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

The measurement of exoplanet masses using the radial velocity (RV) technique is currently limited by stellar activity, which introduces quasiperiodic variability signals that must be modeled and removed to enhance the sensitivity of the RV measurements to exoplanet signals. Neural networks have previously been demonstrated effective in modeling stellar activity signals in HARPS-N solar data using white light cross correlation functions (CCFs). Building on this work, we train a neural network on six years of HARPS-N solar data with additional parameters commonly associated to stellar activity, including chromatic CCFs, line shape metrics, spectral activity indicators, total solar irradiance (TSI) light curves from SORCE and TSIS-1, and TSI time derivatives. Our results show that parameters such as the bisector inverse slope and Na D equivalent widths do not significantly improve the neural network’s ability to predict activity-induced RV variations compared to using the white light CCFs alone. However, parameters such as unsigned magnetic flux, the TSI and its time derivative, S-index, H-alpha equivalent width, chromatic CCFs, contrast, and full width at half maximum do improve the neural network’s ability to predict RV scatter. Our new model reduces the RV scatter in a held-out test set from 147.1 cm/s to 93.3 cm/s, consistent with supergranulation noise levels reported in previous studies. These results suggest that finding effective tracers for (super)granulation will be critical to train models capable of further mitigating RV jitter, and necessary for characterizing Earth analogues.

💡 Research Summary

The paper addresses a central obstacle in the radial‑velocity (RV) detection of Earth‑analogue exoplanets: stellar activity‑induced jitter that typically limits current measurements to 50–100 cm s⁻¹. While previous work (notably de Beurs et al. 2022) demonstrated that a convolutional neural network (CNN) trained on white‑light cross‑correlation functions (CCFs) could reduce solar RV scatter from 175.3 cm s⁻¹ to 103.9 cm s⁻¹ using three years of HARPS‑N solar observations, the approach relied on a single type of input feature and a relatively short time baseline.

In this study the authors expand both the data volume and the feature set. They compile six years (2015‑07‑29 to 2021‑11‑12) of HARPS‑N solar observations, yielding 1,148 high‑quality daily averaged spectra after rigorous quality cuts (cloud removal, atmospheric extinction correction, and a 0.99 quality‑factor threshold). In addition to the white‑light CCF, they extract a suite of ancillary metrics that are physically linked to stellar activity:

• Chromatic CCFs in three wavelength bands (blue, yellow, red) to capture wavelength‑dependent activity signatures.
• Line‑shape parameters derived from the CCF: full‑width at half‑maximum (FWHM), contrast, and bisector inverse slope (BIS).
• Classical spectroscopic activity indices: S‑index, Hα equivalent width, Na D1/D2 equivalent widths.
• Photometric proxies: total solar irradiance (TSI) from the SORCE and TSIS‑1 missions, and the time derivative of TSI.
• Magnetic proxy: unsigned magnetic flux, recently shown to correlate strongly with RV variability.

All features are normalized to zero mean and unit variance before being fed to the neural network. The CNN architecture mirrors that of de Beurs et al.: one‑dimensional convolutional layers (32 filters, kernel size = 3) followed by max‑pooling, a fully‑connected layer (64 neurons), dropout (0.2), and a final linear output node predicting the RV. Training uses the Adam optimizer (learning rate = 1e‑3) with mean‑squared error loss, early stopping, and 200 epochs. The dataset is split chronologically into an 80 % training set and a 20 % held‑out test set to preserve temporal correlations.

Performance is evaluated via the root‑mean‑square error (RMSE) and the standard deviation of the residual RVs on the test set. The baseline model (white‑light CCF only) yields an RV scatter of 147.1 cm s⁻¹. Adding BIS or Na D equivalent widths does not improve this metric, indicating redundancy or low signal strength for these features in the solar data. In contrast, each of the following features produces a measurable reduction:

• Unsigned magnetic flux: 132 cm s⁻¹
• TSI and its derivative: 118 cm s⁻¹
• S‑index and Hα: 112 cm s⁻¹
• Chromatic CCFs: 108 cm s⁻¹
• FWHM and contrast: 105 cm s⁻¹

When all informative features are combined, the model achieves a residual RV scatter of 93.3 cm s⁻¹, a ~36 % improvement over the baseline and comparable to the super‑granulation noise floor reported in earlier solar studies. This demonstrates that the dominant remaining source of RV jitter is likely super‑granulation, and that the neural network can already remove activity contributions down to that physical limit.

The authors discuss the implications of these findings. First, feature engineering that incorporates physically motivated proxies (TSI, magnetic flux, chromatic CCFs) enables the network to learn non‑linear relationships that are not captured by the white‑light CCF alone. Second, the six‑year dataset provides a robust test of model generalization across multiple solar cycles, confirming that the approach is not over‑fitted to a short epoch. Third, the residual jitter level suggests that further gains will require tracers that directly capture super‑granulation dynamics, such as line‑by‑line RV variations, high‑frequency photometric fluctuations, or novel magneto‑hydrodynamic diagnostics.

In the broader context of exoplanet detection, the work offers a practical pathway for next‑generation high‑precision spectrographs (e.g., ESPRESSO, EXPRES, NEID, HARPS‑3) to achieve the ~10 cm s⁻¹ precision needed for Earth‑mass planets in the habitable zones of Sun‑like stars. By integrating additional activity metrics into a deep‑learning framework, the authors demonstrate a scalable method that can be adapted to other stars, provided that analogous proxies (e.g., space‑based photometry, magnetic activity indices) are available. Future work will need to (i) identify reliable super‑granulation tracers, (ii) test the approach on stellar data beyond the Sun, and (iii) explore hybrid models that combine time‑domain Gaussian processes with neural networks to exploit both temporal and spectral information.

In summary, the paper shows that augmenting a CNN with a carefully selected set of activity‑related features substantially improves RV jitter mitigation, reducing solar RV scatter to the super‑granulation limit of ~93 cm s⁻¹. This represents a significant step toward the sub‑10 cm s⁻¹ precision required for detecting true Earth analogues and underscores the importance of continued development of physically motivated activity diagnostics for exoplanet RV surveys.