Normal modes of rotating magnetic stars

We investigate the effect of a magnetic field on the global oscillation modes of a rotating fluid star in the magnetohydrodynamic approximation. We present general equations for the modi cation of any type of fluid mode due to a general magnetic field that is not aligned with the star's spin axis. In the case of any internal dipole magnetic field, we derive the equations for the frequency corrections to the r-modes. We solve for the frequency correction explicitly for the case when the internal dipole field is force-free, including the uniform density case. In the weak-field limit, the spatial form of the r-mode velocity perturbation is unchanged, but the magnitude of the frequency in the rotating frame increases.