A machine learning approach for correcting radial velocities using physical observables

¹ Institut de Ciències de l’Espai (ICE, CSIC), Campus UAB, Carrer de Can Magrans s/n, 08193 Bellaterra, Spain
e-mail: perger@ice.cat
² Institut d’Estudis Espacials de Catalunya (IEEC), c/ Gran Capità 2-4, 08034 Barcelona, Spain
³ Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
⁴ Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía s/n, 18008 Granada, Spain
⁵ School of Physical Sciences, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK
⁶ Centro de Astrobiología (CAB), CSIC-INTA, ESAC, Camino bajo del castillo s/n, 28692 Villanueva de la Canada, Madrid, Spain
⁷ Max Planck Institut für Sonnensystemforschung (MPS), Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany
⁸ Landessternwarte, Zentrum für Astronomie der Universität Heidelberg, Königstuhl 12, 69117 Heidelberg, Germany
⁹ Institut für Astrophysik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany

Received: 29 September 2022
Accepted: 5 February 2023

Abstract

Context. Precision radial velocity (RV) measurements continue to be a key tool for detecting and characterising extrasolar planets. While instrumental precision keeps improving, stellar activity remains a barrier to obtaining reliable measurements below 1–2 m s⁻¹ accuracy.

Aims. Using simulations and real data, we investigate the capabilities of a deep neural network approach to producing activity-free Doppler measurements of stars.

Methods. As case studies we used observations of two known stars, ϵ Eridani and AU Microscopii, both of which have clear signals of activity-induced Doppler variability. Synthetic observations using the starsim code were generated for the observables (inputs) and the resulting Doppler signal (labels), and then they were used to train a deep neural network algorithm to predict Doppler corrections. We identified a relatively simple architecture, consisting of convolutional layers followed by fully connected layers, that is adequate for the task. The indices investigated are mean line-profile parameters (width, bisector, and contrast) and multi-band photometry.

Results. We demonstrate that the RV-independent approach can drastically reduce spurious Doppler variability from known physical effects, such as spots, rotation, and convective blueshift. We identify the combinations of activity indices with the most predictive power. When applied to real observations, we observe a good match of the correction with the observed variability, but we also find that the noise reduction is not as good as in the simulations, probably due to a lack of detail in the simulated physics.

Conclusions. We demonstrate that a model-driven machine learning approach is sufficient to clean Doppler signals from activity-induced variability for well-known physical effects. There are dozens of known activity-related observables whose inversion power remains unexplored, indicating that the use of additional indicators, more complete models, and more observations with optimised sampling strategies can lead to significant improvements in our detrending capabilities for new and existing datasets.