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Astron. Astrophys. 354, 296-304 (2000)

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Appendix A

System (1) can be Fourier-analyzed in terms of [FORMULA], with the [FORMULA] sign according to (2, 3), to obtain a set of algebraic equations:

[EQUATION]

The linearized variables can be put in a non dimensional form, as described in Sect. 2, and Eqs. (A.1), (A.2) and (A.3) can be solved to obtain [FORMULA], with [FORMULA] and K specifying relations between density, velocities and pressure in the plane-wave solutions as:

[EQUATION]

Appendix B

The amplitudes [FORMULA] for an initial pressure pulse are:

[EQUATION]

[EQUATION]

where [FORMULA], [FORMULA] is the solution of dispersion relation for acoustic modes and [FORMULA] is the solution for internal gravity modes. [FORMULA] and [FORMULA] are the amplitudes of acoustic modes while [FORMULA] and [FORMULA] are the amplitude of internal gravity modes.

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© European Southern Observatory (ESO) 2000

Online publication: January 31, 2000
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