Oscillations in a magnetic solar model I. Parallel propagation in a chromospheric and coronal magnetic field with constant Alfvén speed

Oscillation eigenmodes are studied for a planar solar model with a non-uniform horizontal magnetic field in the atmosphere. The three layer atmospheric model is the same as in Tirry et al. (1998). The analysis in that paper is extended to a wide range of parameters. Different types of oscillation modes are determined for a wide range of the magnetic field strength and for different degrees of the spherical harmonic. The emphasis is on the possible coupling of global solar oscillation modes to localized continuum eigenmodes of the magnetic atmosphere. For propagation parallel to the magnetic field, the global oscillation modes can couple only to slow continuum modes and this is found to occur for a rather large range of parameters. In addition to the damping of global oscillation modes due to resonant absorption it was found that the interaction of global eigenmodes with slow continuum modes leads to unanticipated behaviour of global eigenmodes. The rather strange behaviour in the slow continuum involves the disappearance and appearance of global modes and splitting and merging of global modes. Additionally, frequency shifts of global modes due to the magnetic field have been examined. The shifts are compared to observations.