ASYMPTOTIC REPRESENTATION OF HIGH-FREQUENCY, LOW-DEGREE P-MODES IN STARS AND IN THE SUN

A second-order asymptotic representation of high-frequency, low-degree non-radial p-modes in stars and in the Sun is derived by means of asy mptotic expansion procedures applying to singular perturbation problem s. In imitation of Tassoul (1990), a system of two second-order differ ential equations in the divergence and the radial component of the Lag rangian displacement is used in which the terms containing the Euleria n perturbation of the gravitational potential are kept. A comparison i s made with Tassoul's second-order asymptotic representation based on the application of Olver's asymptotic procedure. The asymptotic approa ch fits very well in the conception that, for the 5-min oscillation mo des, the Sun acts as a resonant cavity almost from its surface to dept hs where the vertical wave numbers of the acoustic waves become equal to zero. Inherent in the asymptotic approach is the implicit assumptio n that the regions outside the resonant cavity near the centre and the surface can be treated as thin boundary layers. Relative to the centr al region in the Sun, the condition is satisfied only for 5-min oscill ation modes associated with spherical harmonics of the lowest degrees.