Effects of a strong magnetic field on internal gravity waves: trapping, phase mixing, reflection, and dynamical chaos

The spectrum of oscillation modes of a star provides information not only about its material properties (e.g. mean density), but also its symmetries. Spherical symmetry can be broken by rotation and/or magnetic fields. It has been postulated that strong magnetic fields in the cores of some red giants are responsible for their anomalously weak dipole mode amplitudes (the 'dipole dichotomy' problem), but a detailed understanding of how gravity waves interact with strong fields is thus far lacking. In this work, we attack the problem through a variety of analytical and numerical techniques, applied to a localized region centred on a null line of a confined axisymmetric magnetic field which is approximated as being cylindrically symmetric. We uncover a rich variety of phenomena that manifest when the field strength exceeds a critical value, beyond which the symmetry is drastically broken by the Lorentz force. When this threshold is reached, the spatial structure of the g modes becomes heavily altered. The dynamics of wave packet propagation transitions from regular to chaotic, which is expected to fundamentally change the organization of the mode spectrum. In addition, depending on their frequency and the orientation of field lines with respect to the stratification, waves impinging on different parts of the magnetized region are found to undergo either reflection or trapping. Trapping regions provide an avenue for energy loss through Alfv' en wave phase mixing. Our results may find application in various astrophysical contexts, including the dipole dichotomy problem, the solar interior, and compact star oscillations.