Magnetism, rotation, and nonthermal emission in cool stars

Average magnetic field measurements in 292 M dwarfs^⋆

¹ Institut für Astrophysik, Georg-August-Universität, 37077, Göttingen, Germany
e-mail: Ansgar.Reiners@phys.uni-goettingen.de
² Instituto de Astrofísica de Andalucía (Consejo Superior de Investigaciones Científicas), 18008 Granada, Spain
³ Institut de Ciències de l’Espai (Consejo Superior de Investigaciones Científicas), 08193 Bellaterra, Barcelona, Spain
⁴ Institut d’Estudis Espacials de Catalunya, 08034 Barcelona, Spain
⁵ Hamburger Sternwarte, Universität Hamburg, 21029 Hamburg, Germany
⁶ Centro de Astrobiología (Consejo Superior de Investigaciones Científicas – Instituto Nacional de Técnica Aeroespacial) 28692, Villanueva de la Cañada, Madrid, Spain
⁷ Centre for Earth Evolution and Dynamics, Department of Geosciences, University of Oslo, Sem Sælands vei 2b, 0315 Oslo, Norway
⁸ Landessternwarte, Zentrum für Astronomie der Universität Heidelberg, 69117 Heidelberg, Germany
⁹ Departamento de Física de la Tierra y Astrofísica & Instituto de Física de Partículas y del Cosmos, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
¹⁰ Max-Planck-Institut für Sonnensystemforschung, 37077 Göttingen, Germany
¹¹ Centro Astronómico Hispano-Alemán, Observatorio de Calar Alto, 04550 Gérgal, Almería, Spain
¹² Instituto de Astrofísica de Canarias, 38205 La Laguna, Tenerife, Spain
¹³ Departamento de Astrofísica, Universidad de La Laguna, 38206 La Laguna, Tenerife, Spain
¹⁴ Thüringer Landessternwarte Tautenburg, 07778 Tautenburg, Germany
¹⁵ Max-Planck-Institut für Astronomie, 69117 Heidelberg, Germany

Received: 2 February 2022
Accepted: 18 March 2022

Abstract

Stellar dynamos generate magnetic fields that are of fundamental importance to the variability and evolution of Sun-like and low-mass stars, and for the development of their planetary systems. As a key to understanding stellar dynamos, empirical relations between stellar parameters and magnetic fields are required for comparison to ab initio predictions from dynamo models. We report measurements of surface-average magnetic fields in 292 M dwarfs from a comparison with radiative transfer calculations; for 260 of them, this is the first measurement of this kind. Our data were obtained from more than 15 000 high-resolution spectra taken during the CARMENES project. They reveal a relation between average field strength, ⟨B⟩, and Rossby number, Ro, resembling the well-studied rotation–activity relation. Among the slowly rotating stars, we find that magnetic flux, Φ_B, is proportional to rotation period, P, and among the rapidly rotating stars that average surface fields do not grow significantly beyond the level set by the available kinetic energy. Furthermore, we find close relations between nonthermal coronal X-ray emission, chromospheric Hα and Ca H&K emission, and magnetic flux. Taken together, these relations demonstrate empirically that the rotation–activity relation can be traced back to a dependence of the magnetic dynamo on rotation. We advocate the picture that the magnetic dynamo generates magnetic flux on the stellar surface proportional to rotation rate with a saturation limit set by the available kinetic energy, and we provide relations for average field strengths and nonthermal emission that are independent of the choice of the convective turnover time. We also find that Ca H&K emission saturates at average field strengths of ⟨B⟩≈800 G while Hα and X-ray emission grow further with stronger fields in the more rapidly rotating stars. This is in conflict with the coronal stripping scenario predicting that in the most rapidly rotating stars coronal plasma would be cooled to chromospheric temperatures.