A dispersion law for solar oscillations

The simple model of p-mode solar oscillations of Liebacher and Stein (1981), in which the acoustic vibrations are trapped in a resonant cavity taking the form of a spherical shell below the solar surface, is compared with Doppler shift observations of vertical velocities. The model is shown to predict a modified dispersion law in which the sound travel time across the cavity is a function of the ratio of the temporal frequency to the horizontal wavenumber, resulting in a single curve when the temporal frequency is plotted against the wavenumber. Frequencies derived from a two-dimensional power spectrum of velocity observations are found to conform to a modified version of the dispersion relation, and that only when the fundamental mode is excluded. Results thus suggest that all modes with the same frequency/wavenumber ratio are trapped in an identical cavity, or, more plausibly, that the difference in upper boundary conditions for different modes has minimal effect on the resulting frequencies.