Origin of eclipsing time variations: Contributions of different modes of the dynamo-generated magnetic field

¹ Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany
e-mail: felipe.navarrete@hs.uni-hamburg.de
² Nordita, Stockholm University and KTH Royal Institute of Technology, Hannes Alfvéns väg 12, 106 91 Stockholm, Sweden
³ Institut für Astrophysik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
⁴ Departamento de Astronomía, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Av. Esteban Iturra s/n Barrio Universitario, Casilla 160-C, Chile

Received: 2 February 2022
Accepted: 22 May 2022

Abstract

Context. The possibility to detect circumbinary planets and to study stellar magnetic fields through eclipsing time variations (ETVs) in binary stars has sparked an increase of interest in this area of research.

Aims. We revisit the connection between stellar magnetic fields and the gravitational quadrupole moment Q_xx and compare different dynamo-generated ETV models with our simulations.

Methods. We present magnetohydrodynamical simulations of solar mass stars with rotation periods of 8.3, 1.2, and 0.8 days and perform a detailed analysis of the magnetic and quadrupole moment using spherical harmonic decomposition.

Results. The extrema of Q_xx are associated with changes in the magnetic field structure. This is evident in the simulation with a rotation period of 1.2 days. Its magnetic field has a more complex behavior than in the other models, as the large-scale nonaxisymmetric field dominates throughout the simulation and the axisymmetric component is predominantly hemispheric. This triggers variations in the density field that follow the magnetic field asymmetry with respect to the equator, affecting the zz component of the inertia tensor, and thus modulating Q_xx. The magnetic fields of the two other runs are less variable in time and more symmetric with respect to the equator, such that the variations in the density are weaker, and therefore only small variations in Q_xx are seen.

Conclusions. If interpreted via the classical Applegate mechanism (tidal locking), the quadrupole moment variations obtained in the current simulations are about two orders of magnitude below those deduced from observations of post-common-envelope binaries. However, if no tidal locking is assumed, our results are compatible with the observed ETVs.