The pressure or p-modes are acoustic vibrations trapped in a resonant cavity below the solar surface. The waves are most easily observed as primarily vertical velocities at the solar surface by Doppler shift techniques. The vertical velocities vary harmonically in time and in space across the solar surface. These harmonic variations lead to a natural description of the oscillation modes in terms of their positions in a diagram of temporal frequency (ω) versus horizontal spatial frequency (kh). Observationally, the positions in the kh–ω diagram are determined from a two-dimensional power spectrum of a series of Doppler shifts of a solar spectrum line measured equidistant in space and time. An example of the observed positions is shown in Fig. 1 (see ref. 1). Theoretically, the mode positions are determined by an analysis of the solar cavity, including an uncertain model of the solar interior. Most theoretical work has consisted of numerical solutions of the equations of motion leading to predicted positions in the kh–ω diagram (see, for instance, ref. 2). This approach has been reasonably successful, yielding inferences about the depth of the convection zone3. Here we compare a simple model of the oscillations discussed by Leibacher and Stein4 with observations.
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