerprint).
Chemical Signatures: Checking for specific elements like Sodium or Hydrogen that act like "smoke signals" for activity.

The Surprising Results

The team expected that adding all these clues would make the AI a genius. However, the results were a mix of "Yes, it helps!" and "No, it doesn't."

The "Useless" Clues: Some metrics, like the specific shape of the Sodium lines or the "bisector" (a measure of how tilted the fingerprint is), didn't actually help the AI. It turns out the AI was already smart enough to figure those out just by looking at the main fingerprint. Adding these extra clues was like trying to help a detective by giving them a map of the city when they already knew the neighborhood by heart.
The "Super" Clues: However, three specific clues were game-changers:
1. Magnetic Flux: Knowing how strong the magnetic field is.
2. Total Brightness (TSI): Knowing how bright the star is overall.
3. The Rate of Change: Knowing how fast the brightness is changing.

When the AI used these three clues alongside the main fingerprint, it became incredibly effective. It reduced the "noise" (the scatter in the data) from 147 cm/s down to 93 cm/s.

The "Supergranulation" Wall

So, is the problem solved? Almost, but not quite.

The team discovered that even with their super-AI, there is still a "floor" of noise they can't break through. They realized this leftover noise comes from supergranulation.

Imagine the surface of the Sun not just as a smooth ocean, but as a giant pot of boiling water. The big bubbles are sunspots (which the AI fixed), but there are also thousands of smaller, churning currents called supergranules. These are like the tiny, constant bubbles in boiling water that never stop moving.

The AI is great at spotting the big "storms" (magnetic activity), but it struggles to filter out the constant "boiling" (supergranulation). This boiling creates a background hum that is currently about 90 cm/s loud.

Why This Matters

To find an Earth twin, we need to detect a wobble of only 10 cm/s. Right now, the "boiling water" of the star is 9 times louder than the planet's whisper.

This paper is a massive step forward because it proves that by combining different types of data (magnetic fields + brightness changes), we can silence the "storms" almost completely. The remaining challenge isn't the AI anymore; it's understanding the physics of the star's "boiling water" better.

The Bottom Line

The scientists have built the best possible "noise-canceling headphones" for stellar storms. They have successfully filtered out the loud, chaotic weather of the star. Now, the only thing standing between us and finding a second Earth is the gentle, constant bubbling of the star's surface. To find that Earth, we need to learn how to tune out the boiling water itself.

1. Problem Statement

The detection of Earth-analog exoplanets via the Radial Velocity (RV) method is currently hindered by a noise floor of approximately 50–100 cm s⁻¹. This noise, known as stellar activity or stellar jitter, arises from physical processes on the stellar surface (spots, faculae, granulation, supergranulation, and magnetic cycles) that induce quasi-periodic RV variations. These variations often mimic or obscure the tiny Doppler signals (approx. 10 cm s⁻¹) produced by Earth-like planets.

While previous work (de Beurs et al. 2022) demonstrated that Convolutional Neural Networks (CNNs) could effectively model and remove stellar activity signals using only white light Cross-Correlation Functions (CCFs), the residual scatter remained too high for Earth-analog detection. This paper investigates whether incorporating additional activity metrics (beyond the white light CCF) can further reduce RV scatter and improve the mitigation of stellar noise.

2. Methodology

Data Sources

The study utilizes 6 years of solar data (doubling the dataset from previous work) from the HARPS-N Solar Telescope (2015–2021). The dataset includes:

HARPS-N Spectra: 5-minute integration exposures reduced to white light CCFs and activity indicators.
Total Solar Irradiance (TSI): Merged data from the SORCE satellite and TSIS-1 sensor.
Magnetic Flux: Disc-averaged, unsigned magnetic flux derived from the Helioseismic and Magnetic Imager (HMI) on the SDO.
Spectral Indicators: Equivalent widths (EW) of Hα and Na D lines, S-index, and various CCF shape metrics (Bisector Inverse Slope, FWHM, Contrast).

Feature Engineering

The authors treated various parameters as "features" for the neural network:

White Light CCFs: The primary input, preprocessed to remove translational shifts (planetary signals) and centered to focus on shape changes (activity).
Chromatic CCFs: CCFs computed separately for Blue, Yellow, and Red wavelength regions to probe depth-dependent convective blueshifts.
Activity Indicators: TSI, TSI time derivative, Unsigned Magnetic Flux (UMF), S-index, and line EWs.
Preprocessing: All features were normalized (mean subtraction, standard deviation division). The TSI datasets were merged and offset-corrected.

Neural Network Architecture

Model Type: Feedforward Convolutional Neural Networks (CNNs).
Input: The white light CCF (49-dimensional array) combined with one or more additional scalar or vector features.
Training Strategy:
- Loss Function: Mean Squared Error (MSE).
- Optimization: Stochastic Gradient Descent (SGD) with momentum.
- Validation: 10-fold cross-validation on the training set, with a separate 10% validation set for hyperparameter tuning and a 10% hold-out test set.
- Robustness: 100 independent training runs per architecture to average out random initialization effects.
Hyperparameter Tuning: Random search over learning rate, kernel size, filter counts, layer depth, and regularization (weight decay).

Evaluation Metrics

$\sigma_{percentile}$ : The primary metric, defined as half the difference between the 84th and 16th percentiles of the RV distribution. This is robust against outliers and non-Gaussian noise, unlike Root Mean Squared Error (RMSE).
Injection-Recovery Tests: Simulated Keplerian planetary signals (K = 0.1–0.4 m s⁻¹) were injected into the data to verify that the model removes activity without suppressing planetary signals.

3. Key Contributions

Expanded Dataset: Doubled the training data volume (3 to 6 years) compared to the baseline de Beurs et al. (2022) study, providing a more comprehensive view of the solar cycle.
Systematic Feature Analysis: Rigorously tested a wide array of additional metrics (TSI, magnetic flux, chromatic CCFs, etc.) to determine which provide complementary information to the white light CCF.
Identification of Critical Tracers: Identified that Unsigned Magnetic Flux (UMF) and the TSI time derivative are the most effective additional features for reducing RV scatter.
Instrumental Artifact Correction: Demonstrated that the CNN, trained primarily on astrophysical data, inadvertently learned to correct for instrumental systematics (specifically cryostat warm-up events) based on CCF shape changes.
Limit Analysis: Provided a quantitative breakdown of the remaining noise floor, attributing it to supergranulation and instrumental wavelength solution drift, rather than magnetic activity.

4. Results

Performance Improvement

Baseline: Using only white light CCFs, the model reduced RV scatter ( $\sigma_{percentile}$ ) from 147.1 cm s⁻¹ (raw) to 95.5 cm s⁻¹ (test set).
Optimal Model: The best-performing model combined white light CCFs with Unsigned Magnetic Flux and the TSI derivative.
Final Scatter: This model reduced the RV scatter to 93.3 cm s⁻¹ (test set) and 91.6 cm s⁻¹ (full dataset).
Ineffective Features: The Bisector Inverse Slope and Sodium D-line EWs did not significantly improve performance, suggesting their information is already captured by the white light CCF.

Signal Removal Analysis

Fourier Domain: Lomb-Scargle periodograms showed the effective removal of peaks corresponding to the solar rotation period ( $P_{rot} \approx 27$ days) and its harmonics, as well as long-term magnetic cycles.
Planetary Recovery: Injection-recovery tests confirmed that the model preserves planetary signals. Signals with semi-amplitudes of 0.40 m s⁻¹ (approx. 5.16 $M_{\oplus}$ ) were successfully recovered, while 0.30 m s⁻¹ signals were weakly detected.

Noise Floor Limitations

The residual scatter of ~90 cm s⁻¹ is significantly higher than the ~10 cm s⁻¹ required for Earth-analog detection. The authors attribute this limit to:

Instrumental Noise: Day-to-day variations in the HARPS-N wavelength solution (~49 cm s⁻¹).
Supergranulation: Non-magnetic convective flows (~68–86 cm s⁻¹) that do not strongly affect the CCF shape or magnetic indicators used in the model.

5. Significance and Future Outlook

Methodological Advancement: This work establishes that while white light CCFs are powerful, integrating magnetic flux and irradiance derivatives provides necessary complementary information to model stellar activity more accurately.
Path to Earth Analogs: The results indicate that current ML techniques have largely solved the problem of magnetic activity mitigation. The remaining barrier to detecting Earth twins is supergranulation and instrumental stability.
Future Directions:
- Developing new tracers specifically for supergranulation (e.g., using ultra-high-resolution spectra or SDO Dopplergrams).
- Applying these linear regression/ML hybrids to other stars, potentially using chromatic CCFs and magnetic proxies adapted for unresolved stars.
- Designing next-generation spectrographs with stability better than 10 cm s⁻¹ to overcome the instrumental noise floor.

In conclusion, this paper demonstrates a significant step forward in stellar activity mitigation, reducing RV scatter to the level of supergranulation noise, but highlights that further breakthroughs in understanding non-magnetic stellar phenomena are required to achieve the extreme precision needed for Earth-analog discovery.