Physical formulation of mixed modes of stellar oscillations

The frequency condition for eigenmodes of nonradial stellar oscillations with a mixed character, which have been extensively detected in red giants and subgiants, is generally examined by a simple physical model based on a progressive-wave picture. The coupling coefficient between the gravity-wave oscillation in the core and the acoustic-wave oscillation in the envelope is expressed in terms of the reflection coefficient at the intermediate evanescent region. This relation is fully consistent with the recent asymptotic analysis for dipolar modes, but disagrees with the conventional asymptotic analysis, which assumes that the coupling is weak. The expression for the amplitude ratio between the core and envelope oscillations is also derived. The upper and lower bounds of the ratio are found to be determined by the reflection coefficient at the intermediate region. It is also argued that the eigenmode condition should appropriately be modified if the wave generated near the surface and transmitted to the core is (partially) lost either by damping or scattering in the core. The developed formulation opens a possibility to characterize the core damping (or scattering) of the red giant stars in terms of the formal reflection coefficient at the inner boundary of the inner cavity, which would provide a valuable insight into those physical processes.