  While surface fields have been measured for stars across the 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 understand better the origin of magnetic fields and their impact on
stellar structure and evolution. We aim to use asteroseismology to
systematically search for internal magnetic fields in red giant stars and to
determine the strengths and geometries of these fields. 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 g-dominated modes than for p-dominated modes and to decrease with
frequency. 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 and the
magnetic frequency shift. By combining these estimates with best-fitting
stellar models, we measured average core magnetic fields ranging from 20 to
150kG, 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. 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.

Solar and Stellar Astrophysics