Oscillations of magnetic stars: I. Axisymmetric shear Alfvén modes of a spherical shell in a dipolar magnetic field

We carry out an investigation of axisymmetric shear Alfvén waves in a spherical layer of an incompressible resistive fluid when a strong dipolar magnetic field is applied. A decomposition on the spherical harmonics base is used to compute the eigenmodes of the system. Numerical results show that the least-damped Alfvénic modes naturally concentrate near the magnetic polar axis. These modes also show internal shear/magnetic layers associated with resonant field lines. This model is useful when modelling planetary cores sustaining a dynamo, magnetic neutron stars or to the magnetic layer of roAp stars. In this latter case, it shows that shear Alfvén waves provide a good instance of non-perturbative effects due to the strong magnetic field of such stars.