Non-axisymmetric oscillations of roAp stars

We calculate the effect of a strong dipole magnetic field on non-axisymmetric oscillations for roAp stars, with a typical range of photospheric magnetic fields B_p [0.5-1.5] kG. As Dziembovvski & Goode (1996), we find that the oscillations are strongly affected by such magnetic fields in two different ways. The first one concerns the stability of modes, which are damped due to dissipation by Alfvénic waves. It leads to a small imaginary part of the frequency, about (1-15μHz). The real part of the frequencies is also affected and is greater in the presence of magnetic field, with a shift of about 1-20 μHz. We find that these shifts are strongly influenced by the geometry of the mode, i.e. the value of the degree ℓ, as it has already been shown by Dziembowski & Goode (1996), and also by m, the azimuthal degree, with a significant amplitude. The magnetic field, because it breaks the spherical symmetry of the problem, raises partially the (2ℓ + 1) degeneracy of frequency in m. We find that the shift of both the real and imaginary parts is always greater than in the case of axisymmetric oscillations (m = 0), except for sectoral modes (ℓ = m), for which the imaginary part is smaller. The second effect of large magnetic fields is to complicate the mode identification. The perturbations cannot be represented by pure single spherical harmonic, but by a series of harmonics due to the angular dependence of the Lorentz force. It is shown that this mixing of spherical harmonics also depends on the value of m. However, our calculations do not explain the observed selection of dipole modes in roAp stars, aligned with the magnetic axis, since they do not minimize energy losses due to Alfvénic waves.