Mean-field interpretation of star-in-a-box simulations of red giants
Context: The origin of magnetic fields and the dynamo mechanism in red giants are still not fully understood. Aims: We aim to interpret the dynamo behaviour of global 3D simulations of red giants using mean-field dynamo models. Methods: We use mean-field models constrained by the differential rotation profile extracted from 3D simulations. We perform $α^2$, $αΩ$, and $α^2Ω$ mean-field dynamo simulations, varying the strength of the $α$ effect and the differential rotation. Results: The mean-field models can reproduce the growth rate of several 3D runs. The morphology of the large-scale magnetic field is better reproduced for the slowly rotating 3D cases than for the rapidly rotating ones. Faster rotation enhances dynamo action and it also modifies the dominant mode of the dynamo. Rapidly rotating 3D runs produce predominantly non-axisymmetric equatorial dipoles instead of axisymmetric fields at slower rotation. Mean-field models are supercritical even in the absence of differential rotation, indicating $α^2$ dynamo action. By contrast, models using the $αΩ$ approximation require sufficiently strong differential rotation to become supercritical. Conclusions: Our results suggest that the magnetic field in red giants requires dynamo action. In our mean-field runs, differential rotation speeds up the magnetic decay, disfavouring the idea of a persistent fossil magnetic field in red giants.