Physical formulation of the eigenfrequency condition of mixed modes of stellar oscillations
Masao Takata (University of Tokyo)

The frequency condition for eigenmodes of mixed character, which have been extensively detected in red giants and sub giants, is generally examined by a simple physial model, which is based on a running-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 different from the conventional asymptotic expression (Shibahashi 1979; Tassoul 1980) in the case of the strong coupling. 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 derived formulae should be helpful in understanding the physics of mixed modes in general, the origin of the red giants with depressed dipolar modes, and the effect of radiative damping in the core of the red giant stars.