Improving Earth-like planet detection in radial velocity using deep learning

TL;DR

Stellar activity obscures low-mass exoplanets in radial velocity measurements, limiting Earth-like planet detection. The authors introduce a CNN that operates on a compact shell spectral representation to model activity-induced line-shape variations and predict RV, FWHM, and BIS, while avoiding fitting planetary signals. They demonstrate substantial gains on the Sun, Alpha Centauri B, and Tau Ceti, achieving detection thresholds down to ~0.2–0.7 m/s over representative period ranges, and show the method can significantly mitigate activity in solar data. The approach is data-driven and star-adaptive, scalable via Optuna hyperparameter tuning, and holds promise for approaching Earth-like planet sensitivity with further enhancements such as flux-effect inputs and transfer learning.

Abstract

Many novel methods have been proposed to mitigate stellar activity for exoplanet detection as the presence of stellar activity in radial velocity (RV) measurements is the current major limitation. Unlike traditional methods that model stellar activity in the RV domain, more methods are moving in the direction of disentangling stellar activity at the spectral level. The goal of this paper is to present a novel convolutional neural network-based algorithm that efficiently models stellar activity signals at the spectral level, enhancing the detection of Earth-like planets. We trained a convolutional neural network to build the correlation between the change in the spectral line profile and the corresponding RV, full width at half maximum (FWHM) and bisector span (BIS) values derived from the classical cross-correlation function. This algorithm has been tested on three intensively observed stars: Alpha Centauri B (HD128621), Tau ceti (HD10700), and the Sun. By injecting simulated planetary signals at the spectral level, we demonstrate that our machine learning algorithm can achieve, for HD128621 and HD10700, a detection threshold of 0.5 m/s in semi-amplitude for planets with periods ranging from 10 to 300 days. This threshold would correspond to the detection of a $\sim$4$\mathrm{M}_{\oplus}$ in the habitable zone of those stars. On the HARPS-N solar dataset, our algorithm is even more efficient at mitigating stellar activity signals and can reach a threshold of 0.2 m/s, which would correspond to a 2.2$\mathrm{M}_{\oplus}$ planet on the orbit of the Earth. To the best of our knowledge, it is the first time that such low detection thresholds are reported for the Sun, but also for other stars, and therefore this highlights the efficiency of our convolutional neural network-based algorithm at mitigating stellar activity in RV measurements.

Figures (22)

• Figure 1: Shell spectral representation of two spectral lines at opposite edges of the visible spectral range. Left: Two spectral lines in the $(f_{0}, \frac{df_{0}}{d \lambda} )$ shell space. Line $4203.9790 \AA$ at the blue part of the spectrum has the larger loop than Line $6496.9079 \AA$ at the red part of the spectrum in $(f_{0}, \frac{df_{0}}{d \lambda} )$ space. Right: Line $4203.9790 \AA$ and $6496.9079 \AA$ in the $(f_{0}, \frac{df_{0}}{d v} )$ shell space. The line in the blue part of the spectrum follow the same loop as the line in the red part when considering the common normalized flux, from 0.9 to 0.4. Therefore, the chromatic effect due to dispersion is suppresed in the $(f_{0}, \frac{df_{0}}{d v} )$ shell space.
• Figure 2: Examples of solar spectral shells in $(f_{0}, \frac{df_{0}}{d v} )$ shell space. Left: An original spectrum from HARPS-N observation is transformed into the $(f_{0}, \frac{df_{0}}{d v} )$ shell space. Middle: Solar spectral shell due to a Doppler effect. The Doppler shell is obtained by injecting a $5\,\rm{m/s}$ Doppler shift into the HARPS-N solar master spectrum $f_{0}$. Right: Solar spectral shell due to spectral shape change. We derived the shape shell by projecting the original shell onto the Doppler shell and subtracting the component due to Doppler effect from the original shell.
• Figure 3: Demonstration of a neural network architecture to be optimized by $Optuna$. Shape shell with dimension of $10\times 10$ is feed into the neural network. The neural network consists of convolutional blocks, an adaptive layer and fully connected layers. In order to avoid overfitting planetary signals in RV time series, the calcium activity indicator $\log(R'_{HK})$ is used as output of the neural network to search for its best architecture.
• Figure 4: Results of stellar activity modeling on the calcium activity index derived from the HARPS-N solar data with our trained neural network. Top: The calcium activity index time series derived from HARPS-N solar spectra is labeled in red, while the predicted calcium activity index time series, obtained using the neural network optimized by $Optuna$, is labeled in black. Bottom: The residual time series of the calcium activity index.
• Figure 5: Demonstration of a neural network architecture to predict the RV, FWHM, and BIS components of stellar activity. The FC blocks connected to each output have the same architecture and share the same feature maps from the convolutional blocks.