This is an Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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. © The Authors 2023.
CARMENES is an instrument at the Centro Astronómico Hispano en Andalucía (CAHA) at Calar Alto (Almería, Spain), operated jointly by the Junta de Andalucía and the Institute de Astrofísica de Andalucía (CSIC). CARMENES was funded by the Max-Planck-Gesellschaft (MPG), the Consejo Superior de Investigaciones Científicas (CSIC), the Ministerio de Economía y Competitividad (MINECO) and the European Regional Development Fund (ERDF) through projects FICTS-2011-02, ICTS-2017-07-CAHA-4, and CAHA16-CE-3978, and the members of the CARMENES Consortium (Max-Planck-Institut für Astronomie, Instituto de Astrofísica de Andalucía, Landessternwarte Königstuhl, Institut de Ciències de l’Espai, Institut für Astrophysik Göttingen, Universidad Complutense de Madrid, Thüringer Landessternwarte Tautenburg, Instituto de Astrofísica de Canarias, Hamburger Sternwarte, Cen-tro de Astrobiología and Centro Astronómico Hispano-Alemán), with additional contributions by the MINECO, the Deutsche Forschungsgemeinschaft through the Major Research Instrumentation Programme and Research Unit FOR2544 “Blue Planets around Red Stars”, the Klaus Tschira Stiftung, the states of Baden-Württemberg and Niedersachsen, and by the Junta de Andalucía. We acknowledge financial support from the Agencia Estatal de Investigación of the Ministerio de Ciencia e Innovación MCIN/AEI/10.13039/501100011033 and the ERDF “A way of making Europe” through projects PID2020-120375GB-I00, PID2019-109522GB-C5[1:4], PGC2018-098153-B-C33, and the Centre of Excellence “Severo Ochoa” and “Maria de Maeztu” awards to the Institut de Ciències de l’Espai (CEX2020-001058-M) Instituto de Astrofísica de Canarias (CEX2019-000920-S), Instituto de Astrofísica de Andalucía (SEV-2017-0709), and Centro de Astrobiolog a (MDM-2017-0737); the Generalitat de Catalunya/CERCA programme; and the DFG through priority program SPP 1992 “Exploring the Diversity of Extrasolar Planets” (JE 701/5-1). Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere under ESO programme 0104.C-0863(A); also called Red Dots.
With funding from the Spanish government through the "Severo Ochoa Centre of Excellence" accreditation (CEX2021-001131-S).