Asymptotic representation of high-frequency, low-degree p-modes in stars and in the Sun.

Details Asymptotic representation of high-frequency, low-degree p-modes in stars and in the Sun. Asymptotic representation of high-frequency, low-degree p-modes in stars and in the Sun.

Mar 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996a%26a...307..105s&link_type=abstract

Astronomy and Astrophysics, v.307, p.105

Astronomy and Astrophysics

Astrophysics

5

Stars: Variable, Stars: Oscillations, Sun: Oscillations

Scientific paper

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 asymptotic expansion procedures applying to singular perturbation problems. In imitation of Tassoul (1990), a system of two second-order differential equations in the divergence and the radial component of the Lagrangian displacement is used in which the terms containing the Eulerian perturbation of the gravitational potential are kept. A comparison is made with Tassoul's second-order asymptotic representation based on the application of Olver's asymptotic procedure. The asymptotic approach fits very well in the conception that, for the 5-min oscillation modes, the Sun acts as a resonant cavity almost from its surface to depths where the vertical wave numbers of the acoustic waves become equal to zero. Inherent in the asymptotic approach is the implicit assumption that the regions outside the resonant cavity near the centre and the surface can be treated as thin boundary layers. Relative to the central region in the Sun, the condition is satisfied only for 5-min oscillation modes associated with spherical harmonics of the lowest degrees.

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