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

We carry out an investigation of axisymmetric shear Alfven 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 Alfvenic 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 Alfven waves provide a good instance of non-perturbative effects due to the strong magnetic field of such stars.