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Astron. Astrophys. 361, 303-320 (2000)

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Appendix A: the fastest growing mode

The most unstable wavenumber, [FORMULA], can be found from Eq. (49) by applying the necessary and sufficient conditions for [FORMULA]:

[EQUATION]

The first condition yields

[EQUATION]

and therefore

[EQUATION]

Condition (ii) requires

[EQUATION]

where [FORMULA] and [FORMULA] are shorthand for the expressions in square and curly brackets in Eq. (A.1).

In Eq. (A.3) the term in curly brackets vanishes for [FORMULA] and the term in square brackets is [FORMULA] which is real and positive for [FORMULA]. The term in round brackets is always negative and hence [FORMULA].

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© European Southern Observatory (ESO) 2000

Online publication: January 29, 2001
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