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

Oscillation eigenmodes are studied for a planar solar model with a non-unif orm horizontal magnetic field in the atmosphere. The three layer atmospheri c model is the same as in Tiny 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 harmoni c. The emphasis is on the possible coupling of global solar oscillation mod es to localized continuum eigenmodes of the magnetic atmosphere. For propag ation parallel to the magnetic field, the global oscillation modes can coup le only to slow continuum modes and this is found to occur for a rather lar ge range of parameters. In addition to the damping of global oscillation modes due to resonant abso rption it was found that the interaction of global eigenmodes with slow con tinuum modes leads to unanticipated behaviour of global eigenmodes. The rat her 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 ha ve been examined. The shifts are compared to observations.