The CARMENES search for exoplanets around M dwarfs

Cluster analysis of signals from spectral activity indicators to search for shared periods

¹ Landessternwarte, Zentrum für Astronomie der Universität Heidelberg, Königstuhl 12, 69117 Heidelberg, Germany
² Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
³ Centre for Exoplanets and Habitability, University of Warwick, Coventry CV4 7AL, UK
⁴ Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany
⁵ Centre for Earth Evolution and Dynamics, Department of Geosciences, Universitetet i Oslo, Sem Sælands vei 2b, 0315 Oslo, Norway
⁶ Institut für Astrophysik, Georg-August-Universität, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
⁷ Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía s/n, 18008 Granada, Spain
⁸ Thüringer Landessternwarte Tautenburg, Sternwarte 5, 07778 Tautenburg, Germany
⁹ Centro de Astrobiología (CAB, CSIC-INTA), Camino Bajo del Castillo s/n, Campus ESAC, 28692 Villanueva de la Cañada, Madrid, Spain
¹⁰ Institut de Ciències de l’Espai (ICE, CSIC), c/ de Can Magrans s/n, Campus UAB, 08193 Cerdanyola del Vallès, Spain
¹¹ Institut d’Estudis Espacials de Catalunya (IEEC), c/ Gran Capità 2–4, 08034 Barcelona, Spain
¹² Instituto de Astrofísica de Canarias (IAC), 38205 La Laguna, Tenerife, Spain
¹³ Departamento de Astrofísica, Universidad de La Laguna, 38206 La Laguna, Tenerife, Spain
¹⁴ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
¹⁵ Centro Astronónomico Hispano en Andalucía, Observatorio de Calar Alto, Sierra de los Filabres, 04550 Gérgal, Spain
¹⁶ Departamento de Física de la Tierra y Astrofísica & IPARCOS-UCM (Instituto de Física de Partículas y del Cosmos de la UCM), Facultad de Ciencias Físicas, Universidad Complutense de Madrid, 28040 Madrid, Spain

^★ Corresponding author.

Received: 30 May 2023
Accepted: 26 February 2025

Abstract

Context. A multitude of spectral activity indicators are routinely computed nowadays from the spectra generated as part of planet-hunting radial velocity surveys. Searching for shared periods among them can help to robustly identify astrophysical quantities of interest, such as the stellar rotation period. However, this identification can be complicated due to the fact that many different peaks occur in the periodograms. This is especially true in the presence of aliasing and spurious signals caused by environmental influences affecting the instrument.

Aims. Our goal is to test a clustering algorithm to find signals with the same periodicity, (i.e. with the stellar rotation period) in the periodograms of a large number of activity indicators. On this basis, we have looked to evaluate the correlations between activity indicators and fundamental stellar parameters.

Methods. We used generalised Lomb–Scargle periodograms to find periodic signals in 24 activity indicators, spanning the VIS and NIR channels of the CARMENES spectrograph. Common periods were subsequently determined by a machine learning algorithm for density-based spatial clustering of applications with noise (DBSCAN).

Results. The clustering analysis of the signals apparent in the spectral activity indicators is a powerful tool for the detection of stellar rotation periods. It is straightforward to implement and can be easily automated, so that large data sets can be analysed. For a sample of 136 stars, we were able to recover the stellar rotation period in a total of 59 cases, including 3 with a previously unknown rotation period. In addition, we analysed spurious signals frequently occurring at the period of one year and its integer fractions, concluding that they are likely aliases of one underlying signal. Furthermore, we reproduced the results of several previous studies on the relationships between activity indicators and the stellar characteristics.