Abstract
In the context of white dwarf asteroseismology, we investigate the vibrational properties of a non-convective solid star with an axisymmetric purely toroidal intrinsic magnetic field of two different shapes. Focus is laid on the regime of node-free global Lorentz-force-driven vibrations about the symmetry axis at which material displacements have one and the same form as those for nodeless spheroidal and torsional vibrations restored by Hooke's force of elastic shear stresses. Particular attention is given to the even-parity poloidal Alfvén modes whose frequency spectra are computed in analytic form, showing how the purely toroidal magnetic fields completely buried beneath the star surface can manifest itself in seismic vibrations of non-magnetic white dwarfs. The spectral formulae obtained are discussed in juxtaposition with those for Alfvén modes in the solid star model with the poloidal, homogeneous internal and dipolar external, magnetic field whose inferences are relevant to Alfvén vibrations in magnetic white dwarfs. © Springer Science+Business Media B.V. 2010.