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

Appendix A: the fastest growing mode

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

The first condition yields

and therefore

Condition (ii) requires

where and 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 and the term in square brackets is which is real and positive for . The term in round brackets is always negative and hence .

© European Southern Observatory (ESO) 2000

Online publication: January 29, 2001
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