The CARMENES search for exoplanets around M dwarfs

Understanding the wavelength dependence of radial velocity measurements

¹ Thüringer Landessternwarte Tautenburg, Sternwarte 5, 07778 Tautenburg, Germany
² School of Physical Sciences, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK
³ Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía s/n, 18008 Granada, Spain
⁴ Landessternwarte, Zentrum für Astronomie der Universität Heidelberg, Königstuhl 12, 69117 Heidelberg, Germany
⁵ Instituto de Astrofísica de Canarias, c/ Vía Láctea s/n, 38205 La Laguna, Tenerife, Spain
⁶ Departamento de Astrofísica, Universidad de La Laguna, 38206 Tenerife, Spain
⁷ Institut für Astrophysik and Geophysik, Georg-August-Universität, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
⁸ Centre for Planetary Habitability, Department of Geosciences, University of Oslo, Sem Saelands vei 2b, 0315 Oslo, Norway
⁹ Centro de Astrobiología (CSIC-INTA), ESAC, Camino Bajo del Castillo s/n, 28692 Villanueva de la Cañada, Madrid, Spain
¹⁰ Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany
¹¹ Institut de Ciències de l’Espai (CSIC), Campus UAB, c/ de Can Magrans s/n, 08193 Bellaterra, Barcelona, Spain
¹² Institut d’Estudis Espacials de Catalunya, 08034 Barcelona, Spain
¹³ Centro Astronómico Hispano en Andalucía (CAHA), Observatorio de Calar Alto, Sierra de los Filabres, 04550 Gérgal, Almería, Spain
¹⁴ Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
¹⁵ Centre for Exoplanets and Habitability, University of Warwick, Coventry CV4 7AL, UK
¹⁶ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
¹⁷ Fakultät für Physik, Universitäts-Sternwarte, Ludwig-Maximilians-Universität München, Scheinerstr. 1, 81679 München, Germany
¹⁸ Facultad de Ciencias Físicas, Departamento de Física de la Tierra y Astrofísica & IPARCOS-UCM (Instituto de Física de Partículas y del Cosmos de la UCM), Universidad Complutense de Madrid, 28040 Madrid, Spain

^★ Corresponding author; sandrajeffers.astro@gmail.com

Received: 20 July 2023
Accepted: 20 October 2024

Abstract

Context. Current exoplanet surveys are focused on detecting small exoplanets orbiting in the liquid-water habitable zones of their host stars. Despite recent significant advancements in instrumentation, the main limitation in detecting these exoplanets is the intrinsic variability of the host star itself.

Aims. Our aim is to investigate the wavelength dependence of high-precision radial velocities (RV), as stellar activity induced RVs should exhibit a wavelength dependence while the RV variation due to an orbiting planet will be wavelength independent.

Methods. We used the chromatic index (CRX) to quantify the slope of the measured RVs as a function of logarithmic wavelength of the full CARMENES guaranteed time observations (GTO) data set spanning more than eight years of observations of over 350 stars. We investigated the dependence of the CRX in the full Carmenes GTO sample on 24 stellar activity indices in the visible and near-infrared channels of the CARMENES spectrograph and each star’s stellar parameters. We also present an updated convective turnover time scaling for the calculation of the stellar Rossby number for M dwarfs.

Results. Our results show that approximately 17% of GTO stars show a strong or a moderate correlation between the CRX and RV. We can improve the measured RVs by a factor of up to nearly 4 in terms of the root mean square (rms) by subtracting the RV predicted by the CRX-RV correlation from the measured RVs. Mid-M dwarfs with moderate rotational velocities and moderate CRX-gradients, with quasi-stable activity features, have the best rms improvement factors.

Conclusions. We conclude that the CRX is a powerful diagnostic in mitigation of stellar activity and the search for low mass rocky planets.