= Oscillatory marginality in vertical-field magnetoconvection
{title2=$\omega^2=\sigma\zeta(1-\zeta)Q\pi^2/(1+\sigma)-\zeta^2s^2$}
A nonzero imaginary root of the <vertical-field magnetoconvection dispersion relation> requires $0<\zeta<1$ and $Q>\zeta(1+\sigma)s^2/[\sigma(1-\zeta)\pi^2]$. Its marginal curve is $R^{(o)}=Cs^3/k^2+DQ\pi^2s/k^2$, with $C=(\sigma+\zeta)(1+\zeta)/\sigma$ and $D=\zeta(\sigma+\zeta)/(1+\sigma)$. A formal minimum of that algebraic curve is a physical oscillatory threshold only if the frequency squared there is positive.
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