Context. Magnetic fields affect stars at all evolutionary stages. While surface fields have been measured for stars across the Hertzsprung–Russell (HR) diagram, internal magnetic fields remain largely unknown. The recent seismic detection of magnetic fields in the cores of several Kepler red giants has opened a new avenue to better understand the origin of magnetic fields and their impact on stellar structure and evolution. Aims. The goal of our study is to use asteroseismology to systematically search for internal magnetic fields in red giant stars observed with the Kepler satellite, and to determine the strengths and geometries of these fields. Methods. Magnetic fields are known to break the symmetry of rotational multiplets. In red giants, oscillation modes are mixed, behaving as pressure modes in the envelope and as gravity modes in the core. Magnetism-induced asymmetries are expected to be stronger for gravity-dominated modes than for pressure-dominated modes, and to decrease with frequency. Among Kepler red giants, we searched for stars that exhibit asymmetries satisfying these properties. Results. After collecting a sample of ∼2500 Kepler red giant stars with clear mixed-mode patterns, we specifically searched for targets among ∼1200 stars with dipole triplets. We identified 13 stars exhibiting clear asymmetric multiplets and measured their parameters, especially the asymmetry parameter a and the magnetic frequency shift δνg. By combining these estimates with best-fitting stellar models, we measured average core magnetic fields ranging from ∼20 to ∼150 kG, corresponding to ∼5% to ∼30% of the critical field strengths. We showed that the detected core fields have various horizontal geometries, some of which significantly differ from a dipolar configuration. We found that the field strengths decrease with stellar evolution, despite the fact that the cores of these stars are contracting. Additionally, even though these stars have strong internal magnetic fields, they display normal core rotation rates, suggesting no significantly different histories of angular momentum transport compared to other red giant stars. We also discuss the possible origin of the detected fields.
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